TSTP Solution File: GRP114-1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP114-1 : TPTP v8.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n032.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 16:51:31 EDT 2024
% Result : Unsatisfiable 14.04s 14.28s
% Output : Proof 14.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP114-1 : TPTP v8.2.0. Released v1.2.0.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sun May 26 19:30:53 EDT 2024
% 0.11/0.30 % CPUTime :
% 0.15/0.39 %----Proving TF0_NAR, FOF, or CNF
% 0.15/0.40 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.39/10.65 --- Run --no-e-matching --full-saturate-quant at 5...
% 14.04/14.28 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.M5fmuYpmzG/cvc5---1.0.5_11251.smt2
% 14.04/14.28 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.M5fmuYpmzG/cvc5---1.0.5_11251.smt2
% 14.11/14.34 (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 14.11/14.34 (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 14.11/14.34 (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 14.11/14.34 (assume a3 (= (tptp.inverse tptp.identity) tptp.identity))
% 14.11/14.34 (assume a4 (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)))
% 14.11/14.34 (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 14.11/14.34 (assume a6 (forall ((X $$unsorted)) (= (tptp.intersection X X) X)))
% 14.11/14.34 (assume a7 (forall ((X $$unsorted)) (= (tptp.union X X) X)))
% 14.11/14.34 (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))))
% 14.11/14.34 (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))))
% 14.11/14.34 (assume a10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z))))
% 14.11/14.34 (assume a11 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z))))
% 14.11/14.34 (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union (tptp.intersection X Y) Y) Y)))
% 14.11/14.34 (assume a13 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.union X Y) Y) Y)))
% 14.11/14.34 (assume a14 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))))
% 14.11/14.34 (assume a15 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z)))))
% 14.11/14.34 (assume a16 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X)))))
% 14.11/14.34 (assume a17 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))))
% 14.11/14.34 (assume a18 (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity))))
% 14.11/14.34 (assume a19 (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity))))
% 14.11/14.34 (assume a20 (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)))
% 14.11/14.34 (step t1 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z)))) :rule implies_neg1)
% 14.11/14.34 (anchor :step t2)
% 14.11/14.34 (assume t2.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z))))
% 14.11/14.34 (step t2.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z)))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule forall_inst :args ((:= X (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a)) (:= Y (tptp.union tptp.identity tptp.a)) (:= Z tptp.a)))
% 14.11/14.34 (step t2.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z)))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) :rule or :premises (t2.t1))
% 14.11/14.34 (step t2.t3 (cl (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) :rule resolution :premises (t2.t2 t2.a0))
% 14.11/14.34 (step t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z)))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) :rule subproof :discharge (t2.a0))
% 14.11/14.34 (step t3 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) :rule resolution :premises (t1 t2))
% 14.11/14.34 (step t4 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule implies_neg2)
% 14.11/14.34 (step t5 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule resolution :premises (t3 t4))
% 14.11/14.34 (step t6 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule contraction :premises (t5))
% 14.11/14.34 (step t7 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.intersection X (tptp.intersection Y Z)) (tptp.intersection (tptp.intersection X Y) Z)))) (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) :rule implies :premises (t6))
% 14.11/14.34 (step t8 (cl (not (= (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))))) (not (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) (or (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule equiv_pos2)
% 14.11/14.34 (step t9 (cl (= (= (= (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) true) (= (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) :rule equiv_simplify)
% 14.11/14.34 (step t10 (cl (not (= (= (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) true)) (= (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule equiv1 :premises (t9))
% 14.11/14.34 (step t11 (cl (= (= (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))))) :rule all_simplify)
% 14.11/14.34 (step t12 (cl (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule refl)
% 14.11/14.34 (step t13 (cl (= (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule all_simplify)
% 14.11/14.34 (step t14 (cl (= (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) :rule cong :premises (t12 t13))
% 14.11/14.34 (step t15 (cl (= (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) true)) :rule all_simplify)
% 14.11/14.34 (step t16 (cl (= (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) true)) :rule trans :premises (t14 t15))
% 14.11/14.34 (step t17 (cl (= (= (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) true)) :rule trans :premises (t11 t16))
% 14.11/14.34 (step t18 (cl (= (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule resolution :premises (t10 t17))
% 14.11/14.34 (step t19 (cl (= (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))))) :rule refl)
% 14.11/14.34 (step t20 (cl (= (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))))) :rule refl)
% 14.11/14.34 (step t21 (cl (= (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))))) :rule refl)
% 14.11/14.34 (step t22 (cl (= (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))))) :rule refl)
% 14.11/14.34 (step t23 (cl (= (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))))) :rule refl)
% 14.11/14.34 (step t24 (cl (= (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))))) :rule refl)
% 14.11/14.34 (step t25 (cl (= (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule refl)
% 14.11/14.34 (step t26 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule refl)
% 14.11/14.34 (step t27 (cl (= (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))))) :rule refl)
% 14.11/14.34 (step t28 (cl (= (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))))) :rule refl)
% 14.11/14.34 (step t29 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule refl)
% 14.11/14.34 (step t30 (cl (= (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))))) :rule refl)
% 14.11/14.34 (step t31 (cl (= (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))))) :rule refl)
% 14.11/14.34 (step t32 (cl (= (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))))) :rule refl)
% 14.11/14.34 (step t33 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 14.11/14.34 (step t34 (cl (= (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule refl)
% 14.11/14.34 (step t35 (cl (= (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))))) :rule refl)
% 14.11/14.34 (step t36 (cl (= (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))))) :rule refl)
% 14.11/14.34 (step t37 (cl (= (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))))) :rule refl)
% 14.11/14.34 (step t38 (cl (= (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))))) :rule refl)
% 14.11/14.34 (step t39 (cl (= (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))))) :rule refl)
% 14.11/14.34 (step t40 (cl (= (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))))) :rule refl)
% 14.11/14.34 (step t41 (cl (= (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))))) :rule refl)
% 14.11/14.34 (step t42 (cl (= (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))))) :rule refl)
% 14.11/14.34 (step t43 (cl (= (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))))) :rule refl)
% 14.11/14.34 (step t44 (cl (= (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))))) :rule refl)
% 14.11/14.34 (step t45 (cl (= (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))))) :rule refl)
% 14.11/14.34 (step t46 (cl (= (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))))) :rule refl)
% 14.11/14.34 (step t47 (cl (= (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))))) :rule refl)
% 14.11/14.34 (step t48 (cl (= (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))))) :rule refl)
% 14.11/14.34 (step t49 (cl (= (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))))) :rule refl)
% 14.11/14.34 (step t50 (cl (= (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule refl)
% 14.11/14.34 (step t51 (cl (= (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))))) :rule cong :premises (t18 t19 t20 t21 t22 t23 t24 t25 t26 t27 t28 t29 t30 t31 t32 t33 t34 t35 t36 t37 t38 t39 t40 t41 t42 t43 t44 t45 t46 t47 t48 t49 t50))
% 14.11/14.34 (step t52 (cl (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) :rule and_neg)
% 14.11/14.34 (step t53 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) :rule implies_neg1)
% 14.11/14.34 (anchor :step t54)
% 14.11/14.34 (assume t54.a0 (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.a1 (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))
% 14.11/14.34 (assume t54.a2 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 14.11/14.34 (assume t54.a3 (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)))
% 14.11/14.34 (assume t54.a4 (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))
% 14.11/14.34 (assume t54.a5 (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)))
% 14.11/14.34 (assume t54.a6 (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)))
% 14.11/14.34 (assume t54.a7 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 14.11/14.34 (assume t54.a8 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.a9 (= tptp.a (tptp.intersection tptp.a tptp.a)))
% 14.11/14.34 (assume t54.a10 (= tptp.a (tptp.union tptp.a tptp.a)))
% 14.11/14.34 (assume t54.a11 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 14.11/14.34 (assume t54.a12 (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)))
% 14.11/14.34 (assume t54.a13 (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))
% 14.11/14.34 (assume t54.a14 (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))
% 14.11/14.34 (assume t54.a15 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 14.11/14.34 (assume t54.a16 (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))
% 14.11/14.34 (assume t54.a17 (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.a18 (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.a19 (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.a20 (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))
% 14.11/14.34 (assume t54.a21 (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))
% 14.11/14.34 (assume t54.a22 (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))))
% 14.11/14.34 (assume t54.a23 (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))))
% 14.11/14.34 (assume t54.a24 (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)))
% 14.11/14.34 (assume t54.a25 (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.a26 (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.a27 (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.a28 (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.a29 (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))))
% 14.11/14.34 (assume t54.a30 (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))))
% 14.11/14.34 (assume t54.a31 (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))
% 14.11/14.34 (step t54.t1 (cl (=> (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) :rule implies_neg1)
% 14.11/14.34 (anchor :step t54.t2)
% 14.11/14.34 (assume t54.t2.a0 (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.t2.a1 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 14.11/14.34 (assume t54.t2.a2 (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))
% 14.11/14.34 (assume t54.t2.a3 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 14.11/14.34 (assume t54.t2.a4 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 14.11/14.34 (assume t54.t2.a5 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 14.11/14.34 (assume t54.t2.a6 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.t2.a7 (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))
% 14.11/14.34 (assume t54.t2.a8 (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)))
% 14.11/14.34 (assume t54.t2.a9 (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.t2.a10 (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.t2.a11 (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.t2.a12 (= tptp.a (tptp.union tptp.a tptp.a)))
% 14.11/14.34 (assume t54.t2.a13 (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.t2.a14 (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.t2.a15 (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))))
% 14.11/14.34 (assume t54.t2.a16 (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))))
% 14.11/14.34 (assume t54.t2.a17 (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)))
% 14.11/14.34 (assume t54.t2.a18 (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)))
% 14.11/14.34 (assume t54.t2.a19 (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))
% 14.11/14.34 (assume t54.t2.a20 (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.t2.a21 (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)))
% 14.11/14.34 (assume t54.t2.a22 (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)))
% 14.11/14.34 (assume t54.t2.a23 (= tptp.a (tptp.intersection tptp.a tptp.a)))
% 14.11/14.34 (assume t54.t2.a24 (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)))
% 14.11/14.34 (assume t54.t2.a25 (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))
% 14.11/14.34 (assume t54.t2.a26 (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))
% 14.11/14.34 (assume t54.t2.a27 (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))))
% 14.11/14.34 (assume t54.t2.a28 (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))))
% 14.11/14.34 (assume t54.t2.a29 (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))))
% 14.11/14.34 (assume t54.t2.a30 (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))
% 14.11/14.34 (assume t54.t2.a31 (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))
% 14.11/14.34 (step t54.t2.t1 (cl (= (= (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)) false) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule equiv_simplify)
% 14.11/14.34 (step t54.t2.t2 (cl (not (= (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)) false)) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule equiv1 :premises (t54.t2.t1))
% 14.11/14.34 (step t54.t2.t3 (cl (= (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a))) :rule refl)
% 14.11/14.34 (step t54.t2.t4 (cl (= (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a) tptp.a)) :rule symm :premises (t54.t2.a9))
% 14.11/14.34 (step t54.t2.t5 (cl (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule cong :premises (t54.t2.t3 t54.t2.t4))
% 14.11/14.34 (step t54.t2.t6 (cl (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a) tptp.a)) :rule symm :premises (t54.t2.a0))
% 14.11/14.34 (step t54.t2.t7 (cl (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) tptp.a)) :rule trans :premises (t54.t2.t5 t54.t2.t6))
% 14.11/14.34 (step t54.t2.t8 (cl (= tptp.a tptp.a)) :rule refl)
% 14.11/14.34 (step t54.t2.t9 (cl (= (tptp.union tptp.a tptp.identity) (tptp.positive_part tptp.a))) :rule symm :premises (t54.t2.a8))
% 14.11/14.34 (step t54.t2.t10 (cl (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule symm :premises (t54.t2.t9))
% 14.11/14.34 (step t54.t2.t11 (cl (= (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)))) :rule cong :premises (t54.t2.t8 t54.t2.t10))
% 14.11/14.34 (step t54.t2.t12 (cl (= (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a7))
% 14.11/14.34 (step t54.t2.t13 (cl (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule symm :premises (t54.t2.t12))
% 14.11/14.34 (step t54.t2.t14 (cl (= (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.a))) :rule refl)
% 14.11/14.34 (step t54.t2.t15 (cl (= (tptp.inverse (tptp.inverse tptp.a)) tptp.a)) :rule symm :premises (t54.t2.a5))
% 14.11/14.34 (step t54.t2.t16 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule symm :premises (t54.t2.t15))
% 14.11/14.34 (step t54.t2.t17 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)) :rule symm :premises (t54.t2.a6))
% 14.11/14.34 (step t54.t2.t18 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule symm :premises (t54.t2.t17))
% 14.11/14.34 (step t54.t2.t19 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t54.t2.t16 t54.t2.t18))
% 14.11/14.34 (step t54.t2.t20 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t54.t2.a4))
% 14.11/14.34 (step t54.t2.t21 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t54.t2.a3))
% 14.11/14.34 (step t54.t2.t22 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity tptp.a))) :rule cong :premises (t54.t2.t21 t54.t2.t8))
% 14.11/14.34 (step t54.t2.t23 (cl (= (tptp.multiply tptp.identity tptp.a) tptp.a)) :rule symm :premises (t54.t2.a1))
% 14.11/14.34 (step t54.t2.t24 (cl (= (tptp.multiply tptp.a tptp.identity) tptp.a)) :rule trans :premises (t54.t2.t19 t54.t2.t20 t54.t2.t22 t54.t2.t23))
% 14.11/14.34 (step t54.t2.t25 (cl (= (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a))) :rule cong :premises (t54.t2.t14 t54.t2.t24))
% 14.11/14.34 (step t54.t2.t26 (cl (= (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a))) :rule trans :premises (t54.t2.t11 t54.t2.t13 t54.t2.t25))
% 14.11/14.34 (step t54.t2.t27 (cl (= (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.multiply tptp.a (tptp.positive_part tptp.a)))) :rule symm :premises (t54.t2.t26))
% 14.11/14.34 (step t54.t2.t28 (cl (= (tptp.union tptp.a tptp.identity) (tptp.union tptp.identity tptp.a))) :rule symm :premises (t54.t2.a31))
% 14.11/14.34 (step t54.t2.t29 (cl (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule symm :premises (t54.t2.t28))
% 14.11/14.34 (step t54.t2.t30 (cl (= (tptp.multiply tptp.identity (tptp.positive_part tptp.a)) (tptp.positive_part tptp.a))) :rule symm :premises (t54.t2.a30))
% 14.11/14.34 (step t54.t2.t31 (cl (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule symm :premises (t54.t2.t30))
% 14.11/14.34 (step t54.t2.t32 (cl (= (tptp.union tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule trans :premises (t54.t2.t29 t54.t2.t9 t54.t2.t31))
% 14.11/14.34 (step t54.t2.t33 (cl (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule cong :premises (t54.t2.t27 t54.t2.t32))
% 14.11/14.34 (step t54.t2.t34 (cl (= (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)))) :rule symm :premises (t54.t2.a29))
% 14.11/14.34 (step t54.t2.t35 (cl (= (tptp.intersection tptp.a tptp.identity) (tptp.negative_part tptp.a))) :rule symm :premises (t54.t2.a17))
% 14.11/14.34 (step t54.t2.t36 (cl (= (tptp.positive_part tptp.a) (tptp.positive_part tptp.a))) :rule refl)
% 14.11/14.34 (step t54.t2.t37 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.multiply (tptp.negative_part tptp.a) (tptp.positive_part tptp.a)))) :rule cong :premises (t54.t2.t35 t54.t2.t36))
% 14.11/14.34 (step t54.t2.t38 (cl (= (tptp.negative_part tptp.a) (tptp.negative_part tptp.a))) :rule refl)
% 14.11/14.34 (step t54.t2.t39 (cl (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.positive_part tptp.a)) (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)))) :rule cong :premises (t54.t2.t38 t54.t2.t10))
% 14.11/14.34 (step t54.t2.t40 (cl (= (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)) (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a28))
% 14.11/14.34 (step t54.t2.t41 (cl (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule symm :premises (t54.t2.t40))
% 14.11/14.34 (step t54.t2.t42 (cl (= (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a))) :rule cong :premises (t54.t2.a17 t54.t2.t8))
% 14.11/14.34 (step t54.t2.t43 (cl (= (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a))) :rule symm :premises (t54.t2.a26))
% 14.11/14.34 (step t54.t2.t44 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule symm :premises (t54.t2.t43))
% 14.11/14.34 (step t54.t2.t45 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t54.t2.t22))
% 14.11/14.34 (step t54.t2.t46 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a tptp.identity))) :rule symm :premises (t54.t2.t19))
% 14.11/14.34 (step t54.t2.t47 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.multiply tptp.a tptp.identity))) :rule trans :premises (t54.t2.t45 t54.t2.a4 t54.t2.t46))
% 14.11/14.34 (step t54.t2.t48 (cl (= (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule cong :premises (t54.t2.t14 t54.t2.t47))
% 14.11/14.34 (step t54.t2.t49 (cl (= (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a25))
% 14.11/14.34 (step t54.t2.t50 (cl (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) :rule cong :premises (t54.t2.t8 t54.t2.t35))
% 14.11/14.34 (step t54.t2.t51 (cl (= (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) :rule trans :premises (t54.t2.t42 t54.t2.t44 t54.t2.t48 t54.t2.t49 t54.t2.t50))
% 14.11/14.34 (step t54.t2.t52 (cl (= tptp.identity tptp.identity)) :rule refl)
% 14.11/14.34 (step t54.t2.t53 (cl (= (tptp.multiply (tptp.negative_part tptp.a) tptp.identity) (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule cong :premises (t54.t2.a17 t54.t2.t52))
% 14.11/14.34 (step t54.t2.t54 (cl (= (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)) (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule symm :premises (t54.t2.a27))
% 14.11/14.34 (step t54.t2.t55 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule symm :premises (t54.t2.t54))
% 14.11/14.34 (step t54.t2.t56 (cl (= (tptp.multiply tptp.identity tptp.identity) tptp.identity)) :rule symm :premises (t54.t2.a2))
% 14.11/14.34 (step t54.t2.t57 (cl (= (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)) (tptp.intersection tptp.a tptp.identity))) :rule cong :premises (t54.t2.t24 t54.t2.t56))
% 14.11/14.34 (step t54.t2.t58 (cl (= (tptp.multiply tptp.identity (tptp.negative_part tptp.a)) (tptp.negative_part tptp.a))) :rule symm :premises (t54.t2.a19))
% 14.11/14.34 (step t54.t2.t59 (cl (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule symm :premises (t54.t2.t58))
% 14.11/14.34 (step t54.t2.t60 (cl (= (tptp.multiply (tptp.negative_part tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule trans :premises (t54.t2.t53 t54.t2.t55 t54.t2.t57 t54.t2.t35 t54.t2.t59))
% 14.11/14.34 (step t54.t2.t61 (cl (= (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.t51 t54.t2.t60))
% 14.11/14.34 (step t54.t2.t62 (cl (= (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)))) :rule symm :premises (t54.t2.a13))
% 14.11/14.34 (step t54.t2.t63 (cl (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) :rule cong :premises (t54.t2.t9 t54.t2.t38))
% 14.11/14.34 (step t54.t2.t64 (cl (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) :rule trans :premises (t54.t2.t33 t54.t2.t34 t54.t2.t37 t54.t2.t39 t54.t2.t41 t54.t2.t61 t54.t2.t62 t54.t2.t63))
% 14.11/14.34 (step t54.t2.t65 (cl (= (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule cong :premises (t54.t2.t64 t54.t2.t8))
% 14.11/14.34 (step t54.t2.t66 (cl (= (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a) (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule symm :premises (t54.t2.a24))
% 14.11/14.34 (step t54.t2.t67 (cl (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) :rule refl)
% 14.11/14.34 (step t54.t2.t68 (cl (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.intersection tptp.a tptp.a) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.a23 t54.t2.t67))
% 14.11/14.34 (step t54.t2.t69 (cl (= (tptp.intersection tptp.a tptp.a) tptp.a)) :rule symm :premises (t54.t2.a23))
% 14.11/14.34 (step t54.t2.t70 (cl (= (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a) tptp.a)) :rule symm :premises (t54.t2.a22))
% 14.11/14.34 (step t54.t2.t71 (cl (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule symm :premises (t54.t2.t70))
% 14.11/14.34 (step t54.t2.t72 (cl (= (tptp.intersection tptp.a tptp.identity) (tptp.intersection tptp.identity tptp.a))) :rule symm :premises (t54.t2.a21))
% 14.11/14.34 (step t54.t2.t73 (cl (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule symm :premises (t54.t2.t72))
% 14.11/14.34 (step t54.t2.t74 (cl (= (tptp.intersection tptp.identity tptp.a) (tptp.negative_part tptp.a))) :rule trans :premises (t54.t2.t73 t54.t2.t35))
% 14.11/14.34 (step t54.t2.t75 (cl (= (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule cong :premises (t54.t2.t74 t54.t2.t8))
% 14.11/14.34 (step t54.t2.t76 (cl (= (tptp.union (tptp.negative_part tptp.a) tptp.a) (tptp.union tptp.a (tptp.negative_part tptp.a)))) :rule symm :premises (t54.t2.a20))
% 14.11/14.34 (step t54.t2.t77 (cl (= (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity) tptp.identity)) :rule symm :premises (t54.t2.a18))
% 14.11/14.34 (step t54.t2.t78 (cl (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule symm :premises (t54.t2.t77))
% 14.11/14.34 (step t54.t2.t79 (cl (= (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) :rule cong :premises (t54.t2.t35 t54.t2.t52))
% 14.11/14.34 (step t54.t2.t80 (cl (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) :rule symm :premises (t54.t2.a16))
% 14.11/14.34 (step t54.t2.t81 (cl (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) :rule symm :premises (t54.t2.t80))
% 14.11/14.34 (step t54.t2.t82 (cl (= tptp.identity (tptp.union tptp.identity (tptp.negative_part tptp.a)))) :rule trans :premises (t54.t2.t78 t54.t2.t79 t54.t2.t81))
% 14.11/14.34 (step t54.t2.t83 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.t8 t54.t2.t82))
% 14.11/14.34 (step t54.t2.t84 (cl (= (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))))) :rule symm :premises (t54.t2.a15))
% 14.11/14.34 (step t54.t2.t85 (cl (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule symm :premises (t54.t2.t84))
% 14.11/14.34 (step t54.t2.t86 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.union tptp.a tptp.a))) :rule trans :premises (t54.t2.t24 t54.t2.a12))
% 14.11/14.34 (step t54.t2.t87 (cl (= (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) :rule refl)
% 14.11/14.34 (step t54.t2.t88 (cl (= (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.t86 t54.t2.t87))
% 14.11/14.34 (step t54.t2.t89 (cl (= tptp.a (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule trans :premises (t54.t2.a1 t54.t2.t45 t54.t2.a4 t54.t2.t46 t54.t2.t83 t54.t2.t85 t54.t2.t88))
% 14.11/14.34 (step t54.t2.t90 (cl (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.t89 t54.t2.t59))
% 14.11/14.34 (step t54.t2.t91 (cl (= (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule symm :premises (t54.t2.a14))
% 14.11/14.34 (step t54.t2.t92 (cl (= (tptp.union tptp.a tptp.a) (tptp.union tptp.a tptp.a))) :rule refl)
% 14.11/14.34 (step t54.t2.t93 (cl (= (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) :rule trans :premises (t54.t2.t62 t54.t2.t63))
% 14.11/14.34 (step t54.t2.t94 (cl (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.t92 t54.t2.t93))
% 14.11/14.34 (step t54.t2.t95 (cl (= (tptp.union tptp.a tptp.a) tptp.a)) :rule symm :premises (t54.t2.a12))
% 14.11/14.34 (step t54.t2.t96 (cl (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.t95 t54.t2.t67))
% 14.11/14.34 (step t54.t2.t97 (cl (= tptp.a (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule trans :premises (t54.t2.t71 t54.t2.t75 t54.t2.t76 t54.t2.t90 t54.t2.t91 t54.t2.t94 t54.t2.t96))
% 14.11/14.34 (step t54.t2.t98 (cl (= (tptp.intersection tptp.a tptp.a) (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule trans :premises (t54.t2.t69 t54.t2.t97))
% 14.11/14.34 (step t54.t2.t99 (cl (= (tptp.intersection (tptp.intersection tptp.a tptp.a) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.t98 t54.t2.t67))
% 14.11/14.34 (step t54.t2.t100 (cl (= (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) :rule symm :premises (t54.t2.a11))
% 14.11/14.34 (step t54.t2.t101 (cl (= (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) :rule trans :premises (t54.t2.t65 t54.t2.t66 t54.t2.t68 t54.t2.t99 t54.t2.t100))
% 14.11/14.34 (step t54.t2.t102 (cl (= (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule cong :premises (t54.t2.t7 t54.t2.t101))
% 14.11/14.34 (step t54.t2.t103 (cl (= (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) false) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) :rule equiv_simplify)
% 14.11/14.34 (step t54.t2.t104 (cl (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) false) (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) :rule equiv2 :premises (t54.t2.t103))
% 14.11/14.34 (step t54.t2.t105 (cl (not (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) :rule not_not)
% 14.11/14.34 (step t54.t2.t106 (cl (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) false) (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) :rule resolution :premises (t54.t2.t104 t54.t2.t105))
% 14.11/14.34 (step t54.t2.t107 (cl (= (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) false)) :rule resolution :premises (t54.t2.t106 t54.t2.a10))
% 14.11/14.34 (step t54.t2.t108 (cl (= (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)) false)) :rule trans :premises (t54.t2.t102 t54.t2.t107))
% 14.11/14.34 (step t54.t2.t109 (cl (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule resolution :premises (t54.t2.t2 t54.t2.t108))
% 14.11/14.34 (step t54.t2 (cl (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule subproof :discharge (t54.t2.a0 t54.t2.a1 t54.t2.a2 t54.t2.a3 t54.t2.a4 t54.t2.a5 t54.t2.a6 t54.t2.a7 t54.t2.a8 t54.t2.a9 t54.t2.a10 t54.t2.a11 t54.t2.a12 t54.t2.a13 t54.t2.a14 t54.t2.a15 t54.t2.a16 t54.t2.a17 t54.t2.a18 t54.t2.a19 t54.t2.a20 t54.t2.a21 t54.t2.a22 t54.t2.a23 t54.t2.a24 t54.t2.a25 t54.t2.a26 t54.t2.a27 t54.t2.a28 t54.t2.a29 t54.t2.a30 t54.t2.a31))
% 14.11/14.34 (step t54.t3 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t4 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t5 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t54.t6 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t54.t7 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t54.t8 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t54.t9 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t10 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 14.11/14.34 (step t54.t11 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t54.t12 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t13 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t54.t14 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t54.t15 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.a (tptp.union tptp.a tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t16 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t54.t17 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t54.t18 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t54.t19 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t54.t20 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t54.t21 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t54.t22 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t54.t23 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t24 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t54.t25 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t26 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= tptp.a (tptp.intersection tptp.a tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t27 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t54.t28 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 14.11/14.34 (step t54.t29 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t54.t30 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule and_pos)
% 14.11/14.34 (step t54.t31 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule and_pos)
% 14.11/14.34 (step t54.t32 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t54.t33 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t54.t34 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t54.t35 (cl (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))))) :rule resolution :premises (t54.t2 t54.t3 t54.t4 t54.t5 t54.t6 t54.t7 t54.t8 t54.t9 t54.t10 t54.t11 t54.t12 t54.t13 t54.t14 t54.t15 t54.t16 t54.t17 t54.t18 t54.t19 t54.t20 t54.t21 t54.t22 t54.t23 t54.t24 t54.t25 t54.t26 t54.t27 t54.t28 t54.t29 t54.t30 t54.t31 t54.t32 t54.t33 t54.t34))
% 14.11/14.34 (step t54.t36 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule reordering :premises (t54.t35))
% 14.11/14.34 (step t54.t37 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule contraction :premises (t54.t36))
% 14.11/14.34 (step t54.t38 (cl (=> (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule resolution :premises (t54.t1 t54.t37))
% 14.11/14.34 (step t54.t39 (cl (=> (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule implies_neg2)
% 14.11/14.34 (step t54.t40 (cl (=> (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (=> (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule resolution :premises (t54.t38 t54.t39))
% 14.11/14.34 (step t54.t41 (cl (=> (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule contraction :premises (t54.t40))
% 14.11/14.34 (step t54.t42 (cl (not (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule implies :premises (t54.t41))
% 14.11/14.34 (step t54.t43 (cl (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) :rule and_neg)
% 14.11/14.34 (step t54.t44 (cl (and (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a)) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) :rule resolution :premises (t54.t43 t54.a31 t54.a7 t54.a1 t54.a11 t54.a15 t54.a2 t54.a8 t54.a13 t54.a5 t54.a19 t54.a0 t54.a25 t54.a10 t54.a26 t54.a28 t54.a27 t54.a22 t54.a6 t54.a12 t54.a16 t54.a17 t54.a3 t54.a18 t54.a9 t54.a24 t54.a14 t54.a20 t54.a23 t54.a29 t54.a30 t54.a21 t54.a4))
% 14.11/14.34 (step t54.t45 (cl (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule resolution :premises (t54.t42 t54.t44))
% 14.11/14.34 (step t54 (cl (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule subproof :discharge (t54.a0 t54.a1 t54.a2 t54.a3 t54.a4 t54.a5 t54.a6 t54.a7 t54.a8 t54.a9 t54.a10 t54.a11 t54.a12 t54.a13 t54.a14 t54.a15 t54.a16 t54.a17 t54.a18 t54.a19 t54.a20 t54.a21 t54.a22 t54.a23 t54.a24 t54.a25 t54.a26 t54.a27 t54.a28 t54.a29 t54.a30 t54.a31))
% 14.11/14.34 (step t55 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t56 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t57 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t58 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t59 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t60 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t61 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t62 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 14.11/14.34 (step t63 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t64 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.a (tptp.intersection tptp.a tptp.a))) :rule and_pos)
% 14.11/14.34 (step t65 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.a (tptp.union tptp.a tptp.a))) :rule and_pos)
% 14.11/14.34 (step t66 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t67 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule and_pos)
% 14.11/14.34 (step t68 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 14.11/14.34 (step t69 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 14.11/14.34 (step t70 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t71 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t72 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t73 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t74 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t75 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t76 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t77 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) :rule and_pos)
% 14.11/14.34 (step t78 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule and_pos)
% 14.11/14.34 (step t79 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t80 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t81 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t82 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t83 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t84 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule and_pos)
% 14.11/14.34 (step t85 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule and_pos)
% 14.11/14.34 (step t86 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule and_pos)
% 14.11/14.34 (step t87 (cl (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))))) :rule resolution :premises (t54 t55 t56 t57 t58 t59 t60 t61 t62 t63 t64 t65 t66 t67 t68 t69 t70 t71 t72 t73 t74 t75 t76 t77 t78 t79 t80 t81 t82 t83 t84 t85 t86))
% 14.11/14.34 (step t88 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule reordering :premises (t87))
% 14.11/14.35 (step t89 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule contraction :premises (t88))
% 14.11/14.35 (step t90 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule resolution :premises (t53 t89))
% 14.11/14.35 (step t91 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule implies_neg2)
% 14.11/14.35 (step t92 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (=> (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule resolution :premises (t90 t91))
% 14.11/14.35 (step t93 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule contraction :premises (t92))
% 14.11/14.35 (step t94 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.intersection tptp.a tptp.a)) (= tptp.a (tptp.union tptp.a tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule implies :premises (t93))
% 14.11/14.35 (step t95 (cl (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule resolution :premises (t52 t94))
% 14.11/14.35 (step t96 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))))) :rule or_neg)
% 14.11/14.35 (step t97 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))))) :rule or_neg)
% 14.11/14.35 (step t98 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))))) :rule or_neg)
% 14.11/14.35 (step t99 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))))) :rule or_neg)
% 14.11/14.35 (step t100 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))))) :rule or_neg)
% 14.11/14.35 (step t101 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))))) :rule or_neg)
% 14.11/14.35 (step t102 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))))) :rule or_neg)
% 14.11/14.35 (step t103 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t104 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t105 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.a (tptp.intersection tptp.a tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t106 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.a (tptp.union tptp.a tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t107 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule or_neg)
% 14.11/14.35 (step t108 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))))) :rule or_neg)
% 14.11/14.35 (step t109 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))))) :rule or_neg)
% 14.11/14.35 (step t110 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))))) :rule or_neg)
% 14.11/14.35 (step t111 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 14.11/14.35 (step t112 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule or_neg)
% 14.11/14.35 (step t113 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t114 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t115 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t116 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))))) :rule or_neg)
% 14.11/14.35 (step t117 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))))) :rule or_neg)
% 14.11/14.35 (step t118 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))))) :rule or_neg)
% 14.11/14.35 (step t119 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))))) :rule or_neg)
% 14.11/14.35 (step t120 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t121 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))))) :rule or_neg)
% 14.11/14.35 (step t122 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))))) :rule or_neg)
% 14.11/14.35 (step t123 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))))) :rule or_neg)
% 14.11/14.35 (step t124 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))))) :rule or_neg)
% 14.11/14.35 (step t125 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))))) :rule or_neg)
% 14.11/14.35 (step t126 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))))) :rule or_neg)
% 14.11/14.35 (step t127 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t128 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (not (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule or_neg)
% 14.11/14.35 (step t129 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule resolution :premises (t95 t96 t97 t98 t99 t100 t101 t102 t103 t104 t105 t106 t107 t108 t109 t110 t111 t112 t113 t114 t115 t116 t117 t118 t119 t120 t121 t122 t123 t124 t125 t126 t127 t128))
% 14.11/14.35 (step t130 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule contraction :premises (t129))
% 14.11/14.35 (step t131 (cl (or (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a))))) :rule resolution :premises (t8 t51 t130))
% 14.11/14.35 (step t132 (cl (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule or :premises (t131))
% 14.11/14.35 (step t133 (cl (not (= tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule not_symm :premises (a20))
% 14.11/14.35 (step t134 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t135)
% 14.11/14.35 (assume t135.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 14.11/14.35 (step t135.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity)))
% 14.11/14.35 (step t135.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule or :premises (t135.t1))
% 14.11/14.35 (step t135.t3 (cl (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule resolution :premises (t135.t2 t135.a0))
% 14.11/14.35 (step t135 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule subproof :discharge (t135.a0))
% 14.11/14.35 (step t136 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule resolution :premises (t134 t135))
% 14.11/14.35 (step t137 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))) :rule implies_neg2)
% 14.11/14.35 (step t138 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t136 t137))
% 14.11/14.35 (step t139 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))) :rule contraction :premises (t138))
% 14.11/14.35 (step t140 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule implies :premises (t139))
% 14.11/14.35 (step t141 (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)
% 14.11/14.35 (anchor :step t142 :args ((X $$unsorted) (:= X X)))
% 14.11/14.35 (step t142.t1 (cl (= X X)) :rule refl)
% 14.11/14.35 (step t142.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 14.11/14.35 (step t142 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 14.11/14.35 (step t143 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t141 t142 a0))
% 14.11/14.35 (step t144 (cl (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule resolution :premises (t140 t143))
% 14.11/14.35 (step t145 (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)
% 14.11/14.35 (anchor :step t146)
% 14.11/14.35 (assume t146.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 14.11/14.35 (step t146.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 14.11/14.35 (step t146.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule or :premises (t146.t1))
% 14.11/14.35 (step t146.t3 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t146.t2 t146.a0))
% 14.11/14.35 (step t146 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule subproof :discharge (t146.a0))
% 14.11/14.35 (step t147 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t145 t146))
% 14.11/14.35 (step t148 (cl (=> (forall ((X $$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)
% 14.11/14.35 (step t149 (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 (t147 t148))
% 14.11/14.35 (step t150 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule contraction :premises (t149))
% 14.11/14.35 (step t151 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule implies :premises (t150))
% 14.11/14.35 (step t152 (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)
% 14.11/14.35 (anchor :step t153 :args ((X $$unsorted) (:= X X)))
% 14.11/14.35 (step t153.t1 (cl (= X X)) :rule refl)
% 14.11/14.35 (step t153.t2 (cl (= (= (tptp.inverse (tptp.inverse X)) X) (= X (tptp.inverse (tptp.inverse X))))) :rule all_simplify)
% 14.11/14.35 (step t153 (cl (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) :rule bind)
% 14.11/14.35 (step t154 (cl (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule resolution :premises (t152 t153 a4))
% 14.11/14.35 (step t155 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t151 t154))
% 14.11/14.35 (step t156 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t157)
% 14.11/14.35 (assume t157.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))))
% 14.11/14.35 (step t157.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 14.11/14.35 (step t157.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule or :premises (t157.t1))
% 14.11/14.35 (step t157.t3 (cl (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule resolution :premises (t157.t2 t157.a0))
% 14.11/14.35 (step t157 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule subproof :discharge (t157.a0))
% 14.11/14.35 (step t158 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule resolution :premises (t156 t157))
% 14.11/14.35 (step t159 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)))) :rule implies_neg2)
% 14.11/14.35 (step t160 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)))) :rule resolution :premises (t158 t159))
% 14.11/14.35 (step t161 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity)))) :rule contraction :premises (t160))
% 14.11/14.35 (step t162 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule implies :premises (t161))
% 14.11/14.35 (step t163 (cl (= (tptp.intersection tptp.identity tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule resolution :premises (t162 a8))
% 14.11/14.35 (step t164 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t165)
% 14.11/14.35 (assume t165.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))))
% 14.11/14.35 (step t165.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 14.11/14.35 (step t165.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule or :premises (t165.t1))
% 14.11/14.35 (step t165.t3 (cl (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule resolution :premises (t165.t2 t165.a0))
% 14.11/14.35 (step t165 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule subproof :discharge (t165.a0))
% 14.11/14.35 (step t166 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule resolution :premises (t164 t165))
% 14.11/14.35 (step t167 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) :rule implies_neg2)
% 14.11/14.35 (step t168 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) :rule resolution :premises (t166 t167))
% 14.11/14.35 (step t169 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity)))) :rule contraction :premises (t168))
% 14.11/14.35 (step t170 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule implies :premises (t169))
% 14.11/14.35 (step t171 (cl (= (tptp.union tptp.identity tptp.a) (tptp.union tptp.a tptp.identity))) :rule resolution :premises (t170 a9))
% 14.11/14.35 (step t172 (cl (=> (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t173)
% 14.11/14.35 (assume t173.a0 (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity))))
% 14.11/14.35 (step t173.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity)))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)))) :rule forall_inst :args ((:= X tptp.a)))
% 14.11/14.35 (step t173.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity)))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule or :premises (t173.t1))
% 14.11/14.35 (step t173.t3 (cl (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule resolution :premises (t173.t2 t173.a0))
% 14.11/14.35 (step t173 (cl (not (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity)))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule subproof :discharge (t173.a0))
% 14.11/14.35 (step t174 (cl (=> (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule resolution :premises (t172 t173))
% 14.11/14.35 (step t175 (cl (=> (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (not (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)))) :rule implies_neg2)
% 14.11/14.35 (step t176 (cl (=> (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) (=> (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)))) :rule resolution :premises (t174 t175))
% 14.11/14.35 (step t177 (cl (=> (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity)))) :rule contraction :premises (t176))
% 14.11/14.35 (step t178 (cl (not (forall ((X $$unsorted)) (= (tptp.positive_part X) (tptp.union X tptp.identity)))) (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule implies :premises (t177))
% 14.11/14.35 (step t179 (cl (= (tptp.positive_part tptp.a) (tptp.union tptp.a tptp.identity))) :rule resolution :premises (t178 a18))
% 14.11/14.35 (step t180 (cl (=> (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t181)
% 14.11/14.35 (assume t181.a0 (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity))))
% 14.11/14.35 (step t181.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity)))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)))) :rule forall_inst :args ((:= X tptp.a)))
% 14.11/14.35 (step t181.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity)))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule or :premises (t181.t1))
% 14.11/14.35 (step t181.t3 (cl (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule resolution :premises (t181.t2 t181.a0))
% 14.11/14.35 (step t181 (cl (not (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity)))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule subproof :discharge (t181.a0))
% 14.11/14.35 (step t182 (cl (=> (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule resolution :premises (t180 t181))
% 14.11/14.35 (step t183 (cl (=> (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (not (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)))) :rule implies_neg2)
% 14.11/14.35 (step t184 (cl (=> (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) (=> (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)))) :rule resolution :premises (t182 t183))
% 14.11/14.35 (step t185 (cl (=> (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity)))) :rule contraction :premises (t184))
% 14.11/14.35 (step t186 (cl (not (forall ((X $$unsorted)) (= (tptp.negative_part X) (tptp.intersection X tptp.identity)))) (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule implies :premises (t185))
% 14.11/14.35 (step t187 (cl (= (tptp.negative_part tptp.a) (tptp.intersection tptp.a tptp.identity))) :rule resolution :premises (t186 a19))
% 14.11/14.35 (step t188 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t189)
% 14.11/14.35 (assume t189.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 14.11/14.35 (step t189.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 14.11/14.35 (step t189.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule or :premises (t189.t1))
% 14.11/14.35 (step t189.t3 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t189.t2 t189.a0))
% 14.11/14.35 (step t189 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule subproof :discharge (t189.a0))
% 14.11/14.35 (step t190 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t188 t189))
% 14.11/14.35 (step t191 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t192 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t190 t191))
% 14.11/14.35 (step t193 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule contraction :premises (t192))
% 14.11/14.35 (step t194 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule implies :premises (t193))
% 14.11/14.35 (step t195 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t194 t143))
% 14.11/14.35 (step t196 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t197)
% 14.11/14.35 (assume t197.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 14.11/14.35 (step t197.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 14.11/14.35 (step t197.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule or :premises (t197.t1))
% 14.11/14.35 (step t197.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t197.t2 t197.a0))
% 14.11/14.35 (step t197 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule subproof :discharge (t197.a0))
% 14.11/14.35 (step t198 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t196 t197))
% 14.11/14.35 (step t199 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t200 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t198 t199))
% 14.11/14.35 (step t201 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule contraction :premises (t200))
% 14.11/14.35 (step t202 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule implies :premises (t201))
% 14.11/14.35 (step t203 (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)
% 14.11/14.35 (anchor :step t204 :args ((X $$unsorted) (:= X X)))
% 14.11/14.35 (step t204.t1 (cl (= X X)) :rule refl)
% 14.11/14.35 (step t204.t2 (cl (= (= (tptp.multiply (tptp.inverse X) X) tptp.identity) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule all_simplify)
% 14.11/14.35 (step t204 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) :rule bind)
% 14.11/14.35 (step t205 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule resolution :premises (t203 t204 a1))
% 14.11/14.35 (step t206 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t202 t205))
% 14.11/14.35 (step t207 (cl (=> (forall ((X $$unsorted)) (= X (tptp.intersection X X))) (= tptp.a (tptp.intersection tptp.a tptp.a))) (forall ((X $$unsorted)) (= X (tptp.intersection X X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t208)
% 14.11/14.35 (assume t208.a0 (forall ((X $$unsorted)) (= X (tptp.intersection X X))))
% 14.11/14.35 (step t208.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.intersection X X)))) (= tptp.a (tptp.intersection tptp.a tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 14.11/14.35 (step t208.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.intersection X X)))) (= tptp.a (tptp.intersection tptp.a tptp.a))) :rule or :premises (t208.t1))
% 14.11/14.35 (step t208.t3 (cl (= tptp.a (tptp.intersection tptp.a tptp.a))) :rule resolution :premises (t208.t2 t208.a0))
% 14.11/14.35 (step t208 (cl (not (forall ((X $$unsorted)) (= X (tptp.intersection X X)))) (= tptp.a (tptp.intersection tptp.a tptp.a))) :rule subproof :discharge (t208.a0))
% 14.11/14.35 (step t209 (cl (=> (forall ((X $$unsorted)) (= X (tptp.intersection X X))) (= tptp.a (tptp.intersection tptp.a tptp.a))) (= tptp.a (tptp.intersection tptp.a tptp.a))) :rule resolution :premises (t207 t208))
% 14.11/14.35 (step t210 (cl (=> (forall ((X $$unsorted)) (= X (tptp.intersection X X))) (= tptp.a (tptp.intersection tptp.a tptp.a))) (not (= tptp.a (tptp.intersection tptp.a tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t211 (cl (=> (forall ((X $$unsorted)) (= X (tptp.intersection X X))) (= tptp.a (tptp.intersection tptp.a tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.intersection X X))) (= tptp.a (tptp.intersection tptp.a tptp.a)))) :rule resolution :premises (t209 t210))
% 14.11/14.35 (step t212 (cl (=> (forall ((X $$unsorted)) (= X (tptp.intersection X X))) (= tptp.a (tptp.intersection tptp.a tptp.a)))) :rule contraction :premises (t211))
% 14.11/14.35 (step t213 (cl (not (forall ((X $$unsorted)) (= X (tptp.intersection X X)))) (= tptp.a (tptp.intersection tptp.a tptp.a))) :rule implies :premises (t212))
% 14.11/14.35 (step t214 (cl (not (= (forall ((X $$unsorted)) (= (tptp.intersection X X) X)) (forall ((X $$unsorted)) (= X (tptp.intersection X X))))) (not (forall ((X $$unsorted)) (= (tptp.intersection X X) X))) (forall ((X $$unsorted)) (= X (tptp.intersection X X)))) :rule equiv_pos2)
% 14.11/14.35 (anchor :step t215 :args ((X $$unsorted) (:= X X)))
% 14.11/14.35 (step t215.t1 (cl (= X X)) :rule refl)
% 14.11/14.35 (step t215.t2 (cl (= (= (tptp.intersection X X) X) (= X (tptp.intersection X X)))) :rule all_simplify)
% 14.11/14.35 (step t215 (cl (= (forall ((X $$unsorted)) (= (tptp.intersection X X) X)) (forall ((X $$unsorted)) (= X (tptp.intersection X X))))) :rule bind)
% 14.11/14.35 (step t216 (cl (forall ((X $$unsorted)) (= X (tptp.intersection X X)))) :rule resolution :premises (t214 t215 a6))
% 14.11/14.35 (step t217 (cl (= tptp.a (tptp.intersection tptp.a tptp.a))) :rule resolution :premises (t213 t216))
% 14.11/14.35 (step t218 (cl (=> (forall ((X $$unsorted)) (= X (tptp.union X X))) (= tptp.a (tptp.union tptp.a tptp.a))) (forall ((X $$unsorted)) (= X (tptp.union X X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t219)
% 14.11/14.35 (assume t219.a0 (forall ((X $$unsorted)) (= X (tptp.union X X))))
% 14.11/14.35 (step t219.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.union X X)))) (= tptp.a (tptp.union tptp.a tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 14.11/14.35 (step t219.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.union X X)))) (= tptp.a (tptp.union tptp.a tptp.a))) :rule or :premises (t219.t1))
% 14.11/14.35 (step t219.t3 (cl (= tptp.a (tptp.union tptp.a tptp.a))) :rule resolution :premises (t219.t2 t219.a0))
% 14.11/14.35 (step t219 (cl (not (forall ((X $$unsorted)) (= X (tptp.union X X)))) (= tptp.a (tptp.union tptp.a tptp.a))) :rule subproof :discharge (t219.a0))
% 14.11/14.35 (step t220 (cl (=> (forall ((X $$unsorted)) (= X (tptp.union X X))) (= tptp.a (tptp.union tptp.a tptp.a))) (= tptp.a (tptp.union tptp.a tptp.a))) :rule resolution :premises (t218 t219))
% 14.11/14.35 (step t221 (cl (=> (forall ((X $$unsorted)) (= X (tptp.union X X))) (= tptp.a (tptp.union tptp.a tptp.a))) (not (= tptp.a (tptp.union tptp.a tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t222 (cl (=> (forall ((X $$unsorted)) (= X (tptp.union X X))) (= tptp.a (tptp.union tptp.a tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.union X X))) (= tptp.a (tptp.union tptp.a tptp.a)))) :rule resolution :premises (t220 t221))
% 14.11/14.35 (step t223 (cl (=> (forall ((X $$unsorted)) (= X (tptp.union X X))) (= tptp.a (tptp.union tptp.a tptp.a)))) :rule contraction :premises (t222))
% 14.11/14.35 (step t224 (cl (not (forall ((X $$unsorted)) (= X (tptp.union X X)))) (= tptp.a (tptp.union tptp.a tptp.a))) :rule implies :premises (t223))
% 14.11/14.35 (step t225 (cl (not (= (forall ((X $$unsorted)) (= (tptp.union X X) X)) (forall ((X $$unsorted)) (= X (tptp.union X X))))) (not (forall ((X $$unsorted)) (= (tptp.union X X) X))) (forall ((X $$unsorted)) (= X (tptp.union X X)))) :rule equiv_pos2)
% 14.11/14.35 (anchor :step t226 :args ((X $$unsorted) (:= X X)))
% 14.11/14.35 (step t226.t1 (cl (= X X)) :rule refl)
% 14.11/14.35 (step t226.t2 (cl (= (= (tptp.union X X) X) (= X (tptp.union X X)))) :rule all_simplify)
% 14.11/14.35 (step t226 (cl (= (forall ((X $$unsorted)) (= (tptp.union X X) X)) (forall ((X $$unsorted)) (= X (tptp.union X X))))) :rule bind)
% 14.11/14.35 (step t227 (cl (forall ((X $$unsorted)) (= X (tptp.union X X)))) :rule resolution :premises (t225 t226 a7))
% 14.11/14.35 (step t228 (cl (= tptp.a (tptp.union tptp.a tptp.a))) :rule resolution :premises (t224 t227))
% 14.11/14.35 (step t229 (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)
% 14.11/14.35 (anchor :step t230)
% 14.11/14.35 (assume t230.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 14.11/14.35 (step t230.t1 (cl (or (not (forall ((X $$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))))
% 14.11/14.35 (step t230.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule or :premises (t230.t1))
% 14.11/14.35 (step t230.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t230.t2 t230.a0))
% 14.11/14.35 (step t230 (cl (not (forall ((X $$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 (t230.a0))
% 14.11/14.35 (step t231 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t229 t230))
% 14.11/14.35 (step t232 (cl (=> (forall ((X $$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)
% 14.11/14.35 (step t233 (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 (t231 t232))
% 14.11/14.35 (step t234 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule contraction :premises (t233))
% 14.11/14.35 (step t235 (cl (not (forall ((X $$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 (t234))
% 14.11/14.35 (step t236 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t235 t205))
% 14.11/14.35 (step t237 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t238)
% 14.11/14.35 (assume t238.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))))
% 14.11/14.35 (step t238.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.identity)))
% 14.11/14.35 (step t238.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule or :premises (t238.t1))
% 14.11/14.35 (step t238.t3 (cl (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule resolution :premises (t238.t2 t238.a0))
% 14.11/14.35 (step t238 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule subproof :discharge (t238.a0))
% 14.11/14.35 (step t239 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule resolution :premises (t237 t238))
% 14.11/14.35 (step t240 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)))) :rule implies_neg2)
% 14.11/14.35 (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t239 t240))
% 14.11/14.35 (step t242 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity)))) :rule contraction :premises (t241))
% 14.11/14.35 (step t243 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule implies :premises (t242))
% 14.11/14.35 (step t244 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union (tptp.intersection X Y) Y) Y)) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union (tptp.intersection X Y) Y) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) :rule equiv_pos2)
% 14.11/14.35 (anchor :step t245 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 14.11/14.35 (step t245.t1 (cl (= X X)) :rule refl)
% 14.11/14.35 (step t245.t2 (cl (= Y Y)) :rule refl)
% 14.11/14.35 (step t245.t3 (cl (= (= (tptp.union (tptp.intersection X Y) Y) Y) (= Y (tptp.union (tptp.intersection X Y) Y)))) :rule all_simplify)
% 14.11/14.35 (step t245 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union (tptp.intersection X Y) Y) Y)) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))))) :rule bind)
% 14.11/14.35 (step t246 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) :rule resolution :premises (t244 t245 a12))
% 14.11/14.35 (step t247 (cl (= tptp.identity (tptp.union (tptp.intersection tptp.a tptp.identity) tptp.identity))) :rule resolution :premises (t243 t246))
% 14.11/14.35 (step t248 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t249)
% 14.11/14.35 (assume t249.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))))
% 14.11/14.35 (step t249.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.a) (:= Z tptp.identity)))
% 14.11/14.35 (step t249.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule or :premises (t249.t1))
% 14.11/14.35 (step t249.t3 (cl (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t249.t2 t249.a0))
% 14.11/14.35 (step t249 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule subproof :discharge (t249.a0))
% 14.11/14.35 (step t250 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t248 t249))
% 14.11/14.35 (step t251 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule implies_neg2)
% 14.11/14.35 (step t252 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule resolution :premises (t250 t251))
% 14.11/14.35 (step t253 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule contraction :premises (t252))
% 14.11/14.35 (step t254 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule implies :premises (t253))
% 14.11/14.35 (step t255 (cl (= (tptp.multiply tptp.a (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t254 a14))
% 14.11/14.35 (step t256 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t257)
% 14.11/14.35 (assume t257.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z)))))
% 14.11/14.35 (step t257.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.a) (:= Z tptp.identity)))
% 14.11/14.35 (step t257.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule or :premises (t257.t1))
% 14.11/14.35 (step t257.t3 (cl (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t257.t2 t257.a0))
% 14.11/14.35 (step t257 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule subproof :discharge (t257.a0))
% 14.11/14.35 (step t258 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t256 t257))
% 14.11/14.35 (step t259 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule implies_neg2)
% 14.11/14.35 (step t260 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule resolution :premises (t258 t259))
% 14.11/14.35 (step t261 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule contraction :premises (t260))
% 14.11/14.35 (step t262 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.intersection Y Z)) (tptp.intersection (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule implies :premises (t261))
% 14.11/14.35 (step t263 (cl (= (tptp.multiply tptp.a (tptp.intersection tptp.a tptp.identity)) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t262 a15))
% 14.11/14.35 (step t264 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t265)
% 14.11/14.35 (assume t265.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 14.11/14.35 (step t265.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.inverse tptp.a)) (:= Z tptp.a)))
% 14.11/14.35 (step t265.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t265.t1))
% 14.11/14.35 (step t265.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t265.t2 t265.a0))
% 14.11/14.35 (step t265 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t265.a0))
% 14.11/14.35 (step t266 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t264 t265))
% 14.11/14.35 (step t267 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 14.11/14.35 (step t268 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t266 t267))
% 14.11/14.35 (step t269 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t268))
% 14.11/14.35 (step t270 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t269))
% 14.11/14.35 (step t271 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t270 a2))
% 14.11/14.35 (step t272 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t273)
% 14.11/14.35 (assume t273.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 14.11/14.35 (step t273.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule forall_inst :args ((:= X (tptp.negative_part tptp.a))))
% 14.11/14.35 (step t273.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule or :premises (t273.t1))
% 14.11/14.35 (step t273.t3 (cl (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule resolution :premises (t273.t2 t273.a0))
% 14.11/14.35 (step t273 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule subproof :discharge (t273.a0))
% 14.11/14.35 (step t274 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule resolution :premises (t272 t273))
% 14.11/14.35 (step t275 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (not (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule implies_neg2)
% 14.11/14.35 (step t276 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule resolution :premises (t274 t275))
% 14.11/14.35 (step t277 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule contraction :premises (t276))
% 14.11/14.35 (step t278 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule implies :premises (t277))
% 14.11/14.35 (step t279 (cl (= (tptp.negative_part tptp.a) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) :rule resolution :premises (t278 t143))
% 14.11/14.35 (step t280 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t281)
% 14.11/14.35 (assume t281.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))))
% 14.11/14.35 (step t281.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.negative_part tptp.a))))
% 14.11/14.35 (step t281.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule or :premises (t281.t1))
% 14.11/14.35 (step t281.t3 (cl (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule resolution :premises (t281.t2 t281.a0))
% 14.11/14.35 (step t281 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule subproof :discharge (t281.a0))
% 14.11/14.35 (step t282 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule resolution :premises (t280 t281))
% 14.11/14.35 (step t283 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (not (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t284 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)))) :rule resolution :premises (t282 t283))
% 14.11/14.35 (step t285 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a)))) :rule contraction :premises (t284))
% 14.11/14.35 (step t286 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule implies :premises (t285))
% 14.11/14.35 (step t287 (cl (= (tptp.union tptp.a (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.a))) :rule resolution :premises (t286 a9))
% 14.11/14.35 (step t288 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t289)
% 14.11/14.35 (assume t289.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))))
% 14.11/14.35 (step t289.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 14.11/14.35 (step t289.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule or :premises (t289.t1))
% 14.11/14.35 (step t289.t3 (cl (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t289.t2 t289.a0))
% 14.11/14.35 (step t289 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule subproof :discharge (t289.a0))
% 14.11/14.35 (step t290 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t288 t289))
% 14.11/14.35 (step t291 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t292 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)))) :rule resolution :premises (t290 t291))
% 14.11/14.35 (step t293 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a)))) :rule contraction :premises (t292))
% 14.11/14.35 (step t294 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.union (tptp.intersection X Y) Y)))) (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule implies :premises (t293))
% 14.11/14.35 (step t295 (cl (= tptp.a (tptp.union (tptp.intersection tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t294 t246))
% 14.11/14.35 (step t296 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t297)
% 14.11/14.35 (assume t297.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))))
% 14.11/14.35 (step t297.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 14.11/14.35 (step t297.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) :rule or :premises (t297.t1))
% 14.11/14.35 (step t297.t3 (cl (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t297.t2 t297.a0))
% 14.11/14.35 (step t297 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) :rule subproof :discharge (t297.a0))
% 14.11/14.35 (step t298 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t296 t297))
% 14.11/14.35 (step t299 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t300 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)))) :rule resolution :premises (t298 t299))
% 14.11/14.35 (step t301 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)))) :rule contraction :premises (t300))
% 14.11/14.35 (step t302 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) :rule implies :premises (t301))
% 14.11/14.35 (step t303 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.union X Y) Y) Y)) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.union X Y) Y) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) :rule equiv_pos2)
% 14.11/14.35 (anchor :step t304 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 14.11/14.35 (step t304.t1 (cl (= X X)) :rule refl)
% 14.11/14.35 (step t304.t2 (cl (= Y Y)) :rule refl)
% 14.11/14.35 (step t304.t3 (cl (= (= (tptp.intersection (tptp.union X Y) Y) Y) (= Y (tptp.intersection (tptp.union X Y) Y)))) :rule all_simplify)
% 14.11/14.35 (step t304 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.union X Y) Y) Y)) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))))) :rule bind)
% 14.11/14.35 (step t305 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) :rule resolution :premises (t303 t304 a13))
% 14.11/14.35 (step t306 (cl (= tptp.a (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t302 t305))
% 14.11/14.35 (step t307 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t308)
% 14.11/14.35 (assume t308.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))))
% 14.11/14.35 (step t308.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z tptp.identity) (:= X tptp.a)))
% 14.11/14.35 (step t308.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule or :premises (t308.t1))
% 14.11/14.35 (step t308.t3 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t308.t2 t308.a0))
% 14.11/14.35 (step t308 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule subproof :discharge (t308.a0))
% 14.11/14.35 (step t309 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t307 t308))
% 14.11/14.35 (step t310 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule implies_neg2)
% 14.11/14.35 (step t311 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t309 t310))
% 14.11/14.35 (step t312 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule contraction :premises (t311))
% 14.11/14.35 (step t313 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule implies :premises (t312))
% 14.11/14.35 (step t314 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.a) (tptp.intersection (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t313 a17))
% 14.11/14.35 (step t315 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t316)
% 14.11/14.35 (assume t316.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 14.11/14.35 (step t316.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule forall_inst :args ((:= X (tptp.positive_part tptp.a))))
% 14.11/14.35 (step t316.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule or :premises (t316.t1))
% 14.11/14.35 (step t316.t3 (cl (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule resolution :premises (t316.t2 t316.a0))
% 14.11/14.35 (step t316 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule subproof :discharge (t316.a0))
% 14.11/14.35 (step t317 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule resolution :premises (t315 t316))
% 14.11/14.35 (step t318 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (not (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule implies_neg2)
% 14.11/14.35 (step t319 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule resolution :premises (t317 t318))
% 14.11/14.35 (step t320 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule contraction :premises (t319))
% 14.11/14.35 (step t321 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule implies :premises (t320))
% 14.11/14.35 (step t322 (cl (= (tptp.positive_part tptp.a) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))) :rule resolution :premises (t321 t143))
% 14.11/14.35 (step t323 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))))) :rule equiv_pos2)
% 14.11/14.35 (step t324 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))))) :rule refl)
% 14.11/14.35 (step t325 (cl (= (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity)) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))))) :rule all_simplify)
% 14.11/14.35 (step t326 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))))) :rule cong :premises (t324 t325))
% 14.11/14.35 (step t327 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t328)
% 14.11/14.35 (assume t328.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))))
% 14.11/14.35 (step t328.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.negative_part tptp.a))))
% 14.11/14.35 (step t328.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) :rule or :premises (t328.t1))
% 14.11/14.35 (step t328.t3 (cl (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) :rule resolution :premises (t328.t2 t328.a0))
% 14.11/14.35 (step t328 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) :rule subproof :discharge (t328.a0))
% 14.11/14.35 (step t329 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) :rule resolution :premises (t327 t328))
% 14.11/14.35 (step t330 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) (not (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity)))) :rule implies_neg2)
% 14.11/14.35 (step t331 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity)))) :rule resolution :premises (t329 t330))
% 14.11/14.35 (step t332 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union tptp.identity (tptp.negative_part tptp.a)) (tptp.union (tptp.negative_part tptp.a) tptp.identity)))) :rule contraction :premises (t331))
% 14.11/14.35 (step t333 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a))))) :rule resolution :premises (t323 t326 t332))
% 14.11/14.35 (step t334 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.union Y X)))) (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) :rule implies :premises (t333))
% 14.11/14.35 (step t335 (cl (= (tptp.union (tptp.negative_part tptp.a) tptp.identity) (tptp.union tptp.identity (tptp.negative_part tptp.a)))) :rule resolution :premises (t334 a9))
% 14.11/14.35 (step t336 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t337)
% 14.11/14.35 (assume t337.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))))
% 14.11/14.35 (step t337.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z tptp.identity) (:= X tptp.identity)))
% 14.11/14.35 (step t337.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule or :premises (t337.t1))
% 14.11/14.35 (step t337.t3 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t337.t2 t337.a0))
% 14.11/14.35 (step t337 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule subproof :discharge (t337.a0))
% 14.11/14.35 (step t338 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t336 t337))
% 14.11/14.35 (step t339 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule implies_neg2)
% 14.11/14.35 (step t340 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule resolution :premises (t338 t339))
% 14.11/14.35 (step t341 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule contraction :premises (t340))
% 14.11/14.35 (step t342 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule implies :premises (t341))
% 14.11/14.35 (step t343 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) tptp.identity) (tptp.intersection (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t342 a17))
% 14.11/14.35 (step t344 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t345)
% 14.11/14.35 (assume t345.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))))
% 14.11/14.35 (step t345.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))
% 14.11/14.35 (step t345.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule or :premises (t345.t1))
% 14.11/14.35 (step t345.t3 (cl (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule resolution :premises (t345.t2 t345.a0))
% 14.11/14.35 (step t345 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule subproof :discharge (t345.a0))
% 14.11/14.35 (step t346 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule resolution :premises (t344 t345))
% 14.11/14.35 (step t347 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (not (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t348 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)))) :rule resolution :premises (t346 t347))
% 14.11/14.35 (step t349 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a)))) :rule contraction :premises (t348))
% 14.11/14.35 (step t350 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection X Y) (tptp.intersection Y X)))) (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule implies :premises (t349))
% 14.11/14.35 (step t351 (cl (= (tptp.intersection tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.intersection (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) tptp.a))) :rule resolution :premises (t350 a8))
% 14.11/14.35 (step t352 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t353)
% 14.11/14.35 (assume t353.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))))
% 14.11/14.35 (step t353.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))
% 14.11/14.35 (step t353.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule or :premises (t353.t1))
% 14.11/14.35 (step t353.t3 (cl (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule resolution :premises (t353.t2 t353.a0))
% 14.11/14.35 (step t353 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule subproof :discharge (t353.a0))
% 14.11/14.35 (step t354 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule resolution :premises (t352 t353))
% 14.11/14.35 (step t355 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) :rule implies_neg2)
% 14.11/14.35 (step t356 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) :rule resolution :premises (t354 t355))
% 14.11/14.35 (step t357 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)))))) :rule contraction :premises (t356))
% 14.11/14.35 (step t358 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule implies :premises (t357))
% 14.11/14.35 (step t359 (cl (= (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a)) (tptp.intersection (tptp.union tptp.a (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))) (tptp.multiply (tptp.positive_part tptp.a) (tptp.negative_part tptp.a))))) :rule resolution :premises (t358 t305))
% 14.11/14.35 (step t360 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t361)
% 14.11/14.35 (assume t361.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X)))))
% 14.11/14.35 (step t361.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z tptp.identity) (:= X (tptp.negative_part tptp.a))))
% 14.11/14.35 (step t361.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule or :premises (t361.t1))
% 14.11/14.35 (step t361.t3 (cl (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule resolution :premises (t361.t2 t361.a0))
% 14.11/14.35 (step t361 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule subproof :discharge (t361.a0))
% 14.11/14.35 (step t362 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule resolution :premises (t360 t361))
% 14.11/14.35 (step t363 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule implies_neg2)
% 14.11/14.35 (step t364 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule resolution :premises (t362 t363))
% 14.11/14.35 (step t365 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule contraction :premises (t364))
% 14.11/14.35 (step t366 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.union Y Z) X) (tptp.union (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule implies :premises (t365))
% 14.11/14.35 (step t367 (cl (= (tptp.multiply (tptp.union tptp.a tptp.identity) (tptp.negative_part tptp.a)) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule resolution :premises (t366 a16))
% 14.11/14.35 (step t368 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t369)
% 14.11/14.35 (assume t369.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))))
% 14.11/14.35 (step t369.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.identity) (:= Z (tptp.negative_part tptp.a))))
% 14.11/14.35 (step t369.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule or :premises (t369.t1))
% 14.11/14.35 (step t369.t3 (cl (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule resolution :premises (t369.t2 t369.a0))
% 14.11/14.35 (step t369 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule subproof :discharge (t369.a0))
% 14.11/14.35 (step t370 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule resolution :premises (t368 t369))
% 14.11/14.35 (step t371 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))))) :rule implies_neg2)
% 14.11/14.35 (step t372 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))))) :rule resolution :premises (t370 t371))
% 14.11/14.35 (step t373 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a)))))) :rule contraction :premises (t372))
% 14.11/14.35 (step t374 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule implies :premises (t373))
% 14.11/14.35 (step t375 (cl (= (tptp.multiply tptp.a (tptp.union tptp.identity (tptp.negative_part tptp.a))) (tptp.union (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.negative_part tptp.a))))) :rule resolution :premises (t374 a14))
% 14.11/14.35 (step t376 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t377)
% 14.11/14.35 (assume t377.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z))))
% 14.11/14.35 (step t377.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule forall_inst :args ((:= X (tptp.union tptp.a tptp.a)) (:= Y (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (:= Z (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))
% 14.11/14.35 (step t377.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule or :premises (t377.t1))
% 14.11/14.35 (step t377.t3 (cl (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule resolution :premises (t377.t2 t377.a0))
% 14.11/14.35 (step t377 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule subproof :discharge (t377.a0))
% 14.11/14.35 (step t378 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule resolution :premises (t376 t377))
% 14.11/14.35 (step t379 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (not (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule implies_neg2)
% 14.11/14.35 (step t380 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule resolution :premises (t378 t379))
% 14.11/14.35 (step t381 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))))) :rule contraction :premises (t380))
% 14.11/14.35 (step t382 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.union X (tptp.union Y Z)) (tptp.union (tptp.union X Y) Z)))) (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule implies :premises (t381))
% 14.11/14.35 (step t383 (cl (= (tptp.union (tptp.union tptp.a tptp.a) (tptp.union (tptp.multiply tptp.a (tptp.negative_part tptp.a)) (tptp.multiply tptp.identity (tptp.negative_part tptp.a)))) (tptp.union (tptp.union (tptp.union tptp.a tptp.a) (tptp.multiply tptp.a (tptp.negative_part tptp.a))) (tptp.multiply tptp.identity (tptp.negative_part tptp.a))))) :rule resolution :premises (t382 a11))
% 14.11/14.35 (step t384 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t385)
% 14.11/14.35 (assume t385.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))))
% 14.11/14.35 (step t385.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.negative_part tptp.a)) (:= Y tptp.a) (:= Z tptp.identity)))
% 14.11/14.35 (step t385.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule or :premises (t385.t1))
% 14.11/14.35 (step t385.t3 (cl (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule resolution :premises (t385.t2 t385.a0))
% 14.11/14.35 (step t385 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule subproof :discharge (t385.a0))
% 14.11/14.35 (step t386 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule resolution :premises (t384 t385))
% 14.11/14.35 (step t387 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))))) :rule implies_neg2)
% 14.11/14.35 (step t388 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))))) :rule resolution :premises (t386 t387))
% 14.11/14.35 (step t389 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity))))) :rule contraction :premises (t388))
% 14.11/14.35 (step t390 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.union Y Z)) (tptp.union (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule implies :premises (t389))
% 14.11/14.35 (step t391 (cl (= (tptp.multiply (tptp.negative_part tptp.a) (tptp.union tptp.a tptp.identity)) (tptp.union (tptp.multiply (tptp.negative_part tptp.a) tptp.a) (tptp.multiply (tptp.negative_part tptp.a) tptp.identity)))) :rule resolution :premises (t390 a14))
% 14.11/14.35 (step t392 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t393)
% 14.11/14.35 (assume t393.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))))
% 14.11/14.35 (step t393.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z tptp.identity) (:= X (tptp.positive_part tptp.a))))
% 14.11/14.35 (step t393.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule or :premises (t393.t1))
% 14.11/14.35 (step t393.t3 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule resolution :premises (t393.t2 t393.a0))
% 14.11/14.35 (step t393 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule subproof :discharge (t393.a0))
% 14.11/14.35 (step t394 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule resolution :premises (t392 t393))
% 14.11/14.35 (step t395 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (not (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))))) :rule implies_neg2)
% 14.11/14.35 (step t396 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))))) :rule resolution :premises (t394 t395))
% 14.11/14.35 (step t397 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a)))))) :rule contraction :premises (t396))
% 14.11/14.35 (step t398 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.intersection Y Z) X) (tptp.intersection (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule implies :premises (t397))
% 14.11/14.35 (step t399 (cl (= (tptp.multiply (tptp.intersection tptp.a tptp.identity) (tptp.positive_part tptp.a)) (tptp.intersection (tptp.multiply tptp.a (tptp.positive_part tptp.a)) (tptp.multiply tptp.identity (tptp.positive_part tptp.a))))) :rule resolution :premises (t398 a17))
% 14.11/14.35 (step t400 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) :rule implies_neg1)
% 14.11/14.35 (anchor :step t401)
% 14.11/14.35 (assume t401.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))))
% 14.11/14.35 (step t401.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a tptp.a)) (:= Y tptp.a)))
% 14.11/14.35 (step t401.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule or :premises (t401.t1))
% 14.11/14.35 (step t401.t3 (cl (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t401.t2 t401.a0))
% 14.11/14.35 (step t401 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule subproof :discharge (t401.a0))
% 14.11/14.35 (step t402 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t400 t401))
% 14.11/14.35 (step t403 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (not (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) :rule implies_neg2)
% 14.11/14.35 (step t404 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) :rule resolution :premises (t402 t403))
% 14.11/14.35 (step t405 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a)))) :rule contraction :premises (t404))
% 14.11/14.35 (step t406 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.intersection (tptp.union X Y) Y)))) (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule implies :premises (t405))
% 14.11/14.35 (step t407 (cl (= tptp.a (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t406 t305))
% 14.11/14.35 (step t408 (cl (not (= (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.intersection (tptp.union tptp.identity tptp.a) tptp.a)) (tptp.intersection (tptp.intersection (tptp.union (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.union tptp.identity tptp.a)) tptp.a)))) :rule resolution :premises (t132 t133 t144 t155 t163 t171 t179 t187 t195 t206 t217 t228 t236 t247 t255 t263 t271 t279 t287 t295 t306 t314 t322 t335 t343 t351 t359 t367 t375 t383 t391 t399 t407))
% 14.11/14.35 (step t409 (cl) :rule resolution :premises (t7 t408 a10))
% 14.11/14.35
% 14.11/14.35 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.M5fmuYpmzG/cvc5---1.0.5_11251.smt2
% 14.11/14.35 % cvc5---1.0.5 exiting
% 14.11/14.36 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------