TSTP Solution File: SEU568^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU568^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n026.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 17:54:09 EDT 2024
% Result : Theorem 0.41s 0.64s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SEU568^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n026.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 27 12:21:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.40/0.56 %----Proving TH0
% 0.41/0.64 --- Run --ho-elim --full-saturate-quant at 10...
% 0.41/0.64 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.oAlRYFhkLd/cvc5---1.0.5_24057.smt2
% 0.41/0.64 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.oAlRYFhkLd/cvc5---1.0.5_24057.smt2
% 0.41/0.64 (assume a0 (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))
% 0.41/0.64 (assume a1 (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (= A B)))))
% 0.41/0.64 (assume a2 (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset)))))
% 0.41/0.64 (assume a3 (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (= (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ (@ tptp.in Xy) A))))))
% 0.41/0.64 (assume a4 (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A)))))))
% 0.41/0.64 (assume a5 (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))
% 0.41/0.64 (assume a6 (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega)))
% 0.41/0.64 (assume a7 (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))
% 0.41/0.64 (assume a8 (= tptp.omegaIndAx (forall ((A $$unsorted)) (=> (and (@ (@ tptp.in tptp.emptyset) A) (forall ((Xx $$unsorted)) (=> (and (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) A)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in Xx) A)))))))
% 0.41/0.64 (assume a9 (= tptp.replAx (forall ((Xphi (-> $$unsorted $$unsorted Bool)) (A $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ tptp.exu (lambda ((Xy $$unsorted)) (@ (@ Xphi Xx) Xy))))) (exists ((B $$unsorted)) (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) B) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx))))))))))
% 0.41/0.64 (assume a10 (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A))))))))))
% 0.41/0.64 (assume a11 (= tptp.wellorderingAx (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (forall ((C $$unsorted)) (=> (@ (@ tptp.in C) B) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) C) (@ (@ tptp.in Xx) A))))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (and (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) A)) (=> (forall ((C $$unsorted)) (=> (@ (@ tptp.in C) B) (= (@ (@ tptp.in Xx) C) (@ (@ tptp.in Xy) C)))) (= Xx Xy)))) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (@ (@ tptp.in C) B) (@ (@ tptp.in D) B)) (or (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) C) (@ (@ tptp.in Xx) D))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) D) (@ (@ tptp.in Xx) C)))))) (forall ((C $$unsorted)) (=> (and (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) C) (@ (@ tptp.in Xx) A))) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) C))) (exists ((D $$unsorted) (Xx $$unsorted)) (and (@ (@ tptp.in D) B) (@ (@ tptp.in Xx) C) (not (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) D) (@ (@ tptp.in Xy) C)))) (forall ((E $$unsorted)) (=> (@ (@ tptp.in E) B) (or (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) E) (@ (@ tptp.in Xy) D))) (@ (@ tptp.in Xx) E)))))))))))))
% 0.41/0.64 (assume a12 (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))
% 0.41/0.64 (assume a13 (= tptp.dsetconstrI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))
% 0.41/0.64 (assume a14 (= tptp.dsetconstrEL (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ (@ tptp.in Xx) A)))))
% 0.41/0.64 (assume a15 (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx)))))
% 0.41/0.64 (assume a16 (= tptp.exuE1 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))))
% 0.41/0.64 (assume a17 (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))
% 0.41/0.64 (assume a18 (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))
% 0.41/0.64 (assume a19 (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))
% 0.41/0.64 (assume a20 (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset)))))
% 0.41/0.64 (assume a21 (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))
% 0.41/0.64 (assume a22 (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A))) (= A B))))))
% 0.41/0.64 (assume a23 (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))
% 0.41/0.64 (assume a24 (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))
% 0.41/0.64 (assume a25 (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))))
% 0.41/0.64 (assume a26 (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))
% 0.41/0.64 (assume a27 (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))
% 0.41/0.64 (assume a28 (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))
% 0.41/0.64 (assume a29 (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))
% 0.41/0.64 (assume a30 (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy)))))
% 0.41/0.64 (assume a31 (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset))))
% 0.41/0.64 (assume a32 (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A))))))
% 0.41/0.64 (assume a33 (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi)))))))
% 0.41/0.64 (assume a34 (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ (@ tptp.in Xy) A))))))
% 0.41/0.64 (assume a35 (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A))))
% 0.41/0.64 (assume a36 (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A))) (@ (@ tptp.in B) (@ tptp.powerset A))))))
% 0.41/0.64 (assume a37 (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A)))))
% 0.41/0.64 (assume a38 (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A)))))
% 0.41/0.64 (assume a39 (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A))))))
% 0.41/0.64 (assume a40 (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) (@ (@ tptp.in Xx) (@ tptp.setunion A)))))))
% 0.41/0.64 (assume a41 (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi))))))
% 0.41/0.64 (assume a42 (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) (@ tptp.powerset (@ tptp.setunion A)))))))
% 0.41/0.64 (assume a43 (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx))))))))
% 0.41/0.64 (assume a44 (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true))))))
% 0.41/0.64 (assume a45 (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))
% 0.41/0.64 (assume a46 (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))
% 0.41/0.64 (assume a47 (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
% 0.41/0.64 (assume a48 (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))
% 0.41/0.64 (assume a49 (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))
% 0.41/0.64 (assume a50 (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
% 0.41/0.64 (assume a51 (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
% 0.41/0.64 (assume a52 (= tptp.emptyE1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (=> (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) tptp.emptyset) false)))))
% 0.41/0.64 (assume a53 (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx)))))
% 0.41/0.64 (assume a54 (= tptp.quantDeMorgan1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))
% 0.41/0.64 (assume a55 (= tptp.quantDeMorgan2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))))
% 0.41/0.64 (assume a56 (= tptp.quantDeMorgan3 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))
% 0.41/0.64 (assume a57 (= tptp.quantDeMorgan4 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))))
% 0.41/0.64 (assume a58 (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi))))))
% 0.41/0.64 (assume a59 (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi))))))
% 0.41/0.64 (assume a60 (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))
% 0.41/0.64 (assume a61 (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))
% 0.41/0.64 (assume a62 (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))
% 0.41/0.64 (assume a63 (= tptp.exuI3 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (@ Xphi Xx)) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))
% 0.41/0.64 (assume a64 (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))
% 0.41/0.64 (assume a65 (= tptp.inCongP (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))
% 0.41/0.64 (assume a66 (= tptp.in__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))
% 0.41/0.64 (assume a67 (= tptp.exuE3u (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))
% 0.41/0.64 (assume a68 (= tptp.exu__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy)))) (= (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))
% 0.41/0.64 (assume a69 (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset)))
% 0.41/0.64 (assume a70 (= tptp.setadjoin__Cong (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (forall ((Xz $$unsorted) (Xu $$unsorted)) (=> (= Xz Xu) (= (@ (@ tptp.setadjoin Xx) Xz) (@ (@ tptp.setadjoin Xy) Xu))))))))
% 0.41/0.64 (assume a71 (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B))))))
% 0.41/0.64 (assume a72 (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B))))))
% 0.41/0.64 (assume a73 (= tptp.omega__Cong (= tptp.omega tptp.omega)))
% 0.41/0.64 (assume a74 (= tptp.exuEu (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))
% 0.41/0.64 (assume a75 (= tptp.descr__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy)))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))) (= (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))))
% 0.41/0.64 (assume a76 (= tptp.dsetconstr__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy))))))) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))))
% 0.41/0.64 (assume a77 (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)))))
% 0.41/0.64 (assume a78 (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A)))))
% 0.41/0.64 (assume a79 (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B)))))
% 0.41/0.64 (assume a80 (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)))))
% 0.41/0.64 (assume a81 (= tptp.emptysetsubset (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A))))
% 0.41/0.64 (assume a82 (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))))
% 0.41/0.64 (assume a83 (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in Xx) A)))))))
% 0.41/0.64 (assume a84 (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.subset A) B)))))))
% 0.41/0.64 (assume a85 (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B))))))
% 0.41/0.64 (assume a86 (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.41/0.64 (assume a87 true)
% 0.41/0.64 (step t1 (cl (not (= (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) false)) (not (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) false) :rule equiv_pos2)
% 0.41/0.64 (step t2 (cl (= tptp.setextAx tptp.setextAx)) :rule refl)
% 0.41/0.64 (step t3 (cl (= tptp.emptysetAx tptp.emptysetAx)) :rule refl)
% 0.41/0.64 (step t4 (cl (= tptp.setadjoinAx tptp.setadjoinAx)) :rule refl)
% 0.41/0.64 (step t5 (cl (= tptp.powersetAx tptp.powersetAx)) :rule refl)
% 0.41/0.64 (step t6 (cl (= tptp.setunionAx tptp.setunionAx)) :rule refl)
% 0.41/0.64 (step t7 (cl (= tptp.omega0Ax tptp.omega0Ax)) :rule refl)
% 0.41/0.64 (step t8 (cl (= tptp.omegaSAx tptp.omegaSAx)) :rule refl)
% 0.41/0.64 (step t9 (cl (= tptp.omegaIndAx tptp.omegaIndAx)) :rule refl)
% 0.41/0.64 (step t10 (cl (= tptp.replAx tptp.replAx)) :rule refl)
% 0.41/0.64 (step t11 (cl (= tptp.foundationAx tptp.foundationAx)) :rule refl)
% 0.41/0.64 (step t12 (cl (= tptp.wellorderingAx tptp.wellorderingAx)) :rule refl)
% 0.41/0.64 (step t13 (cl (= tptp.descrp tptp.descrp)) :rule refl)
% 0.41/0.64 (step t14 (cl (= tptp.dsetconstrI tptp.dsetconstrI)) :rule refl)
% 0.41/0.64 (step t15 (cl (= tptp.dsetconstrEL tptp.dsetconstrEL)) :rule refl)
% 0.41/0.64 (step t16 (cl (= tptp.dsetconstrER tptp.dsetconstrER)) :rule refl)
% 0.41/0.64 (step t17 (cl (= tptp.exuE1 tptp.exuE1)) :rule refl)
% 0.41/0.64 (step t18 (cl (= tptp.prop2setE tptp.prop2setE)) :rule refl)
% 0.41/0.64 (step t19 (cl (= tptp.emptysetE tptp.emptysetE)) :rule refl)
% 0.41/0.64 (step t20 (cl (= tptp.emptysetimpfalse tptp.emptysetimpfalse)) :rule refl)
% 0.41/0.64 (step t21 (cl (= tptp.notinemptyset tptp.notinemptyset)) :rule refl)
% 0.41/0.64 (step t22 (cl (= tptp.exuE3e tptp.exuE3e)) :rule refl)
% 0.41/0.64 (step t23 (cl (= tptp.setext tptp.setext)) :rule refl)
% 0.41/0.64 (step t24 (cl (= tptp.emptyI tptp.emptyI)) :rule refl)
% 0.41/0.64 (step t25 (cl (= tptp.noeltsimpempty tptp.noeltsimpempty)) :rule refl)
% 0.41/0.64 (step t26 (cl (= tptp.setbeta tptp.setbeta)) :rule refl)
% 0.41/0.64 (step t27 (cl (= tptp.nonemptyE1 tptp.nonemptyE1)) :rule refl)
% 0.41/0.64 (step t28 (cl (= tptp.nonemptyI tptp.nonemptyI)) :rule refl)
% 0.41/0.64 (step t29 (cl (= tptp.nonemptyI1 tptp.nonemptyI1)) :rule refl)
% 0.41/0.64 (step t30 (cl (= tptp.setadjoinIL tptp.setadjoinIL)) :rule refl)
% 0.41/0.64 (step t31 (cl (= tptp.emptyinunitempty tptp.emptyinunitempty)) :rule refl)
% 0.41/0.64 (step t32 (cl (= tptp.setadjoinIR tptp.setadjoinIR)) :rule refl)
% 0.41/0.64 (step t33 (cl (= tptp.setadjoinE tptp.setadjoinE)) :rule refl)
% 0.41/0.64 (step t34 (cl (= tptp.setadjoinOr tptp.setadjoinOr)) :rule refl)
% 0.41/0.64 (step t35 (cl (= tptp.setoftrueEq tptp.setoftrueEq)) :rule refl)
% 0.41/0.64 (step t36 (cl (= tptp.powersetI tptp.powersetI)) :rule refl)
% 0.41/0.64 (step t37 (cl (= tptp.emptyinPowerset tptp.emptyinPowerset)) :rule refl)
% 0.41/0.64 (step t38 (cl (= tptp.emptyInPowerset tptp.emptyInPowerset)) :rule refl)
% 0.41/0.64 (step t39 (cl (= tptp.powersetE tptp.powersetE)) :rule refl)
% 0.41/0.64 (step t40 (cl (= tptp.setunionI tptp.setunionI)) :rule refl)
% 0.41/0.64 (step t41 (cl (= tptp.setunionE tptp.setunionE)) :rule refl)
% 0.41/0.64 (step t42 (cl (= tptp.subPowSU tptp.subPowSU)) :rule refl)
% 0.41/0.64 (step t43 (cl (= tptp.exuE2 tptp.exuE2)) :rule refl)
% 0.41/0.64 (step t44 (cl (= tptp.nonemptyImpWitness tptp.nonemptyImpWitness)) :rule refl)
% 0.41/0.64 (step t45 (cl (= tptp.uniqinunit tptp.uniqinunit)) :rule refl)
% 0.41/0.64 (step t46 (cl (= tptp.notinsingleton tptp.notinsingleton)) :rule refl)
% 0.41/0.64 (step t47 (cl (= tptp.eqinunit tptp.eqinunit)) :rule refl)
% 0.41/0.64 (step t48 (cl (= tptp.singletonsswitch tptp.singletonsswitch)) :rule refl)
% 0.41/0.64 (step t49 (cl (= tptp.upairsetE tptp.upairsetE)) :rule refl)
% 0.41/0.64 (step t50 (cl (= tptp.upairsetIL tptp.upairsetIL)) :rule refl)
% 0.41/0.64 (step t51 (cl (= tptp.upairsetIR tptp.upairsetIR)) :rule refl)
% 0.41/0.64 (step t52 (cl (= tptp.emptyE1 tptp.emptyE1)) :rule refl)
% 0.41/0.64 (step t53 (cl (= tptp.vacuousDall tptp.vacuousDall)) :rule refl)
% 0.41/0.64 (step t54 (cl (= tptp.quantDeMorgan1 tptp.quantDeMorgan1)) :rule refl)
% 0.41/0.64 (step t55 (cl (= tptp.quantDeMorgan2 tptp.quantDeMorgan2)) :rule refl)
% 0.41/0.64 (step t56 (cl (= tptp.quantDeMorgan3 tptp.quantDeMorgan3)) :rule refl)
% 0.41/0.64 (step t57 (cl (= tptp.quantDeMorgan4 tptp.quantDeMorgan4)) :rule refl)
% 0.41/0.64 (step t58 (cl (= tptp.prop2setI tptp.prop2setI)) :rule refl)
% 0.41/0.64 (step t59 (cl (= tptp.prop2set2propI tptp.prop2set2propI)) :rule refl)
% 0.41/0.64 (step t60 (cl (= tptp.notdexE tptp.notdexE)) :rule refl)
% 0.41/0.64 (step t61 (cl (= tptp.notdallE tptp.notdallE)) :rule refl)
% 0.41/0.64 (step t62 (cl (= tptp.exuI1 tptp.exuI1)) :rule refl)
% 0.41/0.64 (step t63 (cl (= tptp.exuI3 tptp.exuI3)) :rule refl)
% 0.41/0.64 (step t64 (cl (= tptp.exuI2 tptp.exuI2)) :rule refl)
% 0.41/0.64 (step t65 (cl (= tptp.inCongP tptp.inCongP)) :rule refl)
% 0.41/0.64 (step t66 (cl (= tptp.in__Cong tptp.in__Cong)) :rule refl)
% 0.41/0.64 (step t67 (cl (= tptp.exuE3u tptp.exuE3u)) :rule refl)
% 0.41/0.64 (step t68 (cl (= tptp.exu__Cong tptp.exu__Cong)) :rule refl)
% 0.41/0.64 (step t69 (cl (= tptp.emptyset__Cong tptp.emptyset__Cong)) :rule refl)
% 0.41/0.64 (step t70 (cl (= tptp.setadjoin__Cong tptp.setadjoin__Cong)) :rule refl)
% 0.41/0.64 (step t71 (cl (= tptp.powerset__Cong tptp.powerset__Cong)) :rule refl)
% 0.41/0.64 (step t72 (cl (= tptp.setunion__Cong tptp.setunion__Cong)) :rule refl)
% 0.41/0.64 (step t73 (cl (= tptp.omega__Cong tptp.omega__Cong)) :rule refl)
% 0.41/0.64 (step t74 (cl (= tptp.exuEu tptp.exuEu)) :rule refl)
% 0.41/0.64 (step t75 (cl (= tptp.descr__Cong tptp.descr__Cong)) :rule refl)
% 0.41/0.64 (step t76 (cl (= tptp.dsetconstr__Cong tptp.dsetconstr__Cong)) :rule refl)
% 0.41/0.64 (step t77 (cl (= tptp.subsetI1 tptp.subsetI1)) :rule refl)
% 0.41/0.64 (step t78 (cl (= tptp.eqimpsubset2 tptp.eqimpsubset2)) :rule refl)
% 0.41/0.64 (step t79 (cl (= tptp.eqimpsubset1 tptp.eqimpsubset1)) :rule refl)
% 0.41/0.64 (step t80 (cl (= tptp.subsetI2 tptp.subsetI2)) :rule refl)
% 0.41/0.64 (step t81 (cl (= tptp.emptysetsubset tptp.emptysetsubset)) :rule refl)
% 0.41/0.64 (step t82 (cl (= tptp.subsetE tptp.subsetE)) :rule refl)
% 0.41/0.64 (step t83 (cl (= tptp.subsetE2 tptp.subsetE2)) :rule refl)
% 0.41/0.64 (step t84 (cl (= tptp.notsubsetI tptp.notsubsetI)) :rule refl)
% 0.41/0.64 (step t85 (cl (= tptp.notequalI1 tptp.notequalI1)) :rule refl)
% 0.41/0.64 (step t86 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))) (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B) (not (= A B)))))) :rule all_simplify)
% 0.41/0.64 (step t87 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B) (not (= A B)))) (forall ((B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B) (not (= B B)))))) :rule all_simplify)
% 0.41/0.64 (anchor :step t88 :args ((B $$unsorted) (:= B B) (Xx $$unsorted) (:= Xx Xx)))
% 0.41/0.64 (step t88.t1 (cl (= B B)) :rule refl)
% 0.41/0.64 (step t88.t2 (cl (= Xx Xx)) :rule refl)
% 0.41/0.64 (step t88.t3 (cl (= (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in Xx) B)))) :rule refl)
% 0.41/0.64 (step t88.t4 (cl (= (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) B))) :rule refl)
% 0.41/0.64 (step t88.t5 (cl (= (= B B) true)) :rule all_simplify)
% 0.41/0.64 (step t88.t6 (cl (= (not (= B B)) (not true))) :rule cong :premises (t88.t5))
% 0.41/0.64 (step t88.t7 (cl (= (not true) false)) :rule all_simplify)
% 0.41/0.64 (step t88.t8 (cl (= (not (= B B)) false)) :rule trans :premises (t88.t6 t88.t7))
% 0.41/0.64 (step t88.t9 (cl (= (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B) (not (= B B))) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B) false))) :rule cong :premises (t88.t3 t88.t4 t88.t8))
% 0.41/0.64 (step t88.t10 (cl (= (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B) false) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B)))) :rule all_simplify)
% 0.41/0.64 (step t88.t11 (cl (= (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B) (not (= B B))) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B)))) :rule trans :premises (t88.t9 t88.t10))
% 0.41/0.64 (step t88 (cl (= (forall ((B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B) (not (= B B)))) (forall ((B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B))))) :rule bind)
% 0.41/0.64 (step t89 (cl (= (forall ((B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B))) (forall ((B $$unsorted) (Xx $$unsorted)) true))) :rule all_simplify)
% 0.41/0.64 (step t90 (cl (= (forall ((B $$unsorted) (Xx $$unsorted)) true) true)) :rule all_simplify)
% 0.41/0.64 (step t91 (cl (= (forall ((B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B))) true)) :rule trans :premises (t89 t90))
% 0.41/0.64 (step t92 (cl (= (forall ((B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B) (not (= B B)))) true)) :rule trans :premises (t88 t91))
% 0.41/0.64 (step t93 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B) (not (= A B)))) true)) :rule trans :premises (t87 t92))
% 0.41/0.64 (step t94 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))) true)) :rule trans :premises (t86 t93))
% 0.41/0.64 (step t95 (cl (= (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))) (=> tptp.notequalI1 true))) :rule cong :premises (t85 t94))
% 0.41/0.64 (step t96 (cl (= (=> tptp.notequalI1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t97 (cl (= (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))) true)) :rule trans :premises (t95 t96))
% 0.41/0.64 (step t98 (cl (= (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))) (=> tptp.notsubsetI true))) :rule cong :premises (t84 t97))
% 0.41/0.64 (step t99 (cl (= (=> tptp.notsubsetI true) true)) :rule all_simplify)
% 0.41/0.64 (step t100 (cl (= (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))) true)) :rule trans :premises (t98 t99))
% 0.41/0.64 (step t101 (cl (= (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))) (=> tptp.subsetE2 true))) :rule cong :premises (t83 t100))
% 0.41/0.64 (step t102 (cl (= (=> tptp.subsetE2 true) true)) :rule all_simplify)
% 0.41/0.64 (step t103 (cl (= (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))) true)) :rule trans :premises (t101 t102))
% 0.41/0.64 (step t104 (cl (= (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))) (=> tptp.subsetE true))) :rule cong :premises (t82 t103))
% 0.41/0.64 (step t105 (cl (= (=> tptp.subsetE true) true)) :rule all_simplify)
% 0.41/0.64 (step t106 (cl (= (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))) true)) :rule trans :premises (t104 t105))
% 0.41/0.64 (step t107 (cl (= (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))) (=> tptp.emptysetsubset true))) :rule cong :premises (t81 t106))
% 0.41/0.64 (step t108 (cl (= (=> tptp.emptysetsubset true) true)) :rule all_simplify)
% 0.41/0.64 (step t109 (cl (= (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))) true)) :rule trans :premises (t107 t108))
% 0.41/0.64 (step t110 (cl (= (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))) (=> tptp.subsetI2 true))) :rule cong :premises (t80 t109))
% 0.41/0.64 (step t111 (cl (= (=> tptp.subsetI2 true) true)) :rule all_simplify)
% 0.41/0.64 (step t112 (cl (= (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))) true)) :rule trans :premises (t110 t111))
% 0.41/0.64 (step t113 (cl (= (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))) (=> tptp.eqimpsubset1 true))) :rule cong :premises (t79 t112))
% 0.41/0.64 (step t114 (cl (= (=> tptp.eqimpsubset1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t115 (cl (= (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))) true)) :rule trans :premises (t113 t114))
% 0.41/0.64 (step t116 (cl (= (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))) (=> tptp.eqimpsubset2 true))) :rule cong :premises (t78 t115))
% 0.41/0.64 (step t117 (cl (= (=> tptp.eqimpsubset2 true) true)) :rule all_simplify)
% 0.41/0.64 (step t118 (cl (= (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))) true)) :rule trans :premises (t116 t117))
% 0.41/0.64 (step t119 (cl (= (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))) (=> tptp.subsetI1 true))) :rule cong :premises (t77 t118))
% 0.41/0.64 (step t120 (cl (= (=> tptp.subsetI1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t121 (cl (= (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))) true)) :rule trans :premises (t119 t120))
% 0.41/0.64 (step t122 (cl (= (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))) (=> tptp.dsetconstr__Cong true))) :rule cong :premises (t76 t121))
% 0.41/0.64 (step t123 (cl (= (=> tptp.dsetconstr__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t124 (cl (= (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))) true)) :rule trans :premises (t122 t123))
% 0.41/0.64 (step t125 (cl (= (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))) (=> tptp.descr__Cong true))) :rule cong :premises (t75 t124))
% 0.41/0.64 (step t126 (cl (= (=> tptp.descr__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t127 (cl (= (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))) true)) :rule trans :premises (t125 t126))
% 0.41/0.64 (step t128 (cl (= (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))) (=> tptp.exuEu true))) :rule cong :premises (t74 t127))
% 0.41/0.64 (step t129 (cl (= (=> tptp.exuEu true) true)) :rule all_simplify)
% 0.41/0.64 (step t130 (cl (= (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))) true)) :rule trans :premises (t128 t129))
% 0.41/0.64 (step t131 (cl (= (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))) (=> tptp.omega__Cong true))) :rule cong :premises (t73 t130))
% 0.41/0.64 (step t132 (cl (= (=> tptp.omega__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t133 (cl (= (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))) true)) :rule trans :premises (t131 t132))
% 0.41/0.64 (step t134 (cl (= (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))) (=> tptp.setunion__Cong true))) :rule cong :premises (t72 t133))
% 0.41/0.64 (step t135 (cl (= (=> tptp.setunion__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t136 (cl (= (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))) true)) :rule trans :premises (t134 t135))
% 0.41/0.64 (step t137 (cl (= (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))) (=> tptp.powerset__Cong true))) :rule cong :premises (t71 t136))
% 0.41/0.64 (step t138 (cl (= (=> tptp.powerset__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t139 (cl (= (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))) true)) :rule trans :premises (t137 t138))
% 0.41/0.64 (step t140 (cl (= (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))) (=> tptp.setadjoin__Cong true))) :rule cong :premises (t70 t139))
% 0.41/0.64 (step t141 (cl (= (=> tptp.setadjoin__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t142 (cl (= (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))) true)) :rule trans :premises (t140 t141))
% 0.41/0.64 (step t143 (cl (= (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))) (=> tptp.emptyset__Cong true))) :rule cong :premises (t69 t142))
% 0.41/0.64 (step t144 (cl (= (=> tptp.emptyset__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t145 (cl (= (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))) true)) :rule trans :premises (t143 t144))
% 0.41/0.64 (step t146 (cl (= (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))) (=> tptp.exu__Cong true))) :rule cong :premises (t68 t145))
% 0.41/0.64 (step t147 (cl (= (=> tptp.exu__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t148 (cl (= (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))) true)) :rule trans :premises (t146 t147))
% 0.41/0.64 (step t149 (cl (= (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))) (=> tptp.exuE3u true))) :rule cong :premises (t67 t148))
% 0.41/0.64 (step t150 (cl (= (=> tptp.exuE3u true) true)) :rule all_simplify)
% 0.41/0.64 (step t151 (cl (= (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))) true)) :rule trans :premises (t149 t150))
% 0.41/0.64 (step t152 (cl (= (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))) (=> tptp.in__Cong true))) :rule cong :premises (t66 t151))
% 0.41/0.64 (step t153 (cl (= (=> tptp.in__Cong true) true)) :rule all_simplify)
% 0.41/0.64 (step t154 (cl (= (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))) true)) :rule trans :premises (t152 t153))
% 0.41/0.64 (step t155 (cl (= (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))) (=> tptp.inCongP true))) :rule cong :premises (t65 t154))
% 0.41/0.64 (step t156 (cl (= (=> tptp.inCongP true) true)) :rule all_simplify)
% 0.41/0.64 (step t157 (cl (= (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))) true)) :rule trans :premises (t155 t156))
% 0.41/0.64 (step t158 (cl (= (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))) (=> tptp.exuI2 true))) :rule cong :premises (t64 t157))
% 0.41/0.64 (step t159 (cl (= (=> tptp.exuI2 true) true)) :rule all_simplify)
% 0.41/0.64 (step t160 (cl (= (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))) true)) :rule trans :premises (t158 t159))
% 0.41/0.64 (step t161 (cl (= (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))) (=> tptp.exuI3 true))) :rule cong :premises (t63 t160))
% 0.41/0.64 (step t162 (cl (= (=> tptp.exuI3 true) true)) :rule all_simplify)
% 0.41/0.64 (step t163 (cl (= (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))) true)) :rule trans :premises (t161 t162))
% 0.41/0.64 (step t164 (cl (= (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))) (=> tptp.exuI1 true))) :rule cong :premises (t62 t163))
% 0.41/0.64 (step t165 (cl (= (=> tptp.exuI1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t166 (cl (= (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))) true)) :rule trans :premises (t164 t165))
% 0.41/0.64 (step t167 (cl (= (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))) (=> tptp.notdallE true))) :rule cong :premises (t61 t166))
% 0.41/0.64 (step t168 (cl (= (=> tptp.notdallE true) true)) :rule all_simplify)
% 0.41/0.64 (step t169 (cl (= (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))) true)) :rule trans :premises (t167 t168))
% 0.41/0.64 (step t170 (cl (= (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))) (=> tptp.notdexE true))) :rule cong :premises (t60 t169))
% 0.41/0.64 (step t171 (cl (= (=> tptp.notdexE true) true)) :rule all_simplify)
% 0.41/0.64 (step t172 (cl (= (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))) true)) :rule trans :premises (t170 t171))
% 0.41/0.64 (step t173 (cl (= (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))) (=> tptp.prop2set2propI true))) :rule cong :premises (t59 t172))
% 0.41/0.64 (step t174 (cl (= (=> tptp.prop2set2propI true) true)) :rule all_simplify)
% 0.41/0.64 (step t175 (cl (= (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))) true)) :rule trans :premises (t173 t174))
% 0.41/0.64 (step t176 (cl (= (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))) (=> tptp.prop2setI true))) :rule cong :premises (t58 t175))
% 0.41/0.64 (step t177 (cl (= (=> tptp.prop2setI true) true)) :rule all_simplify)
% 0.41/0.64 (step t178 (cl (= (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t176 t177))
% 0.41/0.64 (step t179 (cl (= (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))) (=> tptp.quantDeMorgan4 true))) :rule cong :premises (t57 t178))
% 0.41/0.64 (step t180 (cl (= (=> tptp.quantDeMorgan4 true) true)) :rule all_simplify)
% 0.41/0.64 (step t181 (cl (= (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t179 t180))
% 0.41/0.64 (step t182 (cl (= (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))) (=> tptp.quantDeMorgan3 true))) :rule cong :premises (t56 t181))
% 0.41/0.64 (step t183 (cl (= (=> tptp.quantDeMorgan3 true) true)) :rule all_simplify)
% 0.41/0.64 (step t184 (cl (= (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t182 t183))
% 0.41/0.64 (step t185 (cl (= (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))) (=> tptp.quantDeMorgan2 true))) :rule cong :premises (t55 t184))
% 0.41/0.64 (step t186 (cl (= (=> tptp.quantDeMorgan2 true) true)) :rule all_simplify)
% 0.41/0.64 (step t187 (cl (= (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t185 t186))
% 0.41/0.64 (step t188 (cl (= (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))) (=> tptp.quantDeMorgan1 true))) :rule cong :premises (t54 t187))
% 0.41/0.64 (step t189 (cl (= (=> tptp.quantDeMorgan1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t190 (cl (= (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t188 t189))
% 0.41/0.64 (step t191 (cl (= (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))) (=> tptp.vacuousDall true))) :rule cong :premises (t53 t190))
% 0.41/0.64 (step t192 (cl (= (=> tptp.vacuousDall true) true)) :rule all_simplify)
% 0.41/0.64 (step t193 (cl (= (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t191 t192))
% 0.41/0.64 (step t194 (cl (= (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyE1 true))) :rule cong :premises (t52 t193))
% 0.41/0.64 (step t195 (cl (= (=> tptp.emptyE1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t196 (cl (= (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t194 t195))
% 0.41/0.64 (step t197 (cl (= (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))) (=> tptp.upairsetIR true))) :rule cong :premises (t51 t196))
% 0.41/0.64 (step t198 (cl (= (=> tptp.upairsetIR true) true)) :rule all_simplify)
% 0.41/0.64 (step t199 (cl (= (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t197 t198))
% 0.41/0.64 (step t200 (cl (= (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairsetIL true))) :rule cong :premises (t50 t199))
% 0.41/0.64 (step t201 (cl (= (=> tptp.upairsetIL true) true)) :rule all_simplify)
% 0.41/0.64 (step t202 (cl (= (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t200 t201))
% 0.41/0.64 (step t203 (cl (= (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairsetE true))) :rule cong :premises (t49 t202))
% 0.41/0.64 (step t204 (cl (= (=> tptp.upairsetE true) true)) :rule all_simplify)
% 0.41/0.64 (step t205 (cl (= (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t203 t204))
% 0.41/0.64 (step t206 (cl (= (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))) (=> tptp.singletonsswitch true))) :rule cong :premises (t48 t205))
% 0.41/0.64 (step t207 (cl (= (=> tptp.singletonsswitch true) true)) :rule all_simplify)
% 0.41/0.64 (step t208 (cl (= (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t206 t207))
% 0.41/0.64 (step t209 (cl (= (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))) (=> tptp.eqinunit true))) :rule cong :premises (t47 t208))
% 0.41/0.64 (step t210 (cl (= (=> tptp.eqinunit true) true)) :rule all_simplify)
% 0.41/0.64 (step t211 (cl (= (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t209 t210))
% 0.41/0.64 (step t212 (cl (= (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notinsingleton true))) :rule cong :premises (t46 t211))
% 0.41/0.64 (step t213 (cl (= (=> tptp.notinsingleton true) true)) :rule all_simplify)
% 0.41/0.64 (step t214 (cl (= (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t212 t213))
% 0.41/0.64 (step t215 (cl (= (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.uniqinunit true))) :rule cong :premises (t45 t214))
% 0.41/0.64 (step t216 (cl (= (=> tptp.uniqinunit true) true)) :rule all_simplify)
% 0.41/0.64 (step t217 (cl (= (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t215 t216))
% 0.41/0.64 (step t218 (cl (= (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.nonemptyImpWitness true))) :rule cong :premises (t44 t217))
% 0.41/0.64 (step t219 (cl (= (=> tptp.nonemptyImpWitness true) true)) :rule all_simplify)
% 0.41/0.64 (step t220 (cl (= (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t218 t219))
% 0.41/0.64 (step t221 (cl (= (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuE2 true))) :rule cong :premises (t43 t220))
% 0.41/0.64 (step t222 (cl (= (=> tptp.exuE2 true) true)) :rule all_simplify)
% 0.41/0.64 (step t223 (cl (= (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t221 t222))
% 0.41/0.64 (step t224 (cl (= (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subPowSU true))) :rule cong :premises (t42 t223))
% 0.41/0.64 (step t225 (cl (= (=> tptp.subPowSU true) true)) :rule all_simplify)
% 0.41/0.64 (step t226 (cl (= (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t224 t225))
% 0.41/0.64 (step t227 (cl (= (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionE true))) :rule cong :premises (t41 t226))
% 0.41/0.64 (step t228 (cl (= (=> tptp.setunionE true) true)) :rule all_simplify)
% 0.41/0.64 (step t229 (cl (= (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t227 t228))
% 0.41/0.64 (step t230 (cl (= (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionI true))) :rule cong :premises (t40 t229))
% 0.41/0.64 (step t231 (cl (= (=> tptp.setunionI true) true)) :rule all_simplify)
% 0.41/0.64 (step t232 (cl (= (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t230 t231))
% 0.41/0.64 (step t233 (cl (= (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetE true))) :rule cong :premises (t39 t232))
% 0.41/0.64 (step t234 (cl (= (=> tptp.powersetE true) true)) :rule all_simplify)
% 0.41/0.64 (step t235 (cl (= (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t233 t234))
% 0.41/0.64 (step t236 (cl (= (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyInPowerset true))) :rule cong :premises (t38 t235))
% 0.41/0.64 (step t237 (cl (= (=> tptp.emptyInPowerset true) true)) :rule all_simplify)
% 0.41/0.64 (step t238 (cl (= (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t236 t237))
% 0.41/0.64 (step t239 (cl (= (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyinPowerset true))) :rule cong :premises (t37 t238))
% 0.41/0.64 (step t240 (cl (= (=> tptp.emptyinPowerset true) true)) :rule all_simplify)
% 0.41/0.64 (step t241 (cl (= (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t239 t240))
% 0.41/0.64 (step t242 (cl (= (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetI true))) :rule cong :premises (t36 t241))
% 0.41/0.64 (step t243 (cl (= (=> tptp.powersetI true) true)) :rule all_simplify)
% 0.41/0.64 (step t244 (cl (= (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t242 t243))
% 0.41/0.64 (step t245 (cl (= (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setoftrueEq true))) :rule cong :premises (t35 t244))
% 0.41/0.64 (step t246 (cl (= (=> tptp.setoftrueEq true) true)) :rule all_simplify)
% 0.41/0.64 (step t247 (cl (= (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t245 t246))
% 0.41/0.64 (step t248 (cl (= (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinOr true))) :rule cong :premises (t34 t247))
% 0.41/0.64 (step t249 (cl (= (=> tptp.setadjoinOr true) true)) :rule all_simplify)
% 0.41/0.64 (step t250 (cl (= (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t248 t249))
% 0.41/0.64 (step t251 (cl (= (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinE true))) :rule cong :premises (t33 t250))
% 0.41/0.64 (step t252 (cl (= (=> tptp.setadjoinE true) true)) :rule all_simplify)
% 0.41/0.64 (step t253 (cl (= (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t251 t252))
% 0.41/0.64 (step t254 (cl (= (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinIR true))) :rule cong :premises (t32 t253))
% 0.41/0.64 (step t255 (cl (= (=> tptp.setadjoinIR true) true)) :rule all_simplify)
% 0.41/0.64 (step t256 (cl (= (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t254 t255))
% 0.41/0.64 (step t257 (cl (= (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyinunitempty true))) :rule cong :premises (t31 t256))
% 0.41/0.64 (step t258 (cl (= (=> tptp.emptyinunitempty true) true)) :rule all_simplify)
% 0.41/0.64 (step t259 (cl (= (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t257 t258))
% 0.41/0.64 (step t260 (cl (= (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinIL true))) :rule cong :premises (t30 t259))
% 0.41/0.64 (step t261 (cl (= (=> tptp.setadjoinIL true) true)) :rule all_simplify)
% 0.41/0.64 (step t262 (cl (= (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t260 t261))
% 0.41/0.64 (step t263 (cl (= (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.nonemptyI1 true))) :rule cong :premises (t29 t262))
% 0.41/0.64 (step t264 (cl (= (=> tptp.nonemptyI1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t265 (cl (= (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t263 t264))
% 0.41/0.64 (step t266 (cl (= (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.nonemptyI true))) :rule cong :premises (t28 t265))
% 0.41/0.64 (step t267 (cl (= (=> tptp.nonemptyI true) true)) :rule all_simplify)
% 0.41/0.64 (step t268 (cl (= (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t266 t267))
% 0.41/0.64 (step t269 (cl (= (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.nonemptyE1 true))) :rule cong :premises (t27 t268))
% 0.41/0.64 (step t270 (cl (= (=> tptp.nonemptyE1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t271 (cl (= (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t269 t270))
% 0.41/0.64 (step t272 (cl (= (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setbeta true))) :rule cong :premises (t26 t271))
% 0.41/0.64 (step t273 (cl (= (=> tptp.setbeta true) true)) :rule all_simplify)
% 0.41/0.64 (step t274 (cl (= (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t272 t273))
% 0.41/0.64 (step t275 (cl (= (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.noeltsimpempty true))) :rule cong :premises (t25 t274))
% 0.41/0.64 (step t276 (cl (= (=> tptp.noeltsimpempty true) true)) :rule all_simplify)
% 0.41/0.64 (step t277 (cl (= (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t275 t276))
% 0.41/0.64 (step t278 (cl (= (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyI true))) :rule cong :premises (t24 t277))
% 0.41/0.64 (step t279 (cl (= (=> tptp.emptyI true) true)) :rule all_simplify)
% 0.41/0.64 (step t280 (cl (= (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t278 t279))
% 0.41/0.64 (step t281 (cl (= (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setext true))) :rule cong :premises (t23 t280))
% 0.41/0.64 (step t282 (cl (= (=> tptp.setext true) true)) :rule all_simplify)
% 0.41/0.64 (step t283 (cl (= (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t281 t282))
% 0.41/0.64 (step t284 (cl (= (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuE3e true))) :rule cong :premises (t22 t283))
% 0.41/0.64 (step t285 (cl (= (=> tptp.exuE3e true) true)) :rule all_simplify)
% 0.41/0.64 (step t286 (cl (= (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t284 t285))
% 0.41/0.64 (step t287 (cl (= (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notinemptyset true))) :rule cong :premises (t21 t286))
% 0.41/0.64 (step t288 (cl (= (=> tptp.notinemptyset true) true)) :rule all_simplify)
% 0.41/0.64 (step t289 (cl (= (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t287 t288))
% 0.41/0.64 (step t290 (cl (= (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptysetimpfalse true))) :rule cong :premises (t20 t289))
% 0.41/0.64 (step t291 (cl (= (=> tptp.emptysetimpfalse true) true)) :rule all_simplify)
% 0.41/0.64 (step t292 (cl (= (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t290 t291))
% 0.41/0.64 (step t293 (cl (= (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptysetE true))) :rule cong :premises (t19 t292))
% 0.41/0.64 (step t294 (cl (= (=> tptp.emptysetE true) true)) :rule all_simplify)
% 0.41/0.64 (step t295 (cl (= (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t293 t294))
% 0.41/0.64 (step t296 (cl (= (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.prop2setE true))) :rule cong :premises (t18 t295))
% 0.41/0.64 (step t297 (cl (= (=> tptp.prop2setE true) true)) :rule all_simplify)
% 0.41/0.64 (step t298 (cl (= (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t296 t297))
% 0.41/0.64 (step t299 (cl (= (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuE1 true))) :rule cong :premises (t17 t298))
% 0.41/0.64 (step t300 (cl (= (=> tptp.exuE1 true) true)) :rule all_simplify)
% 0.41/0.64 (step t301 (cl (= (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t299 t300))
% 0.41/0.64 (step t302 (cl (= (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.dsetconstrER true))) :rule cong :premises (t16 t301))
% 0.41/0.64 (step t303 (cl (= (=> tptp.dsetconstrER true) true)) :rule all_simplify)
% 0.41/0.64 (step t304 (cl (= (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t302 t303))
% 0.41/0.64 (step t305 (cl (= (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.dsetconstrEL true))) :rule cong :premises (t15 t304))
% 0.41/0.64 (step t306 (cl (= (=> tptp.dsetconstrEL true) true)) :rule all_simplify)
% 0.41/0.64 (step t307 (cl (= (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t305 t306))
% 0.41/0.64 (step t308 (cl (= (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.dsetconstrI true))) :rule cong :premises (t14 t307))
% 0.41/0.64 (step t309 (cl (= (=> tptp.dsetconstrI true) true)) :rule all_simplify)
% 0.41/0.64 (step t310 (cl (= (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t308 t309))
% 0.41/0.64 (step t311 (cl (= (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.descrp true))) :rule cong :premises (t13 t310))
% 0.41/0.64 (step t312 (cl (= (=> tptp.descrp true) true)) :rule all_simplify)
% 0.41/0.64 (step t313 (cl (= (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t311 t312))
% 0.41/0.64 (step t314 (cl (= (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.wellorderingAx true))) :rule cong :premises (t12 t313))
% 0.41/0.64 (step t315 (cl (= (=> tptp.wellorderingAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t316 (cl (= (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t314 t315))
% 0.41/0.64 (step t317 (cl (= (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.foundationAx true))) :rule cong :premises (t11 t316))
% 0.41/0.64 (step t318 (cl (= (=> tptp.foundationAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t319 (cl (= (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t317 t318))
% 0.41/0.64 (step t320 (cl (= (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.replAx true))) :rule cong :premises (t10 t319))
% 0.41/0.64 (step t321 (cl (= (=> tptp.replAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t322 (cl (= (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t320 t321))
% 0.41/0.64 (step t323 (cl (= (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.omegaIndAx true))) :rule cong :premises (t9 t322))
% 0.41/0.64 (step t324 (cl (= (=> tptp.omegaIndAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t325 (cl (= (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t323 t324))
% 0.41/0.64 (step t326 (cl (= (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.omegaSAx true))) :rule cong :premises (t8 t325))
% 0.41/0.64 (step t327 (cl (= (=> tptp.omegaSAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t328 (cl (= (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t326 t327))
% 0.41/0.64 (step t329 (cl (= (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.omega0Ax true))) :rule cong :premises (t7 t328))
% 0.41/0.64 (step t330 (cl (= (=> tptp.omega0Ax true) true)) :rule all_simplify)
% 0.41/0.64 (step t331 (cl (= (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t329 t330))
% 0.41/0.64 (step t332 (cl (= (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionAx true))) :rule cong :premises (t6 t331))
% 0.41/0.64 (step t333 (cl (= (=> tptp.setunionAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t334 (cl (= (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t332 t333))
% 0.41/0.64 (step t335 (cl (= (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetAx true))) :rule cong :premises (t5 t334))
% 0.41/0.64 (step t336 (cl (= (=> tptp.powersetAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t337 (cl (= (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t335 t336))
% 0.41/0.64 (step t338 (cl (= (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinAx true))) :rule cong :premises (t4 t337))
% 0.41/0.64 (step t339 (cl (= (=> tptp.setadjoinAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t340 (cl (= (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t338 t339))
% 0.41/0.64 (step t341 (cl (= (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptysetAx true))) :rule cong :premises (t3 t340))
% 0.41/0.64 (step t342 (cl (= (=> tptp.emptysetAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t343 (cl (= (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t341 t342))
% 0.41/0.64 (step t344 (cl (= (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setextAx true))) :rule cong :premises (t2 t343))
% 0.41/0.64 (step t345 (cl (= (=> tptp.setextAx true) true)) :rule all_simplify)
% 0.41/0.64 (step t346 (cl (= (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t344 t345))
% 0.41/0.64 (step t347 (cl (= (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (not true))) :rule cong :premises (t346))
% 0.41/0.64 (step t348 (cl (= (not true) false)) :rule all_simplify)
% 0.41/0.64 (step t349 (cl (= (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) false)) :rule trans :premises (t347 t348))
% 0.41/0.65 (step t350 (cl false) :rule resolution :premises (t1 t349 a86))
% 0.41/0.65 (step t351 (cl (not false)) :rule false)
% 0.41/0.65 (step t352 (cl) :rule resolution :premises (t350 t351))
% 0.41/0.65
% 0.41/0.65 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.oAlRYFhkLd/cvc5---1.0.5_24057.smt2
% 0.41/0.65 % cvc5---1.0.5 exiting
% 0.41/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------