TSTP Solution File: SEU694^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU694^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n011.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 17:54:42 EDT 2024
% Result : Theorem 0.49s 0.85s
% Output : Proof 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.17 % Problem : SEU694^1 : TPTP v8.2.0. Released v3.7.0.
% 0.17/0.18 % Command : do_cvc5 %s %d
% 0.17/0.39 % Computer : n011.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Mon May 27 11:32:39 EDT 2024
% 0.17/0.39 % CPUTime :
% 0.47/0.64 %----Proving TH0
% 0.49/0.85 --- Run --ho-elim --full-saturate-quant at 10...
% 0.49/0.85 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.WNKjaM55nm/cvc5---1.0.5_16121.smt2
% 0.49/0.85 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.WNKjaM55nm/cvc5---1.0.5_16121.smt2
% 0.49/0.85 (assume a0 (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))
% 0.49/0.85 (assume a1 (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (= A B)))))
% 0.49/0.85 (assume a2 (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset)))))
% 0.49/0.85 (assume a3 (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (= (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ (@ tptp.in Xy) A))))))
% 0.49/0.85 (assume a4 (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A)))))))
% 0.49/0.85 (assume a5 (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))
% 0.49/0.85 (assume a6 (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega)))
% 0.49/0.85 (assume a7 (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))
% 0.49/0.85 (assume a8 (= tptp.omegaIndAx (forall ((A $$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)))))))
% 0.49/0.85 (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))))))))))
% 0.49/0.85 (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))))))))))
% 0.49/0.85 (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 $$unsorted)) (=> (@ (@ tptp.in Xy) E) (@ (@ tptp.in Xy) D))) (@ (@ tptp.in Xx) E)))))))))))))
% 0.49/0.85 (assume a12 (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))
% 0.49/0.85 (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)))))))))
% 0.49/0.85 (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)))))
% 0.49/0.85 (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)))))
% 0.49/0.85 (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)))))))))
% 0.49/0.85 (assume a17 (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))
% 0.49/0.85 (assume a18 (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))
% 0.49/0.85 (assume a19 (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))
% 0.49/0.85 (assume a20 (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset)))))
% 0.49/0.85 (assume a21 (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))
% 0.49/0.85 (assume a22 (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A))) (= A B))))))
% 0.49/0.85 (assume a23 (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))
% 0.49/0.85 (assume a24 (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))
% 0.49/0.85 (assume a25 (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))))
% 0.49/0.85 (assume a26 (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))
% 0.49/0.85 (assume a27 (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))
% 0.49/0.85 (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)))))))))
% 0.49/0.85 (assume a29 (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))
% 0.49/0.85 (assume a30 (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy)))))
% 0.49/0.85 (assume a31 (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset))))
% 0.49/0.85 (assume a32 (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A))))))
% 0.49/0.85 (assume a33 (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi)))))))
% 0.49/0.85 (assume a34 (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ (@ tptp.in Xy) A))))))
% 0.49/0.85 (assume a35 (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A))))
% 0.49/0.85 (assume a36 (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A))) (@ (@ tptp.in B) (@ tptp.powerset A))))))
% 0.49/0.85 (assume a37 (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A)))))
% 0.49/0.85 (assume a38 (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A)))))
% 0.49/0.85 (assume a39 (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) A))))))
% 0.49/0.85 (assume a40 (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) (@ (@ tptp.in Xx) (@ tptp.setunion A)))))))
% 0.49/0.85 (assume a41 (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi))))))
% 0.49/0.85 (assume a42 (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) (@ tptp.powerset (@ tptp.setunion A)))))))
% 0.49/0.85 (assume a43 (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx))))))))
% 0.49/0.85 (assume a44 (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true))))))
% 0.49/0.85 (assume a45 (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))
% 0.49/0.85 (assume a46 (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))
% 0.49/0.85 (assume a47 (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
% 0.49/0.85 (assume a48 (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))
% 0.49/0.85 (assume a49 (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))
% 0.49/0.85 (assume a50 (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
% 0.49/0.85 (assume a51 (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
% 0.49/0.85 (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)))))
% 0.49/0.85 (assume a53 (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx)))))
% 0.49/0.85 (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))))))))
% 0.49/0.85 (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))))))))
% 0.49/0.85 (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))))))))
% 0.49/0.85 (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))))))))
% 0.49/0.85 (assume a58 (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi))))))
% 0.49/0.85 (assume a59 (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi))))))
% 0.49/0.85 (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))))))))
% 0.49/0.85 (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))))))))
% 0.49/0.85 (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)))))))
% 0.49/0.85 (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 $$unsorted)) (@ Xphi Xx))))))))
% 0.49/0.85 (assume a64 (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))
% 0.49/0.85 (assume a65 (= tptp.inCongP (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))
% 0.49/0.85 (assume a66 (= tptp.in__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))
% 0.49/0.85 (assume a67 (= tptp.exuE3u (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))
% 0.49/0.85 (assume a68 (= tptp.exu__Cong (forall ((Xphi (-> $$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 $$unsorted)) (@ Xpsi Xx))))))))
% 0.49/0.85 (assume a69 (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset)))
% 0.49/0.85 (assume a70 (= tptp.setadjoin__Cong (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (forall ((Xz $$unsorted) (Xu $$unsorted)) (=> (= Xz Xu) (= (@ (@ tptp.setadjoin Xx) Xz) (@ (@ tptp.setadjoin Xy) Xu))))))))
% 0.49/0.85 (assume a71 (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B))))))
% 0.49/0.85 (assume a72 (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B))))))
% 0.49/0.85 (assume a73 (= tptp.omega__Cong (= tptp.omega tptp.omega)))
% 0.49/0.85 (assume a74 (= tptp.exuEu (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))
% 0.49/0.85 (assume a75 (= tptp.descr__Cong (forall ((Xphi (-> $$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 $$unsorted)) (@ Xpsi Xx))))))))))
% 0.49/0.85 (assume a76 (= tptp.dsetconstr__Cong (forall ((A $$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 $$unsorted)) (@ Xpsi Xx))))))))))
% 0.49/0.85 (assume a77 (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)))))
% 0.49/0.85 (assume a78 (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A)))))
% 0.49/0.85 (assume a79 (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B)))))
% 0.49/0.85 (assume a80 (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)))))
% 0.49/0.85 (assume a81 (= tptp.emptysetsubset (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A))))
% 0.49/0.85 (assume a82 (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))))
% 0.49/0.85 (assume a83 (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in Xx) A)))))))
% 0.49/0.85 (assume a84 (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.subset A) B)))))))
% 0.49/0.85 (assume a85 (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B))))))
% 0.49/0.85 (assume a86 (= tptp.notequalI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (not (= A B)))))))
% 0.49/0.85 (assume a87 (= tptp.subsetRefl (forall ((A $$unsorted)) (@ (@ tptp.subset A) A))))
% 0.49/0.85 (assume a88 (= tptp.subsetTrans (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) C) (@ (@ tptp.subset A) C))))))
% 0.49/0.85 (assume a89 (= tptp.setadjoinSub (forall ((Xx $$unsorted) (A $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) A)))))
% 0.49/0.85 (assume a90 (= tptp.setadjoinSub2 (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) B))))))
% 0.49/0.85 (assume a91 (= tptp.subset2powerset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.in A) (@ tptp.powerset B))))))
% 0.49/0.85 (assume a92 (= tptp.setextsub (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) A) (= A B))))))
% 0.49/0.85 (assume a93 (= tptp.subsetemptysetimpeq (forall ((A $$unsorted)) (=> (@ (@ tptp.subset A) tptp.emptyset) (= A tptp.emptyset)))))
% 0.49/0.85 (assume a94 (= tptp.powersetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (@ (@ tptp.in B) (@ tptp.powerset A))))))
% 0.49/0.85 (assume a95 (= tptp.powersetE1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (@ (@ tptp.subset B) A)))))
% 0.49/0.85 (assume a96 (= tptp.inPowerset (forall ((A $$unsorted)) (@ (@ tptp.in A) (@ tptp.powerset A)))))
% 0.49/0.85 (assume a97 (= tptp.powersetsubset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B))))))
% 0.49/0.85 (assume a98 (= tptp.sepInPowerset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.in (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ tptp.powerset A)))))
% 0.49/0.85 (assume a99 (= tptp.sepSubset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.subset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) A))))
% 0.49/0.85 (assume a100 (= tptp.binunionIL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) (@ (@ tptp.binunion A) B))))))
% 0.49/0.85 (assume a101 (= tptp.upairset2IR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
% 0.49/0.85 (assume a102 (= tptp.binunionIR (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) (@ (@ tptp.binunion A) B))))))
% 0.49/0.85 (assume a103 (= tptp.binunionEcases (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xphi Bool)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.binunion A) B)) (=> (=> (@ (@ tptp.in Xx) A) Xphi) (=> (=> (@ (@ tptp.in Xx) B) Xphi) Xphi))))))
% 0.49/0.85 (assume a104 (= tptp.binunionE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.binunion A) B)) (or (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))))
% 0.49/0.85 (assume a105 (= tptp.binunionLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.binunion A) B)))))
% 0.49/0.85 (assume a106 (= tptp.binunionRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset B) (@ (@ tptp.binunion A) B)))))
% 0.49/0.85 (assume a107 (= tptp.binintersectI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) (@ (@ tptp.binintersect A) B)))))))
% 0.49/0.85 (assume a108 (= tptp.binintersectSubset5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (@ (@ tptp.subset C) A) (=> (@ (@ tptp.subset C) B) (@ (@ tptp.subset C) (@ (@ tptp.binintersect A) B)))))))
% 0.49/0.85 (assume a109 (= tptp.binintersectEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.binintersect A) B)) (@ (@ tptp.in Xx) A)))))
% 0.49/0.85 (assume a110 (= tptp.binintersectLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) A))))
% 0.49/0.85 (assume a111 (= tptp.binintersectSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.binintersect A) B) A)))))
% 0.49/0.85 (assume a112 (= tptp.binintersectSubset3 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) B) (@ (@ tptp.subset B) A)))))
% 0.49/0.85 (assume a113 (= tptp.binintersectER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.binintersect A) B)) (@ (@ tptp.in Xx) B)))))
% 0.49/0.85 (assume a114 (= tptp.disjointsetsI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B)))) (= (@ (@ tptp.binintersect A) B) tptp.emptyset)))))
% 0.49/0.85 (assume a115 (= tptp.binintersectRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) B))))
% 0.49/0.85 (assume a116 (= tptp.binintersectSubset4 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (= (@ (@ tptp.binintersect A) B) B)))))
% 0.49/0.85 (assume a117 (= tptp.binintersectSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) A) (@ (@ tptp.subset A) B)))))
% 0.49/0.85 (assume a118 (= tptp.bs114d (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (@ (@ tptp.binintersect A) (@ (@ tptp.binunion B) C)) (@ (@ tptp.binunion (@ (@ tptp.binintersect A) B)) (@ (@ tptp.binintersect A) C))))))
% 0.49/0.85 (assume a119 (= tptp.setminusI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) (@ (@ tptp.setminus A) B)))))))
% 0.49/0.85 (assume a120 (= tptp.setminusEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setminus A) B)) (@ (@ tptp.in Xx) A)))))
% 0.49/0.85 (assume a121 (= tptp.setminusER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setminus A) B)) (not (@ (@ tptp.in Xx) B))))))
% 0.49/0.85 (assume a122 (= tptp.setminusSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.setminus A) B) tptp.emptyset)))))
% 0.49/0.85 (assume a123 (= tptp.setminusERneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (not (@ (@ tptp.in Xx) (@ (@ tptp.setminus A) B))) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))))
% 0.49/0.85 (assume a124 (= tptp.setminusELneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (not (@ (@ tptp.in Xx) (@ (@ tptp.setminus A) B))) (=> (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in Xx) A)))))))
% 0.49/0.85 (assume a125 (= tptp.setminusILneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in Xx) (@ (@ tptp.setminus A) B)))))))
% 0.49/0.85 (assume a126 (= tptp.setminusIRneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (not (@ (@ tptp.in Xx) (@ (@ tptp.setminus A) B)))))))
% 0.49/0.85 (assume a127 (= tptp.setminusLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.setminus A) B)) A))))
% 0.49/0.85 (assume a128 (= tptp.setminusSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.setminus A) B) tptp.emptyset) (@ (@ tptp.subset A) B)))))
% 0.49/0.85 (assume a129 (= tptp.symdiffE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B)) (forall ((Xphi Bool)) (=> (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) Xphi)) (=> (=> (not (@ (@ tptp.in Xx) A)) (=> (@ (@ tptp.in Xx) B) Xphi)) Xphi)))))))
% 0.49/0.85 (assume a130 (= tptp.symdiffI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B)))))))
% 0.49/0.85 (assume a131 (= tptp.symdiffI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (not (@ (@ tptp.in Xx) A)) (=> (@ (@ tptp.in Xx) B) (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B)))))))
% 0.49/0.85 (assume a132 (= tptp.symdiffIneg1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ (@ tptp.in Xx) B) (not (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B))))))))
% 0.49/0.85 (assume a133 (= tptp.symdiffIneg2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (not (@ (@ tptp.in Xx) A)) (=> (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B))))))))
% 0.49/0.85 (assume a134 (= tptp.secondinupair (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
% 0.49/0.85 (assume a135 (= tptp.setukpairIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ tptp.setunion (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))
% 0.49/0.85 (assume a136 (= tptp.setukpairIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ tptp.setunion (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))
% 0.49/0.85 (assume a137 (= tptp.kpairiskpair (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ tptp.iskpair (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))))))
% 0.49/0.85 (assume a138 (= tptp.kpairp (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ tptp.iskpair (@ (@ tptp.kpair Xx) Xy)))))
% 0.49/0.85 (assume a139 (= tptp.singletonsubset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) tptp.emptyset)) A)))))
% 0.49/0.85 (assume a140 (= tptp.singletoninpowerset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset A))))))
% 0.49/0.85 (assume a141 (= tptp.singletoninpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))
% 0.49/0.85 (assume a142 (= tptp.upairset2E (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))
% 0.49/0.85 (assume a143 (= tptp.upairsubunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ (@ tptp.binunion A) B))))))))
% 0.49/0.85 (assume a144 (= tptp.upairinpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))
% 0.49/0.85 (assume a145 (= tptp.ubforcartprodlem1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))
% 0.49/0.85 (assume a146 (= tptp.ubforcartprodlem2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))))
% 0.49/0.85 (assume a147 (= tptp.ubforcartprodlem3 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))))
% 0.49/0.85 (assume a148 (= tptp.cartprodpairin (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B))))))))
% 0.49/0.85 (assume a149 (= tptp.cartprodmempair1 (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) B) (= Xu (@ (@ tptp.kpair Xx) Xy))))))))))
% 0.49/0.85 (assume a150 (= tptp.cartprodmempair (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ tptp.iskpair Xu)))))
% 0.49/0.85 (assume a151 (= tptp.setunionE2 (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((X $$unsorted)) (and (@ (@ tptp.in X) A) (@ (@ tptp.in Xx) X)))))))
% 0.49/0.85 (assume a152 (= tptp.setunionsingleton1 (forall ((A $$unsorted)) (@ (@ tptp.subset (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))) A))))
% 0.49/0.85 (assume a153 (= tptp.setunionsingleton2 (forall ((A $$unsorted)) (@ (@ tptp.subset A) (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))))))
% 0.49/0.85 (assume a154 (= tptp.setunionsingleton (forall ((Xx $$unsorted)) (= (@ tptp.setunion (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xx))))
% 0.49/0.85 (assume a155 (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))
% 0.49/0.85 (assume a156 (= tptp.singletonprop (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))
% 0.49/0.85 (assume a157 (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))
% 0.49/0.85 (assume a158 (= tptp.ex1E1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))))))
% 0.49/0.85 (assume a159 (= tptp.ex1I (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (=> (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xy) (= Xy Xx)))) (@ (@ tptp.ex1 A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))
% 0.49/0.85 (assume a160 (= tptp.ex1I2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))
% 0.49/0.85 (assume a161 (= tptp.singletonsuniq (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))
% 0.49/0.85 (assume a162 (= tptp.setukpairinjL1 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (= Xx Xz)))))
% 0.49/0.85 (assume a163 (= tptp.kfstsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xu))))))))
% 0.49/0.85 (assume a164 (= tptp.theprop (forall ((X $$unsorted)) (=> (@ tptp.singleton X) (@ (@ tptp.in (@ tptp.setunion X)) X)))))
% 0.49/0.85 (assume a165 (= tptp.kfstpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx))))
% 0.49/0.85 (assume a166 (= tptp.cartprodfstin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.kfst Xu)) A)))))
% 0.49/0.85 (assume a167 (= tptp.setukpairinjL2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xz) (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xx Xz)))))
% 0.49/0.85 (assume a168 (= tptp.setukpairinjL (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xx Xz)))))
% 0.49/0.85 (assume a169 (= tptp.setukpairinjR11 (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))
% 0.49/0.85 (assume a170 (= tptp.setukpairinjR12 (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) tptp.emptyset))))))
% 0.49/0.85 (assume a171 (= tptp.setukpairinjR1 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xz) (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (=> (= Xz Xu) (= Xy Xu))))))
% 0.49/0.85 (assume a172 (= tptp.upairequniteq (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (= Xx Xy)))))
% 0.49/0.85 (assume a173 (= tptp.setukpairinjR2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (@ (@ tptp.setadjoin (@ (@ tptp.setadjoin Xz) (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xy Xu)))))
% 0.49/0.85 (assume a174 (= tptp.setukpairinjR (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xy Xu)))))
% 0.49/0.85 (assume a175 (= tptp.ksndsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (= Xu (@ (@ tptp.kpair (@ tptp.kfst Xu)) Xx)))))))))
% 0.49/0.85 (assume a176 (= tptp.ksndpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy))))
% 0.49/0.85 (assume a177 (= tptp.kpairsurjEq (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu)))))
% 0.49/0.85 (assume a178 (= tptp.cartprodsndin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.ksnd Xu)) B)))))
% 0.49/0.85 (assume a179 (= tptp.cartprodpairmemEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xx) A)))))
% 0.49/0.85 (assume a180 (= tptp.cartprodpairmemER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xy) B)))))
% 0.49/0.85 (assume a181 (= tptp.cartprodmempaircEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xx) Xy))))))))
% 0.49/0.85 (assume a182 (= tptp.cartprodfstpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx)))))))
% 0.49/0.85 (assume a183 (= tptp.cartprodsndpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy)))))))
% 0.49/0.85 (assume a184 (= tptp.cartprodpairsurjEq (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu)))))
% 0.49/0.85 (assume a185 (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))))
% 0.49/0.85 (assume a186 (= tptp.dpsetconstrI (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ Xphi Xx) Xy) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))))))))))
% 0.49/0.85 (assume a187 (= tptp.dpsetconstrSub (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.subset (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))) (@ (@ tptp.cartprod A) B)))))
% 0.49/0.85 (assume a188 (= tptp.setOfPairsIsBReln (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ (@ tptp.breln A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))))))
% 0.49/0.85 (assume a189 (= tptp.dpsetconstrERa (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy))))))))
% 0.49/0.85 (assume a190 (= tptp.dpsetconstrEL1 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xx) A)))))
% 0.49/0.85 (assume a191 (= tptp.dpsetconstrEL2 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xy) B)))))
% 0.49/0.85 (assume a192 (= tptp.dpsetconstrER (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy)))))
% 0.49/0.85 (assume a193 (= tptp.funcImageSingleton (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ tptp.singleton (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))))))
% 0.49/0.85 (assume a194 (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B)))))))
% 0.49/0.85 (assume a195 (= tptp.app (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))))
% 0.49/0.85 (assume a196 (= tptp.infuncsetfunc (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (@ (@ (@ tptp.func A) B) Xf)))))
% 0.49/0.85 (assume a197 (= tptp.ap2p (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))))
% 0.49/0.85 (assume a198 (= tptp.funcinfuncset (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B))))))
% 0.49/0.85 (assume a199 (= tptp.lamProp (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (= (@ Xf Xx) Xy))))))))
% 0.49/0.85 (assume a200 (= tptp.lam (lambda ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (= (@ Xf Xx) Xy))))))
% 0.49/0.85 (assume a201 (= tptp.lamp (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx))))))))
% 0.49/0.85 (assume a202 (= tptp.lam2p (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ tptp.in (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx)))) (@ (@ tptp.funcSet A) B))))))
% 0.49/0.85 (assume a203 (= tptp.brelnall1 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R) (@ Xphi (@ (@ tptp.kpair Xx) Xy))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx)))))))))
% 0.49/0.85 (assume a204 (= tptp.brelnall2 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R) (@ Xphi (@ (@ tptp.kpair Xx) Xy))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx)))))))))
% 0.49/0.85 (assume a205 (= tptp.ex1E2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))))))))))
% 0.49/0.85 (assume a206 (= tptp.funcGraphProp1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))))
% 0.49/0.85 (assume a207 (= tptp.funcGraphProp3 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))))
% 0.49/0.85 (assume a208 (= tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy))))))))))
% 0.49/0.85 (assume a209 (= tptp.funcextLem (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xg) Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xg) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf)))))))))))))
% 0.49/0.85 (assume a210 (= tptp.funcGraphProp4 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy))))))))))
% 0.49/0.85 (assume a211 (= tptp.subbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((S $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) S)))))) (@ (@ tptp.subset R) S))))))))
% 0.49/0.85 (assume a212 (= tptp.eqbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((S $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) S)))))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) S) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) (= R S)))))))))
% 0.49/0.85 (assume a213 (= tptp.funcext (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xg) Xx)))) (= Xf Xg))))))))
% 0.49/0.85 (assume a214 (= tptp.funcext2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xg $$unsorted)) (=> (@ (@ tptp.in Xg) (@ (@ tptp.funcSet A) B)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xg) Xx)))) (= Xf Xg))))))))
% 0.49/0.85 (assume a215 (= tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))
% 0.49/0.85 (assume a216 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.49/0.85 (assume a217 true)
% 0.49/0.85 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) false) :rule equiv_pos2)
% 0.49/0.85 (step t2 (cl (= tptp.setextAx tptp.setextAx)) :rule refl)
% 0.49/0.85 (step t3 (cl (= tptp.emptysetAx tptp.emptysetAx)) :rule refl)
% 0.49/0.85 (step t4 (cl (= tptp.setadjoinAx tptp.setadjoinAx)) :rule refl)
% 0.49/0.85 (step t5 (cl (= tptp.powersetAx tptp.powersetAx)) :rule refl)
% 0.49/0.85 (step t6 (cl (= tptp.setunionAx tptp.setunionAx)) :rule refl)
% 0.49/0.85 (step t7 (cl (= tptp.omega0Ax tptp.omega0Ax)) :rule refl)
% 0.49/0.85 (step t8 (cl (= tptp.omegaSAx tptp.omegaSAx)) :rule refl)
% 0.49/0.85 (step t9 (cl (= tptp.omegaIndAx tptp.omegaIndAx)) :rule refl)
% 0.49/0.85 (step t10 (cl (= tptp.replAx tptp.replAx)) :rule refl)
% 0.49/0.85 (step t11 (cl (= tptp.foundationAx tptp.foundationAx)) :rule refl)
% 0.49/0.85 (step t12 (cl (= tptp.wellorderingAx tptp.wellorderingAx)) :rule refl)
% 0.49/0.85 (step t13 (cl (= tptp.descrp tptp.descrp)) :rule refl)
% 0.49/0.85 (step t14 (cl (= tptp.dsetconstrI tptp.dsetconstrI)) :rule refl)
% 0.49/0.85 (step t15 (cl (= tptp.dsetconstrEL tptp.dsetconstrEL)) :rule refl)
% 0.49/0.85 (step t16 (cl (= tptp.dsetconstrER tptp.dsetconstrER)) :rule refl)
% 0.49/0.85 (step t17 (cl (= tptp.exuE1 tptp.exuE1)) :rule refl)
% 0.49/0.85 (step t18 (cl (= tptp.prop2setE tptp.prop2setE)) :rule refl)
% 0.49/0.85 (step t19 (cl (= tptp.emptysetE tptp.emptysetE)) :rule refl)
% 0.49/0.85 (step t20 (cl (= tptp.emptysetimpfalse tptp.emptysetimpfalse)) :rule refl)
% 0.49/0.85 (step t21 (cl (= tptp.notinemptyset tptp.notinemptyset)) :rule refl)
% 0.49/0.85 (step t22 (cl (= tptp.exuE3e tptp.exuE3e)) :rule refl)
% 0.49/0.85 (step t23 (cl (= tptp.setext tptp.setext)) :rule refl)
% 0.49/0.85 (step t24 (cl (= tptp.emptyI tptp.emptyI)) :rule refl)
% 0.49/0.85 (step t25 (cl (= tptp.noeltsimpempty tptp.noeltsimpempty)) :rule refl)
% 0.49/0.85 (step t26 (cl (= tptp.setbeta tptp.setbeta)) :rule refl)
% 0.49/0.85 (step t27 (cl (= tptp.nonemptyE1 tptp.nonemptyE1)) :rule refl)
% 0.49/0.85 (step t28 (cl (= tptp.nonemptyI tptp.nonemptyI)) :rule refl)
% 0.49/0.85 (step t29 (cl (= tptp.nonemptyI1 tptp.nonemptyI1)) :rule refl)
% 0.49/0.85 (step t30 (cl (= tptp.setadjoinIL tptp.setadjoinIL)) :rule refl)
% 0.49/0.85 (step t31 (cl (= tptp.emptyinunitempty tptp.emptyinunitempty)) :rule refl)
% 0.49/0.85 (step t32 (cl (= tptp.setadjoinIR tptp.setadjoinIR)) :rule refl)
% 0.49/0.85 (step t33 (cl (= tptp.setadjoinE tptp.setadjoinE)) :rule refl)
% 0.49/0.85 (step t34 (cl (= tptp.setadjoinOr tptp.setadjoinOr)) :rule refl)
% 0.49/0.85 (step t35 (cl (= tptp.setoftrueEq tptp.setoftrueEq)) :rule refl)
% 0.49/0.85 (step t36 (cl (= tptp.powersetI tptp.powersetI)) :rule refl)
% 0.49/0.85 (step t37 (cl (= tptp.emptyinPowerset tptp.emptyinPowerset)) :rule refl)
% 0.49/0.85 (step t38 (cl (= tptp.emptyInPowerset tptp.emptyInPowerset)) :rule refl)
% 0.49/0.85 (step t39 (cl (= tptp.powersetE tptp.powersetE)) :rule refl)
% 0.49/0.85 (step t40 (cl (= tptp.setunionI tptp.setunionI)) :rule refl)
% 0.49/0.85 (step t41 (cl (= tptp.setunionE tptp.setunionE)) :rule refl)
% 0.49/0.85 (step t42 (cl (= tptp.subPowSU tptp.subPowSU)) :rule refl)
% 0.49/0.85 (step t43 (cl (= tptp.exuE2 tptp.exuE2)) :rule refl)
% 0.49/0.85 (step t44 (cl (= tptp.nonemptyImpWitness tptp.nonemptyImpWitness)) :rule refl)
% 0.49/0.85 (step t45 (cl (= tptp.uniqinunit tptp.uniqinunit)) :rule refl)
% 0.49/0.85 (step t46 (cl (= tptp.notinsingleton tptp.notinsingleton)) :rule refl)
% 0.49/0.85 (step t47 (cl (= tptp.eqinunit tptp.eqinunit)) :rule refl)
% 0.49/0.85 (step t48 (cl (= tptp.singletonsswitch tptp.singletonsswitch)) :rule refl)
% 0.49/0.85 (step t49 (cl (= tptp.upairsetE tptp.upairsetE)) :rule refl)
% 0.49/0.85 (step t50 (cl (= tptp.upairsetIL tptp.upairsetIL)) :rule refl)
% 0.49/0.85 (step t51 (cl (= tptp.upairsetIR tptp.upairsetIR)) :rule refl)
% 0.49/0.85 (step t52 (cl (= tptp.emptyE1 tptp.emptyE1)) :rule refl)
% 0.49/0.85 (step t53 (cl (= tptp.vacuousDall tptp.vacuousDall)) :rule refl)
% 0.49/0.85 (step t54 (cl (= tptp.quantDeMorgan1 tptp.quantDeMorgan1)) :rule refl)
% 0.49/0.85 (step t55 (cl (= tptp.quantDeMorgan2 tptp.quantDeMorgan2)) :rule refl)
% 0.49/0.85 (step t56 (cl (= tptp.quantDeMorgan3 tptp.quantDeMorgan3)) :rule refl)
% 0.49/0.85 (step t57 (cl (= tptp.quantDeMorgan4 tptp.quantDeMorgan4)) :rule refl)
% 0.49/0.85 (step t58 (cl (= tptp.prop2setI tptp.prop2setI)) :rule refl)
% 0.49/0.85 (step t59 (cl (= tptp.prop2set2propI tptp.prop2set2propI)) :rule refl)
% 0.49/0.85 (step t60 (cl (= tptp.notdexE tptp.notdexE)) :rule refl)
% 0.49/0.85 (step t61 (cl (= tptp.notdallE tptp.notdallE)) :rule refl)
% 0.49/0.85 (step t62 (cl (= tptp.exuI1 tptp.exuI1)) :rule refl)
% 0.49/0.85 (step t63 (cl (= tptp.exuI3 tptp.exuI3)) :rule refl)
% 0.49/0.85 (step t64 (cl (= tptp.exuI2 tptp.exuI2)) :rule refl)
% 0.49/0.85 (step t65 (cl (= tptp.inCongP tptp.inCongP)) :rule refl)
% 0.49/0.85 (step t66 (cl (= tptp.in__Cong tptp.in__Cong)) :rule refl)
% 0.49/0.85 (step t67 (cl (= tptp.exuE3u tptp.exuE3u)) :rule refl)
% 0.49/0.85 (step t68 (cl (= tptp.exu__Cong tptp.exu__Cong)) :rule refl)
% 0.49/0.85 (step t69 (cl (= tptp.emptyset__Cong tptp.emptyset__Cong)) :rule refl)
% 0.49/0.85 (step t70 (cl (= tptp.setadjoin__Cong tptp.setadjoin__Cong)) :rule refl)
% 0.49/0.85 (step t71 (cl (= tptp.powerset__Cong tptp.powerset__Cong)) :rule refl)
% 0.49/0.85 (step t72 (cl (= tptp.setunion__Cong tptp.setunion__Cong)) :rule refl)
% 0.49/0.85 (step t73 (cl (= tptp.omega__Cong tptp.omega__Cong)) :rule refl)
% 0.49/0.85 (step t74 (cl (= tptp.exuEu tptp.exuEu)) :rule refl)
% 0.49/0.85 (step t75 (cl (= tptp.descr__Cong tptp.descr__Cong)) :rule refl)
% 0.49/0.85 (step t76 (cl (= tptp.dsetconstr__Cong tptp.dsetconstr__Cong)) :rule refl)
% 0.49/0.85 (step t77 (cl (= tptp.subsetI1 tptp.subsetI1)) :rule refl)
% 0.49/0.85 (step t78 (cl (= tptp.eqimpsubset2 tptp.eqimpsubset2)) :rule refl)
% 0.49/0.85 (step t79 (cl (= tptp.eqimpsubset1 tptp.eqimpsubset1)) :rule refl)
% 0.49/0.85 (step t80 (cl (= tptp.subsetI2 tptp.subsetI2)) :rule refl)
% 0.49/0.86 (step t81 (cl (= tptp.emptysetsubset tptp.emptysetsubset)) :rule refl)
% 0.49/0.86 (step t82 (cl (= tptp.subsetE tptp.subsetE)) :rule refl)
% 0.49/0.86 (step t83 (cl (= tptp.subsetE2 tptp.subsetE2)) :rule refl)
% 0.49/0.86 (step t84 (cl (= tptp.notsubsetI tptp.notsubsetI)) :rule refl)
% 0.49/0.86 (step t85 (cl (= tptp.notequalI1 tptp.notequalI1)) :rule refl)
% 0.49/0.86 (step t86 (cl (= tptp.notequalI2 tptp.notequalI2)) :rule refl)
% 0.49/0.86 (step t87 (cl (= tptp.subsetRefl tptp.subsetRefl)) :rule refl)
% 0.49/0.86 (step t88 (cl (= tptp.subsetTrans tptp.subsetTrans)) :rule refl)
% 0.49/0.86 (step t89 (cl (= tptp.setadjoinSub tptp.setadjoinSub)) :rule refl)
% 0.49/0.86 (step t90 (cl (= tptp.setadjoinSub2 tptp.setadjoinSub2)) :rule refl)
% 0.49/0.86 (step t91 (cl (= tptp.subset2powerset tptp.subset2powerset)) :rule refl)
% 0.49/0.86 (step t92 (cl (= tptp.setextsub tptp.setextsub)) :rule refl)
% 0.49/0.86 (step t93 (cl (= tptp.subsetemptysetimpeq tptp.subsetemptysetimpeq)) :rule refl)
% 0.49/0.86 (step t94 (cl (= tptp.powersetI1 tptp.powersetI1)) :rule refl)
% 0.49/0.86 (step t95 (cl (= tptp.powersetE1 tptp.powersetE1)) :rule refl)
% 0.49/0.86 (step t96 (cl (= tptp.inPowerset tptp.inPowerset)) :rule refl)
% 0.49/0.86 (step t97 (cl (= tptp.powersetsubset tptp.powersetsubset)) :rule refl)
% 0.49/0.86 (step t98 (cl (= tptp.sepInPowerset tptp.sepInPowerset)) :rule refl)
% 0.49/0.86 (step t99 (cl (= tptp.sepSubset tptp.sepSubset)) :rule refl)
% 0.49/0.86 (step t100 (cl (= tptp.binunionIL tptp.binunionIL)) :rule refl)
% 0.49/0.86 (step t101 (cl (= tptp.upairset2IR tptp.upairset2IR)) :rule refl)
% 0.49/0.86 (step t102 (cl (= tptp.binunionIR tptp.binunionIR)) :rule refl)
% 0.49/0.86 (step t103 (cl (= tptp.binunionEcases tptp.binunionEcases)) :rule refl)
% 0.49/0.86 (step t104 (cl (= tptp.binunionE tptp.binunionE)) :rule refl)
% 0.49/0.86 (step t105 (cl (= tptp.binunionLsub tptp.binunionLsub)) :rule refl)
% 0.49/0.86 (step t106 (cl (= tptp.binunionRsub tptp.binunionRsub)) :rule refl)
% 0.49/0.86 (step t107 (cl (= tptp.binintersectI tptp.binintersectI)) :rule refl)
% 0.49/0.86 (step t108 (cl (= tptp.binintersectSubset5 tptp.binintersectSubset5)) :rule refl)
% 0.49/0.86 (step t109 (cl (= tptp.binintersectEL tptp.binintersectEL)) :rule refl)
% 0.49/0.86 (step t110 (cl (= tptp.binintersectLsub tptp.binintersectLsub)) :rule refl)
% 0.49/0.86 (step t111 (cl (= tptp.binintersectSubset2 tptp.binintersectSubset2)) :rule refl)
% 0.49/0.86 (step t112 (cl (= tptp.binintersectSubset3 tptp.binintersectSubset3)) :rule refl)
% 0.49/0.86 (step t113 (cl (= tptp.binintersectER tptp.binintersectER)) :rule refl)
% 0.49/0.86 (step t114 (cl (= tptp.disjointsetsI1 tptp.disjointsetsI1)) :rule refl)
% 0.49/0.86 (step t115 (cl (= tptp.binintersectRsub tptp.binintersectRsub)) :rule refl)
% 0.49/0.86 (step t116 (cl (= tptp.binintersectSubset4 tptp.binintersectSubset4)) :rule refl)
% 0.49/0.86 (step t117 (cl (= tptp.binintersectSubset1 tptp.binintersectSubset1)) :rule refl)
% 0.49/0.86 (step t118 (cl (= tptp.bs114d tptp.bs114d)) :rule refl)
% 0.49/0.86 (step t119 (cl (= tptp.setminusI tptp.setminusI)) :rule refl)
% 0.49/0.86 (step t120 (cl (= tptp.setminusEL tptp.setminusEL)) :rule refl)
% 0.49/0.86 (step t121 (cl (= tptp.setminusER tptp.setminusER)) :rule refl)
% 0.49/0.86 (step t122 (cl (= tptp.setminusSubset2 tptp.setminusSubset2)) :rule refl)
% 0.49/0.86 (step t123 (cl (= tptp.setminusERneg tptp.setminusERneg)) :rule refl)
% 0.49/0.86 (step t124 (cl (= tptp.setminusELneg tptp.setminusELneg)) :rule refl)
% 0.49/0.86 (step t125 (cl (= tptp.setminusILneg tptp.setminusILneg)) :rule refl)
% 0.49/0.86 (step t126 (cl (= tptp.setminusIRneg tptp.setminusIRneg)) :rule refl)
% 0.49/0.86 (step t127 (cl (= tptp.setminusLsub tptp.setminusLsub)) :rule refl)
% 0.49/0.86 (step t128 (cl (= tptp.setminusSubset1 tptp.setminusSubset1)) :rule refl)
% 0.49/0.86 (step t129 (cl (= tptp.symdiffE tptp.symdiffE)) :rule refl)
% 0.49/0.86 (step t130 (cl (= tptp.symdiffI1 tptp.symdiffI1)) :rule refl)
% 0.49/0.86 (step t131 (cl (= tptp.symdiffI2 tptp.symdiffI2)) :rule refl)
% 0.49/0.86 (step t132 (cl (= tptp.symdiffIneg1 tptp.symdiffIneg1)) :rule refl)
% 0.49/0.86 (step t133 (cl (= tptp.symdiffIneg2 tptp.symdiffIneg2)) :rule refl)
% 0.49/0.86 (step t134 (cl (= tptp.secondinupair tptp.secondinupair)) :rule refl)
% 0.49/0.86 (step t135 (cl (= tptp.setukpairIL tptp.setukpairIL)) :rule refl)
% 0.49/0.86 (step t136 (cl (= tptp.setukpairIR tptp.setukpairIR)) :rule refl)
% 0.49/0.86 (step t137 (cl (= tptp.kpairiskpair tptp.kpairiskpair)) :rule refl)
% 0.49/0.86 (step t138 (cl (= tptp.kpairp tptp.kpairp)) :rule refl)
% 0.49/0.86 (step t139 (cl (= tptp.singletonsubset tptp.singletonsubset)) :rule refl)
% 0.49/0.86 (step t140 (cl (= tptp.singletoninpowerset tptp.singletoninpowerset)) :rule refl)
% 0.49/0.86 (step t141 (cl (= tptp.singletoninpowunion tptp.singletoninpowunion)) :rule refl)
% 0.49/0.86 (step t142 (cl (= tptp.upairset2E tptp.upairset2E)) :rule refl)
% 0.49/0.86 (step t143 (cl (= tptp.upairsubunion tptp.upairsubunion)) :rule refl)
% 0.49/0.86 (step t144 (cl (= tptp.upairinpowunion tptp.upairinpowunion)) :rule refl)
% 0.49/0.86 (step t145 (cl (= tptp.ubforcartprodlem1 tptp.ubforcartprodlem1)) :rule refl)
% 0.49/0.86 (step t146 (cl (= tptp.ubforcartprodlem2 tptp.ubforcartprodlem2)) :rule refl)
% 0.49/0.86 (step t147 (cl (= tptp.ubforcartprodlem3 tptp.ubforcartprodlem3)) :rule refl)
% 0.49/0.86 (step t148 (cl (= tptp.cartprodpairin tptp.cartprodpairin)) :rule refl)
% 0.49/0.86 (step t149 (cl (= tptp.cartprodmempair1 tptp.cartprodmempair1)) :rule refl)
% 0.49/0.86 (step t150 (cl (= tptp.cartprodmempair tptp.cartprodmempair)) :rule refl)
% 0.49/0.86 (step t151 (cl (= tptp.setunionE2 tptp.setunionE2)) :rule refl)
% 0.49/0.86 (step t152 (cl (= tptp.setunionsingleton1 tptp.setunionsingleton1)) :rule refl)
% 0.49/0.86 (step t153 (cl (= tptp.setunionsingleton2 tptp.setunionsingleton2)) :rule refl)
% 0.49/0.86 (step t154 (cl (= tptp.setunionsingleton tptp.setunionsingleton)) :rule refl)
% 0.49/0.86 (step t155 (cl (= tptp.singletonprop tptp.singletonprop)) :rule refl)
% 0.49/0.86 (step t156 (cl (= tptp.ex1E1 tptp.ex1E1)) :rule refl)
% 0.49/0.86 (step t157 (cl (= tptp.ex1I tptp.ex1I)) :rule refl)
% 0.49/0.86 (step t158 (cl (= tptp.ex1I2 tptp.ex1I2)) :rule refl)
% 0.49/0.86 (step t159 (cl (= tptp.singletonsuniq tptp.singletonsuniq)) :rule refl)
% 0.49/0.86 (step t160 (cl (= tptp.setukpairinjL1 tptp.setukpairinjL1)) :rule refl)
% 0.49/0.86 (step t161 (cl (= tptp.kfstsingleton tptp.kfstsingleton)) :rule refl)
% 0.49/0.86 (step t162 (cl (= tptp.theprop tptp.theprop)) :rule refl)
% 0.49/0.86 (step t163 (cl (= tptp.kfstpairEq tptp.kfstpairEq)) :rule refl)
% 0.49/0.86 (step t164 (cl (= tptp.cartprodfstin tptp.cartprodfstin)) :rule refl)
% 0.49/0.86 (step t165 (cl (= tptp.setukpairinjL2 tptp.setukpairinjL2)) :rule refl)
% 0.49/0.86 (step t166 (cl (= tptp.setukpairinjL tptp.setukpairinjL)) :rule refl)
% 0.49/0.86 (step t167 (cl (= tptp.setukpairinjR11 tptp.setukpairinjR11)) :rule refl)
% 0.49/0.86 (step t168 (cl (= tptp.setukpairinjR12 tptp.setukpairinjR12)) :rule refl)
% 0.49/0.86 (step t169 (cl (= tptp.setukpairinjR1 tptp.setukpairinjR1)) :rule refl)
% 0.49/0.86 (step t170 (cl (= tptp.upairequniteq tptp.upairequniteq)) :rule refl)
% 0.49/0.86 (step t171 (cl (= tptp.setukpairinjR2 tptp.setukpairinjR2)) :rule refl)
% 0.49/0.86 (step t172 (cl (= tptp.setukpairinjR tptp.setukpairinjR)) :rule refl)
% 0.49/0.86 (step t173 (cl (= tptp.ksndsingleton tptp.ksndsingleton)) :rule refl)
% 0.49/0.86 (step t174 (cl (= tptp.ksndpairEq tptp.ksndpairEq)) :rule refl)
% 0.49/0.86 (step t175 (cl (= tptp.kpairsurjEq tptp.kpairsurjEq)) :rule refl)
% 0.49/0.86 (step t176 (cl (= tptp.cartprodsndin tptp.cartprodsndin)) :rule refl)
% 0.49/0.86 (step t177 (cl (= tptp.cartprodpairmemEL tptp.cartprodpairmemEL)) :rule refl)
% 0.49/0.86 (step t178 (cl (= tptp.cartprodpairmemER tptp.cartprodpairmemER)) :rule refl)
% 0.49/0.86 (step t179 (cl (= tptp.cartprodmempaircEq tptp.cartprodmempaircEq)) :rule refl)
% 0.49/0.86 (step t180 (cl (= tptp.cartprodfstpairEq tptp.cartprodfstpairEq)) :rule refl)
% 0.49/0.86 (step t181 (cl (= tptp.cartprodsndpairEq tptp.cartprodsndpairEq)) :rule refl)
% 0.49/0.86 (step t182 (cl (= tptp.cartprodpairsurjEq tptp.cartprodpairsurjEq)) :rule refl)
% 0.49/0.86 (step t183 (cl (= tptp.dpsetconstrI tptp.dpsetconstrI)) :rule refl)
% 0.49/0.86 (step t184 (cl (= tptp.dpsetconstrSub tptp.dpsetconstrSub)) :rule refl)
% 0.49/0.86 (step t185 (cl (= tptp.setOfPairsIsBReln tptp.setOfPairsIsBReln)) :rule refl)
% 0.49/0.86 (step t186 (cl (= tptp.dpsetconstrERa tptp.dpsetconstrERa)) :rule refl)
% 0.49/0.86 (step t187 (cl (= tptp.dpsetconstrEL1 tptp.dpsetconstrEL1)) :rule refl)
% 0.49/0.86 (step t188 (cl (= tptp.dpsetconstrEL2 tptp.dpsetconstrEL2)) :rule refl)
% 0.49/0.86 (step t189 (cl (= tptp.dpsetconstrER tptp.dpsetconstrER)) :rule refl)
% 0.49/0.86 (step t190 (cl (= tptp.funcImageSingleton tptp.funcImageSingleton)) :rule refl)
% 0.49/0.86 (step t191 (cl (= tptp.apProp tptp.apProp)) :rule refl)
% 0.49/0.86 (step t192 (cl (= tptp.app tptp.app)) :rule refl)
% 0.49/0.86 (step t193 (cl (= tptp.infuncsetfunc tptp.infuncsetfunc)) :rule refl)
% 0.49/0.86 (step t194 (cl (= tptp.ap2p tptp.ap2p)) :rule refl)
% 0.49/0.86 (step t195 (cl (= tptp.funcinfuncset tptp.funcinfuncset)) :rule refl)
% 0.49/0.86 (step t196 (cl (= tptp.lamProp tptp.lamProp)) :rule refl)
% 0.49/0.86 (step t197 (cl (= tptp.lamp tptp.lamp)) :rule refl)
% 0.49/0.86 (step t198 (cl (= tptp.lam2p tptp.lam2p)) :rule refl)
% 0.49/0.86 (step t199 (cl (= tptp.brelnall1 tptp.brelnall1)) :rule refl)
% 0.49/0.86 (step t200 (cl (= tptp.brelnall2 tptp.brelnall2)) :rule refl)
% 0.49/0.86 (step t201 (cl (= tptp.ex1E2 tptp.ex1E2)) :rule refl)
% 0.49/0.86 (step t202 (cl (= tptp.funcGraphProp1 tptp.funcGraphProp1)) :rule refl)
% 0.49/0.86 (step t203 (cl (= tptp.funcGraphProp3 tptp.funcGraphProp3)) :rule refl)
% 0.49/0.86 (step t204 (cl (= tptp.funcGraphProp2 tptp.funcGraphProp2)) :rule refl)
% 0.49/0.86 (step t205 (cl (= tptp.funcextLem tptp.funcextLem)) :rule refl)
% 0.49/0.86 (step t206 (cl (= tptp.funcGraphProp4 tptp.funcGraphProp4)) :rule refl)
% 0.49/0.86 (step t207 (cl (= tptp.subbreln tptp.subbreln)) :rule refl)
% 0.49/0.86 (step t208 (cl (= tptp.eqbreln tptp.eqbreln)) :rule refl)
% 0.49/0.86 (step t209 (cl (= tptp.funcext tptp.funcext)) :rule refl)
% 0.49/0.86 (step t210 (cl (= tptp.funcext2 tptp.funcext2)) :rule refl)
% 0.49/0.86 (step t211 (cl (= tptp.ap2apEq1 tptp.ap2apEq1)) :rule refl)
% 0.49/0.86 (anchor :step t212 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf)))
% 0.49/0.86 (step t212.t1 (cl (= A A)) :rule refl)
% 0.49/0.86 (step t212.t2 (cl (= B B)) :rule refl)
% 0.49/0.86 (step t212.t3 (cl (= Xf Xf)) :rule refl)
% 0.49/0.86 (step t212.t4 (cl (= (@ (@ (@ tptp.func A) B) Xf) (@ (@ (@ tptp.func A) B) Xf))) :rule refl)
% 0.49/0.86 (anchor :step t212.t5 :args ((Xx $$unsorted) (:= Xx Xx)))
% 0.49/0.86 (step t212.t5.t1 (cl (= Xx Xx)) :rule refl)
% 0.49/0.86 (step t212.t5.t2 (cl (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) A))) :rule refl)
% 0.49/0.86 (step t212.t5.t3 (cl (= (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) true)) :rule all_simplify)
% 0.49/0.86 (step t212.t5.t4 (cl (= (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) (=> (@ (@ tptp.in Xx) A) true))) :rule cong :premises (t212.t5.t2 t212.t5.t3))
% 0.49/0.86 (step t212.t5.t5 (cl (= (=> (@ (@ tptp.in Xx) A) true) true)) :rule all_simplify)
% 0.49/0.86 (step t212.t5.t6 (cl (= (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) true)) :rule trans :premises (t212.t5.t4 t212.t5.t5))
% 0.49/0.86 (step t212.t5 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))) (forall ((Xx $$unsorted)) true))) :rule bind)
% 0.49/0.86 (step t212.t6 (cl (= (forall ((Xx $$unsorted)) true) true)) :rule all_simplify)
% 0.49/0.86 (step t212.t7 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))) true)) :rule trans :premises (t212.t5 t212.t6))
% 0.49/0.86 (step t212.t8 (cl (= (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))) (=> (@ (@ (@ tptp.func A) B) Xf) true))) :rule cong :premises (t212.t4 t212.t7))
% 0.49/0.86 (step t212.t9 (cl (= (=> (@ (@ (@ tptp.func A) B) Xf) true) true)) :rule all_simplify)
% 0.49/0.86 (step t212.t10 (cl (= (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))) true)) :rule trans :premises (t212.t8 t212.t9))
% 0.49/0.86 (step t212 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) true))) :rule bind)
% 0.49/0.86 (step t213 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) true) true)) :rule all_simplify)
% 0.49/0.86 (step t214 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))) true)) :rule trans :premises (t212 t213))
% 0.49/0.86 (step t215 (cl (= (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))) (=> tptp.ap2apEq1 true))) :rule cong :premises (t211 t214))
% 0.49/0.86 (step t216 (cl (= (=> tptp.ap2apEq1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t217 (cl (= (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))) true)) :rule trans :premises (t215 t216))
% 0.49/0.86 (step t218 (cl (= (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))) (=> tptp.funcext2 true))) :rule cong :premises (t210 t217))
% 0.49/0.86 (step t219 (cl (= (=> tptp.funcext2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t220 (cl (= (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))) true)) :rule trans :premises (t218 t219))
% 0.49/0.86 (step t221 (cl (= (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))) (=> tptp.funcext true))) :rule cong :premises (t209 t220))
% 0.49/0.86 (step t222 (cl (= (=> tptp.funcext true) true)) :rule all_simplify)
% 0.49/0.86 (step t223 (cl (= (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))) true)) :rule trans :premises (t221 t222))
% 0.49/0.86 (step t224 (cl (= (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))) (=> tptp.eqbreln true))) :rule cong :premises (t208 t223))
% 0.49/0.86 (step t225 (cl (= (=> tptp.eqbreln true) true)) :rule all_simplify)
% 0.49/0.86 (step t226 (cl (= (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))) true)) :rule trans :premises (t224 t225))
% 0.49/0.86 (step t227 (cl (= (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))) (=> tptp.subbreln true))) :rule cong :premises (t207 t226))
% 0.49/0.86 (step t228 (cl (= (=> tptp.subbreln true) true)) :rule all_simplify)
% 0.49/0.86 (step t229 (cl (= (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))) true)) :rule trans :premises (t227 t228))
% 0.49/0.86 (step t230 (cl (= (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))) (=> tptp.funcGraphProp4 true))) :rule cong :premises (t206 t229))
% 0.49/0.86 (step t231 (cl (= (=> tptp.funcGraphProp4 true) true)) :rule all_simplify)
% 0.49/0.86 (step t232 (cl (= (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))) true)) :rule trans :premises (t230 t231))
% 0.49/0.86 (step t233 (cl (= (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))) (=> tptp.funcextLem true))) :rule cong :premises (t205 t232))
% 0.49/0.86 (step t234 (cl (= (=> tptp.funcextLem true) true)) :rule all_simplify)
% 0.49/0.86 (step t235 (cl (= (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))) true)) :rule trans :premises (t233 t234))
% 0.49/0.86 (step t236 (cl (= (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))) (=> tptp.funcGraphProp2 true))) :rule cong :premises (t204 t235))
% 0.49/0.86 (step t237 (cl (= (=> tptp.funcGraphProp2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t238 (cl (= (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))) true)) :rule trans :premises (t236 t237))
% 0.49/0.86 (step t239 (cl (= (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))) (=> tptp.funcGraphProp3 true))) :rule cong :premises (t203 t238))
% 0.49/0.86 (step t240 (cl (= (=> tptp.funcGraphProp3 true) true)) :rule all_simplify)
% 0.49/0.86 (step t241 (cl (= (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))) true)) :rule trans :premises (t239 t240))
% 0.49/0.86 (step t242 (cl (= (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))) (=> tptp.funcGraphProp1 true))) :rule cong :premises (t202 t241))
% 0.49/0.86 (step t243 (cl (= (=> tptp.funcGraphProp1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t244 (cl (= (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))) true)) :rule trans :premises (t242 t243))
% 0.49/0.86 (step t245 (cl (= (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))) (=> tptp.ex1E2 true))) :rule cong :premises (t201 t244))
% 0.49/0.86 (step t246 (cl (= (=> tptp.ex1E2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t247 (cl (= (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))) true)) :rule trans :premises (t245 t246))
% 0.49/0.86 (step t248 (cl (= (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))) (=> tptp.brelnall2 true))) :rule cong :premises (t200 t247))
% 0.49/0.86 (step t249 (cl (= (=> tptp.brelnall2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t250 (cl (= (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))) true)) :rule trans :premises (t248 t249))
% 0.49/0.86 (step t251 (cl (= (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))) (=> tptp.brelnall1 true))) :rule cong :premises (t199 t250))
% 0.49/0.86 (step t252 (cl (= (=> tptp.brelnall1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t253 (cl (= (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))) true)) :rule trans :premises (t251 t252))
% 0.49/0.86 (step t254 (cl (= (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))) (=> tptp.lam2p true))) :rule cong :premises (t198 t253))
% 0.49/0.86 (step t255 (cl (= (=> tptp.lam2p true) true)) :rule all_simplify)
% 0.49/0.86 (step t256 (cl (= (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))) true)) :rule trans :premises (t254 t255))
% 0.49/0.86 (step t257 (cl (= (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))) (=> tptp.lamp true))) :rule cong :premises (t197 t256))
% 0.49/0.86 (step t258 (cl (= (=> tptp.lamp true) true)) :rule all_simplify)
% 0.49/0.86 (step t259 (cl (= (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))) true)) :rule trans :premises (t257 t258))
% 0.49/0.86 (step t260 (cl (= (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))) (=> tptp.lamProp true))) :rule cong :premises (t196 t259))
% 0.49/0.86 (step t261 (cl (= (=> tptp.lamProp true) true)) :rule all_simplify)
% 0.49/0.86 (step t262 (cl (= (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))) true)) :rule trans :premises (t260 t261))
% 0.49/0.86 (step t263 (cl (= (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))) (=> tptp.funcinfuncset true))) :rule cong :premises (t195 t262))
% 0.49/0.86 (step t264 (cl (= (=> tptp.funcinfuncset true) true)) :rule all_simplify)
% 0.49/0.86 (step t265 (cl (= (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))) true)) :rule trans :premises (t263 t264))
% 0.49/0.86 (step t266 (cl (= (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))) (=> tptp.ap2p true))) :rule cong :premises (t194 t265))
% 0.49/0.86 (step t267 (cl (= (=> tptp.ap2p true) true)) :rule all_simplify)
% 0.49/0.86 (step t268 (cl (= (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))) true)) :rule trans :premises (t266 t267))
% 0.49/0.86 (step t269 (cl (= (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))) (=> tptp.infuncsetfunc true))) :rule cong :premises (t193 t268))
% 0.49/0.86 (step t270 (cl (= (=> tptp.infuncsetfunc true) true)) :rule all_simplify)
% 0.49/0.86 (step t271 (cl (= (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))) true)) :rule trans :premises (t269 t270))
% 0.49/0.86 (step t272 (cl (= (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))) (=> tptp.app true))) :rule cong :premises (t192 t271))
% 0.49/0.86 (step t273 (cl (= (=> tptp.app true) true)) :rule all_simplify)
% 0.49/0.86 (step t274 (cl (= (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))) true)) :rule trans :premises (t272 t273))
% 0.49/0.86 (step t275 (cl (= (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))) (=> tptp.apProp true))) :rule cong :premises (t191 t274))
% 0.49/0.86 (step t276 (cl (= (=> tptp.apProp true) true)) :rule all_simplify)
% 0.49/0.86 (step t277 (cl (= (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))) true)) :rule trans :premises (t275 t276))
% 0.49/0.86 (step t278 (cl (= (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))) (=> tptp.funcImageSingleton true))) :rule cong :premises (t190 t277))
% 0.49/0.86 (step t279 (cl (= (=> tptp.funcImageSingleton true) true)) :rule all_simplify)
% 0.49/0.86 (step t280 (cl (= (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))) true)) :rule trans :premises (t278 t279))
% 0.49/0.86 (step t281 (cl (= (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))) (=> tptp.dpsetconstrER true))) :rule cong :premises (t189 t280))
% 0.49/0.86 (step t282 (cl (= (=> tptp.dpsetconstrER true) true)) :rule all_simplify)
% 0.49/0.86 (step t283 (cl (= (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))) true)) :rule trans :premises (t281 t282))
% 0.49/0.86 (step t284 (cl (= (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))) (=> tptp.dpsetconstrEL2 true))) :rule cong :premises (t188 t283))
% 0.49/0.86 (step t285 (cl (= (=> tptp.dpsetconstrEL2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t286 (cl (= (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))) true)) :rule trans :premises (t284 t285))
% 0.49/0.86 (step t287 (cl (= (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))) (=> tptp.dpsetconstrEL1 true))) :rule cong :premises (t187 t286))
% 0.49/0.86 (step t288 (cl (= (=> tptp.dpsetconstrEL1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t289 (cl (= (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))) true)) :rule trans :premises (t287 t288))
% 0.49/0.86 (step t290 (cl (= (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))) (=> tptp.dpsetconstrERa true))) :rule cong :premises (t186 t289))
% 0.49/0.86 (step t291 (cl (= (=> tptp.dpsetconstrERa true) true)) :rule all_simplify)
% 0.49/0.86 (step t292 (cl (= (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))) true)) :rule trans :premises (t290 t291))
% 0.49/0.86 (step t293 (cl (= (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))) (=> tptp.setOfPairsIsBReln true))) :rule cong :premises (t185 t292))
% 0.49/0.86 (step t294 (cl (= (=> tptp.setOfPairsIsBReln true) true)) :rule all_simplify)
% 0.49/0.86 (step t295 (cl (= (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t293 t294))
% 0.49/0.86 (step t296 (cl (= (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))) (=> tptp.dpsetconstrSub true))) :rule cong :premises (t184 t295))
% 0.49/0.86 (step t297 (cl (= (=> tptp.dpsetconstrSub true) true)) :rule all_simplify)
% 0.49/0.86 (step t298 (cl (= (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t296 t297))
% 0.49/0.86 (step t299 (cl (= (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))) (=> tptp.dpsetconstrI true))) :rule cong :premises (t183 t298))
% 0.49/0.86 (step t300 (cl (= (=> tptp.dpsetconstrI true) true)) :rule all_simplify)
% 0.49/0.86 (step t301 (cl (= (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t299 t300))
% 0.49/0.86 (step t302 (cl (= (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))) (=> tptp.cartprodpairsurjEq true))) :rule cong :premises (t182 t301))
% 0.49/0.86 (step t303 (cl (= (=> tptp.cartprodpairsurjEq true) true)) :rule all_simplify)
% 0.49/0.86 (step t304 (cl (= (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t302 t303))
% 0.49/0.86 (step t305 (cl (= (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodsndpairEq true))) :rule cong :premises (t181 t304))
% 0.49/0.86 (step t306 (cl (= (=> tptp.cartprodsndpairEq true) true)) :rule all_simplify)
% 0.49/0.86 (step t307 (cl (= (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t305 t306))
% 0.49/0.86 (step t308 (cl (= (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodfstpairEq true))) :rule cong :premises (t180 t307))
% 0.49/0.86 (step t309 (cl (= (=> tptp.cartprodfstpairEq true) true)) :rule all_simplify)
% 0.49/0.86 (step t310 (cl (= (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t308 t309))
% 0.49/0.86 (step t311 (cl (= (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodmempaircEq true))) :rule cong :premises (t179 t310))
% 0.49/0.86 (step t312 (cl (= (=> tptp.cartprodmempaircEq true) true)) :rule all_simplify)
% 0.49/0.86 (step t313 (cl (= (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t311 t312))
% 0.49/0.86 (step t314 (cl (= (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodpairmemER true))) :rule cong :premises (t178 t313))
% 0.49/0.86 (step t315 (cl (= (=> tptp.cartprodpairmemER true) true)) :rule all_simplify)
% 0.49/0.86 (step t316 (cl (= (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t314 t315))
% 0.49/0.86 (step t317 (cl (= (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodpairmemEL true))) :rule cong :premises (t177 t316))
% 0.49/0.86 (step t318 (cl (= (=> tptp.cartprodpairmemEL true) true)) :rule all_simplify)
% 0.49/0.86 (step t319 (cl (= (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t317 t318))
% 0.49/0.86 (step t320 (cl (= (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodsndin true))) :rule cong :premises (t176 t319))
% 0.49/0.86 (step t321 (cl (= (=> tptp.cartprodsndin true) true)) :rule all_simplify)
% 0.49/0.86 (step t322 (cl (= (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t320 t321))
% 0.49/0.86 (step t323 (cl (= (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))) (=> tptp.kpairsurjEq true))) :rule cong :premises (t175 t322))
% 0.49/0.86 (step t324 (cl (= (=> tptp.kpairsurjEq true) true)) :rule all_simplify)
% 0.49/0.86 (step t325 (cl (= (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t323 t324))
% 0.49/0.86 (step t326 (cl (= (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))) (=> tptp.ksndpairEq true))) :rule cong :premises (t174 t325))
% 0.49/0.86 (step t327 (cl (= (=> tptp.ksndpairEq true) true)) :rule all_simplify)
% 0.49/0.86 (step t328 (cl (= (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t326 t327))
% 0.49/0.86 (step t329 (cl (= (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.ksndsingleton true))) :rule cong :premises (t173 t328))
% 0.49/0.86 (step t330 (cl (= (=> tptp.ksndsingleton true) true)) :rule all_simplify)
% 0.49/0.86 (step t331 (cl (= (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t329 t330))
% 0.49/0.86 (step t332 (cl (= (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairinjR true))) :rule cong :premises (t172 t331))
% 0.49/0.86 (step t333 (cl (= (=> tptp.setukpairinjR true) true)) :rule all_simplify)
% 0.49/0.86 (step t334 (cl (= (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t332 t333))
% 0.49/0.86 (step t335 (cl (= (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairinjR2 true))) :rule cong :premises (t171 t334))
% 0.49/0.86 (step t336 (cl (= (=> tptp.setukpairinjR2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t337 (cl (= (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t335 t336))
% 0.49/0.86 (step t338 (cl (= (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairequniteq true))) :rule cong :premises (t170 t337))
% 0.49/0.86 (step t339 (cl (= (=> tptp.upairequniteq true) true)) :rule all_simplify)
% 0.49/0.86 (step t340 (cl (= (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t338 t339))
% 0.49/0.86 (step t341 (cl (= (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairinjR1 true))) :rule cong :premises (t169 t340))
% 0.49/0.86 (step t342 (cl (= (=> tptp.setukpairinjR1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t343 (cl (= (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t341 t342))
% 0.49/0.86 (step t344 (cl (= (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairinjR12 true))) :rule cong :premises (t168 t343))
% 0.49/0.86 (step t345 (cl (= (=> tptp.setukpairinjR12 true) true)) :rule all_simplify)
% 0.49/0.86 (step t346 (cl (= (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t344 t345))
% 0.49/0.86 (step t347 (cl (= (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairinjR11 true))) :rule cong :premises (t167 t346))
% 0.49/0.86 (step t348 (cl (= (=> tptp.setukpairinjR11 true) true)) :rule all_simplify)
% 0.49/0.86 (step t349 (cl (= (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t347 t348))
% 0.49/0.86 (step t350 (cl (= (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairinjL true))) :rule cong :premises (t166 t349))
% 0.49/0.86 (step t351 (cl (= (=> tptp.setukpairinjL true) true)) :rule all_simplify)
% 0.49/0.86 (step t352 (cl (= (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t350 t351))
% 0.49/0.86 (step t353 (cl (= (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairinjL2 true))) :rule cong :premises (t165 t352))
% 0.49/0.86 (step t354 (cl (= (=> tptp.setukpairinjL2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t355 (cl (= (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t353 t354))
% 0.49/0.86 (step t356 (cl (= (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodfstin true))) :rule cong :premises (t164 t355))
% 0.49/0.86 (step t357 (cl (= (=> tptp.cartprodfstin true) true)) :rule all_simplify)
% 0.49/0.86 (step t358 (cl (= (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t356 t357))
% 0.49/0.86 (step t359 (cl (= (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.kfstpairEq true))) :rule cong :premises (t163 t358))
% 0.49/0.86 (step t360 (cl (= (=> tptp.kfstpairEq true) true)) :rule all_simplify)
% 0.49/0.86 (step t361 (cl (= (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t359 t360))
% 0.49/0.86 (step t362 (cl (= (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.theprop true))) :rule cong :premises (t162 t361))
% 0.49/0.86 (step t363 (cl (= (=> tptp.theprop true) true)) :rule all_simplify)
% 0.49/0.86 (step t364 (cl (= (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t362 t363))
% 0.49/0.86 (step t365 (cl (= (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.kfstsingleton true))) :rule cong :premises (t161 t364))
% 0.49/0.86 (step t366 (cl (= (=> tptp.kfstsingleton true) true)) :rule all_simplify)
% 0.49/0.86 (step t367 (cl (= (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t365 t366))
% 0.49/0.86 (step t368 (cl (= (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairinjL1 true))) :rule cong :premises (t160 t367))
% 0.49/0.86 (step t369 (cl (= (=> tptp.setukpairinjL1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t370 (cl (= (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t368 t369))
% 0.49/0.86 (step t371 (cl (= (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.singletonsuniq true))) :rule cong :premises (t159 t370))
% 0.49/0.86 (step t372 (cl (= (=> tptp.singletonsuniq true) true)) :rule all_simplify)
% 0.49/0.86 (step t373 (cl (= (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t371 t372))
% 0.49/0.86 (step t374 (cl (= (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.ex1I2 true))) :rule cong :premises (t158 t373))
% 0.49/0.86 (step t375 (cl (= (=> tptp.ex1I2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t376 (cl (= (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t374 t375))
% 0.49/0.86 (step t377 (cl (= (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.ex1I true))) :rule cong :premises (t157 t376))
% 0.49/0.86 (step t378 (cl (= (=> tptp.ex1I true) true)) :rule all_simplify)
% 0.49/0.86 (step t379 (cl (= (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t377 t378))
% 0.49/0.86 (step t380 (cl (= (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.ex1E1 true))) :rule cong :premises (t156 t379))
% 0.49/0.86 (step t381 (cl (= (=> tptp.ex1E1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t382 (cl (= (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t380 t381))
% 0.49/0.86 (step t383 (cl (= (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.singletonprop true))) :rule cong :premises (t155 t382))
% 0.49/0.86 (step t384 (cl (= (=> tptp.singletonprop true) true)) :rule all_simplify)
% 0.49/0.86 (step t385 (cl (= (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t383 t384))
% 0.49/0.86 (step t386 (cl (= (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionsingleton true))) :rule cong :premises (t154 t385))
% 0.49/0.86 (step t387 (cl (= (=> tptp.setunionsingleton true) true)) :rule all_simplify)
% 0.49/0.86 (step t388 (cl (= (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t386 t387))
% 0.49/0.86 (step t389 (cl (= (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionsingleton2 true))) :rule cong :premises (t153 t388))
% 0.49/0.86 (step t390 (cl (= (=> tptp.setunionsingleton2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t391 (cl (= (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t389 t390))
% 0.49/0.86 (step t392 (cl (= (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionsingleton1 true))) :rule cong :premises (t152 t391))
% 0.49/0.86 (step t393 (cl (= (=> tptp.setunionsingleton1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t394 (cl (= (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t392 t393))
% 0.49/0.86 (step t395 (cl (= (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionE2 true))) :rule cong :premises (t151 t394))
% 0.49/0.86 (step t396 (cl (= (=> tptp.setunionE2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t397 (cl (= (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t395 t396))
% 0.49/0.86 (step t398 (cl (= (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodmempair true))) :rule cong :premises (t150 t397))
% 0.49/0.86 (step t399 (cl (= (=> tptp.cartprodmempair true) true)) :rule all_simplify)
% 0.49/0.86 (step t400 (cl (= (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t398 t399))
% 0.49/0.86 (step t401 (cl (= (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodmempair1 true))) :rule cong :premises (t149 t400))
% 0.49/0.86 (step t402 (cl (= (=> tptp.cartprodmempair1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t403 (cl (= (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t401 t402))
% 0.49/0.86 (step t404 (cl (= (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.cartprodpairin true))) :rule cong :premises (t148 t403))
% 0.49/0.86 (step t405 (cl (= (=> tptp.cartprodpairin true) true)) :rule all_simplify)
% 0.49/0.86 (step t406 (cl (= (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t404 t405))
% 0.49/0.86 (step t407 (cl (= (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.ubforcartprodlem3 true))) :rule cong :premises (t147 t406))
% 0.49/0.86 (step t408 (cl (= (=> tptp.ubforcartprodlem3 true) true)) :rule all_simplify)
% 0.49/0.86 (step t409 (cl (= (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t407 t408))
% 0.49/0.86 (step t410 (cl (= (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.ubforcartprodlem2 true))) :rule cong :premises (t146 t409))
% 0.49/0.86 (step t411 (cl (= (=> tptp.ubforcartprodlem2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t412 (cl (= (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t410 t411))
% 0.49/0.86 (step t413 (cl (= (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.ubforcartprodlem1 true))) :rule cong :premises (t145 t412))
% 0.49/0.86 (step t414 (cl (= (=> tptp.ubforcartprodlem1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t415 (cl (= (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t413 t414))
% 0.49/0.86 (step t416 (cl (= (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairinpowunion true))) :rule cong :premises (t144 t415))
% 0.49/0.86 (step t417 (cl (= (=> tptp.upairinpowunion true) true)) :rule all_simplify)
% 0.49/0.86 (step t418 (cl (= (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t416 t417))
% 0.49/0.86 (step t419 (cl (= (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairsubunion true))) :rule cong :premises (t143 t418))
% 0.49/0.86 (step t420 (cl (= (=> tptp.upairsubunion true) true)) :rule all_simplify)
% 0.49/0.86 (step t421 (cl (= (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t419 t420))
% 0.49/0.86 (step t422 (cl (= (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairset2E true))) :rule cong :premises (t142 t421))
% 0.49/0.86 (step t423 (cl (= (=> tptp.upairset2E true) true)) :rule all_simplify)
% 0.49/0.86 (step t424 (cl (= (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t422 t423))
% 0.49/0.86 (step t425 (cl (= (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.singletoninpowunion true))) :rule cong :premises (t141 t424))
% 0.49/0.86 (step t426 (cl (= (=> tptp.singletoninpowunion true) true)) :rule all_simplify)
% 0.49/0.86 (step t427 (cl (= (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t425 t426))
% 0.49/0.86 (step t428 (cl (= (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.singletoninpowerset true))) :rule cong :premises (t140 t427))
% 0.49/0.86 (step t429 (cl (= (=> tptp.singletoninpowerset true) true)) :rule all_simplify)
% 0.49/0.86 (step t430 (cl (= (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t428 t429))
% 0.49/0.86 (step t431 (cl (= (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.singletonsubset true))) :rule cong :premises (t139 t430))
% 0.49/0.86 (step t432 (cl (= (=> tptp.singletonsubset true) true)) :rule all_simplify)
% 0.49/0.86 (step t433 (cl (= (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t431 t432))
% 0.49/0.86 (step t434 (cl (= (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.kpairp true))) :rule cong :premises (t138 t433))
% 0.49/0.86 (step t435 (cl (= (=> tptp.kpairp true) true)) :rule all_simplify)
% 0.49/0.86 (step t436 (cl (= (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t434 t435))
% 0.49/0.86 (step t437 (cl (= (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.kpairiskpair true))) :rule cong :premises (t137 t436))
% 0.49/0.86 (step t438 (cl (= (=> tptp.kpairiskpair true) true)) :rule all_simplify)
% 0.49/0.86 (step t439 (cl (= (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t437 t438))
% 0.49/0.86 (step t440 (cl (= (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairIR true))) :rule cong :premises (t136 t439))
% 0.49/0.86 (step t441 (cl (= (=> tptp.setukpairIR true) true)) :rule all_simplify)
% 0.49/0.86 (step t442 (cl (= (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t440 t441))
% 0.49/0.86 (step t443 (cl (= (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setukpairIL true))) :rule cong :premises (t135 t442))
% 0.49/0.86 (step t444 (cl (= (=> tptp.setukpairIL true) true)) :rule all_simplify)
% 0.49/0.86 (step t445 (cl (= (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t443 t444))
% 0.49/0.86 (step t446 (cl (= (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.secondinupair true))) :rule cong :premises (t134 t445))
% 0.49/0.86 (step t447 (cl (= (=> tptp.secondinupair true) true)) :rule all_simplify)
% 0.49/0.86 (step t448 (cl (= (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t446 t447))
% 0.49/0.86 (step t449 (cl (= (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.symdiffIneg2 true))) :rule cong :premises (t133 t448))
% 0.49/0.86 (step t450 (cl (= (=> tptp.symdiffIneg2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t451 (cl (= (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t449 t450))
% 0.49/0.86 (step t452 (cl (= (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.symdiffIneg1 true))) :rule cong :premises (t132 t451))
% 0.49/0.86 (step t453 (cl (= (=> tptp.symdiffIneg1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t454 (cl (= (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t452 t453))
% 0.49/0.86 (step t455 (cl (= (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.symdiffI2 true))) :rule cong :premises (t131 t454))
% 0.49/0.86 (step t456 (cl (= (=> tptp.symdiffI2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t457 (cl (= (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t455 t456))
% 0.49/0.86 (step t458 (cl (= (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.symdiffI1 true))) :rule cong :premises (t130 t457))
% 0.49/0.86 (step t459 (cl (= (=> tptp.symdiffI1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t460 (cl (= (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t458 t459))
% 0.49/0.86 (step t461 (cl (= (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.symdiffE true))) :rule cong :premises (t129 t460))
% 0.49/0.86 (step t462 (cl (= (=> tptp.symdiffE true) true)) :rule all_simplify)
% 0.49/0.86 (step t463 (cl (= (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t461 t462))
% 0.49/0.86 (step t464 (cl (= (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusSubset1 true))) :rule cong :premises (t128 t463))
% 0.49/0.86 (step t465 (cl (= (=> tptp.setminusSubset1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t466 (cl (= (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t464 t465))
% 0.49/0.86 (step t467 (cl (= (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusLsub true))) :rule cong :premises (t127 t466))
% 0.49/0.86 (step t468 (cl (= (=> tptp.setminusLsub true) true)) :rule all_simplify)
% 0.49/0.86 (step t469 (cl (= (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t467 t468))
% 0.49/0.86 (step t470 (cl (= (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusIRneg true))) :rule cong :premises (t126 t469))
% 0.49/0.86 (step t471 (cl (= (=> tptp.setminusIRneg true) true)) :rule all_simplify)
% 0.49/0.86 (step t472 (cl (= (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t470 t471))
% 0.49/0.86 (step t473 (cl (= (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusILneg true))) :rule cong :premises (t125 t472))
% 0.49/0.86 (step t474 (cl (= (=> tptp.setminusILneg true) true)) :rule all_simplify)
% 0.49/0.86 (step t475 (cl (= (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t473 t474))
% 0.49/0.86 (step t476 (cl (= (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusELneg true))) :rule cong :premises (t124 t475))
% 0.49/0.86 (step t477 (cl (= (=> tptp.setminusELneg true) true)) :rule all_simplify)
% 0.49/0.86 (step t478 (cl (= (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t476 t477))
% 0.49/0.86 (step t479 (cl (= (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusERneg true))) :rule cong :premises (t123 t478))
% 0.49/0.86 (step t480 (cl (= (=> tptp.setminusERneg true) true)) :rule all_simplify)
% 0.49/0.86 (step t481 (cl (= (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t479 t480))
% 0.49/0.86 (step t482 (cl (= (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusSubset2 true))) :rule cong :premises (t122 t481))
% 0.49/0.86 (step t483 (cl (= (=> tptp.setminusSubset2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t484 (cl (= (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t482 t483))
% 0.49/0.86 (step t485 (cl (= (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusER true))) :rule cong :premises (t121 t484))
% 0.49/0.86 (step t486 (cl (= (=> tptp.setminusER true) true)) :rule all_simplify)
% 0.49/0.86 (step t487 (cl (= (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t485 t486))
% 0.49/0.86 (step t488 (cl (= (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusEL true))) :rule cong :premises (t120 t487))
% 0.49/0.86 (step t489 (cl (= (=> tptp.setminusEL true) true)) :rule all_simplify)
% 0.49/0.86 (step t490 (cl (= (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t488 t489))
% 0.49/0.86 (step t491 (cl (= (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setminusI true))) :rule cong :premises (t119 t490))
% 0.49/0.86 (step t492 (cl (= (=> tptp.setminusI true) true)) :rule all_simplify)
% 0.49/0.86 (step t493 (cl (= (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t491 t492))
% 0.49/0.86 (step t494 (cl (= (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.bs114d true))) :rule cong :premises (t118 t493))
% 0.49/0.86 (step t495 (cl (= (=> tptp.bs114d true) true)) :rule all_simplify)
% 0.49/0.86 (step t496 (cl (= (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t494 t495))
% 0.49/0.86 (step t497 (cl (= (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectSubset1 true))) :rule cong :premises (t117 t496))
% 0.49/0.86 (step t498 (cl (= (=> tptp.binintersectSubset1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t499 (cl (= (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t497 t498))
% 0.49/0.86 (step t500 (cl (= (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectSubset4 true))) :rule cong :premises (t116 t499))
% 0.49/0.86 (step t501 (cl (= (=> tptp.binintersectSubset4 true) true)) :rule all_simplify)
% 0.49/0.86 (step t502 (cl (= (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t500 t501))
% 0.49/0.86 (step t503 (cl (= (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectRsub true))) :rule cong :premises (t115 t502))
% 0.49/0.86 (step t504 (cl (= (=> tptp.binintersectRsub true) true)) :rule all_simplify)
% 0.49/0.86 (step t505 (cl (= (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t503 t504))
% 0.49/0.86 (step t506 (cl (= (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.disjointsetsI1 true))) :rule cong :premises (t114 t505))
% 0.49/0.86 (step t507 (cl (= (=> tptp.disjointsetsI1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t508 (cl (= (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t506 t507))
% 0.49/0.86 (step t509 (cl (= (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectER true))) :rule cong :premises (t113 t508))
% 0.49/0.86 (step t510 (cl (= (=> tptp.binintersectER true) true)) :rule all_simplify)
% 0.49/0.86 (step t511 (cl (= (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t509 t510))
% 0.49/0.86 (step t512 (cl (= (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectSubset3 true))) :rule cong :premises (t112 t511))
% 0.49/0.86 (step t513 (cl (= (=> tptp.binintersectSubset3 true) true)) :rule all_simplify)
% 0.49/0.86 (step t514 (cl (= (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t512 t513))
% 0.49/0.86 (step t515 (cl (= (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectSubset2 true))) :rule cong :premises (t111 t514))
% 0.49/0.86 (step t516 (cl (= (=> tptp.binintersectSubset2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t517 (cl (= (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t515 t516))
% 0.49/0.86 (step t518 (cl (= (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectLsub true))) :rule cong :premises (t110 t517))
% 0.49/0.86 (step t519 (cl (= (=> tptp.binintersectLsub true) true)) :rule all_simplify)
% 0.49/0.86 (step t520 (cl (= (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t518 t519))
% 0.49/0.86 (step t521 (cl (= (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectEL true))) :rule cong :premises (t109 t520))
% 0.49/0.86 (step t522 (cl (= (=> tptp.binintersectEL true) true)) :rule all_simplify)
% 0.49/0.86 (step t523 (cl (= (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t521 t522))
% 0.49/0.86 (step t524 (cl (= (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectSubset5 true))) :rule cong :premises (t108 t523))
% 0.49/0.86 (step t525 (cl (= (=> tptp.binintersectSubset5 true) true)) :rule all_simplify)
% 0.49/0.86 (step t526 (cl (= (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t524 t525))
% 0.49/0.86 (step t527 (cl (= (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binintersectI true))) :rule cong :premises (t107 t526))
% 0.49/0.86 (step t528 (cl (= (=> tptp.binintersectI true) true)) :rule all_simplify)
% 0.49/0.86 (step t529 (cl (= (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t527 t528))
% 0.49/0.86 (step t530 (cl (= (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binunionRsub true))) :rule cong :premises (t106 t529))
% 0.49/0.86 (step t531 (cl (= (=> tptp.binunionRsub true) true)) :rule all_simplify)
% 0.49/0.86 (step t532 (cl (= (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t530 t531))
% 0.49/0.86 (step t533 (cl (= (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binunionLsub true))) :rule cong :premises (t105 t532))
% 0.49/0.86 (step t534 (cl (= (=> tptp.binunionLsub true) true)) :rule all_simplify)
% 0.49/0.86 (step t535 (cl (= (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t533 t534))
% 0.49/0.86 (step t536 (cl (= (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binunionE true))) :rule cong :premises (t104 t535))
% 0.49/0.86 (step t537 (cl (= (=> tptp.binunionE true) true)) :rule all_simplify)
% 0.49/0.86 (step t538 (cl (= (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t536 t537))
% 0.49/0.86 (step t539 (cl (= (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binunionEcases true))) :rule cong :premises (t103 t538))
% 0.49/0.86 (step t540 (cl (= (=> tptp.binunionEcases true) true)) :rule all_simplify)
% 0.49/0.86 (step t541 (cl (= (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t539 t540))
% 0.49/0.86 (step t542 (cl (= (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binunionIR true))) :rule cong :premises (t102 t541))
% 0.49/0.86 (step t543 (cl (= (=> tptp.binunionIR true) true)) :rule all_simplify)
% 0.49/0.86 (step t544 (cl (= (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t542 t543))
% 0.49/0.86 (step t545 (cl (= (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairset2IR true))) :rule cong :premises (t101 t544))
% 0.49/0.86 (step t546 (cl (= (=> tptp.upairset2IR true) true)) :rule all_simplify)
% 0.49/0.86 (step t547 (cl (= (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t545 t546))
% 0.49/0.86 (step t548 (cl (= (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.binunionIL true))) :rule cong :premises (t100 t547))
% 0.49/0.86 (step t549 (cl (= (=> tptp.binunionIL true) true)) :rule all_simplify)
% 0.49/0.86 (step t550 (cl (= (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t548 t549))
% 0.49/0.86 (step t551 (cl (= (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.sepSubset true))) :rule cong :premises (t99 t550))
% 0.49/0.86 (step t552 (cl (= (=> tptp.sepSubset true) true)) :rule all_simplify)
% 0.49/0.86 (step t553 (cl (= (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t551 t552))
% 0.49/0.86 (step t554 (cl (= (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.sepInPowerset true))) :rule cong :premises (t98 t553))
% 0.49/0.86 (step t555 (cl (= (=> tptp.sepInPowerset true) true)) :rule all_simplify)
% 0.49/0.86 (step t556 (cl (= (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t554 t555))
% 0.49/0.86 (step t557 (cl (= (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetsubset true))) :rule cong :premises (t97 t556))
% 0.49/0.86 (step t558 (cl (= (=> tptp.powersetsubset true) true)) :rule all_simplify)
% 0.49/0.86 (step t559 (cl (= (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t557 t558))
% 0.49/0.86 (step t560 (cl (= (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.inPowerset true))) :rule cong :premises (t96 t559))
% 0.49/0.86 (step t561 (cl (= (=> tptp.inPowerset true) true)) :rule all_simplify)
% 0.49/0.86 (step t562 (cl (= (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t560 t561))
% 0.49/0.86 (step t563 (cl (= (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetE1 true))) :rule cong :premises (t95 t562))
% 0.49/0.86 (step t564 (cl (= (=> tptp.powersetE1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t565 (cl (= (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t563 t564))
% 0.49/0.86 (step t566 (cl (= (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetI1 true))) :rule cong :premises (t94 t565))
% 0.49/0.86 (step t567 (cl (= (=> tptp.powersetI1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t568 (cl (= (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t566 t567))
% 0.49/0.86 (step t569 (cl (= (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subsetemptysetimpeq true))) :rule cong :premises (t93 t568))
% 0.49/0.86 (step t570 (cl (= (=> tptp.subsetemptysetimpeq true) true)) :rule all_simplify)
% 0.49/0.86 (step t571 (cl (= (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t569 t570))
% 0.49/0.86 (step t572 (cl (= (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setextsub true))) :rule cong :premises (t92 t571))
% 0.49/0.86 (step t573 (cl (= (=> tptp.setextsub true) true)) :rule all_simplify)
% 0.49/0.86 (step t574 (cl (= (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t572 t573))
% 0.49/0.86 (step t575 (cl (= (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subset2powerset true))) :rule cong :premises (t91 t574))
% 0.49/0.86 (step t576 (cl (= (=> tptp.subset2powerset true) true)) :rule all_simplify)
% 0.49/0.86 (step t577 (cl (= (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t575 t576))
% 0.49/0.86 (step t578 (cl (= (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinSub2 true))) :rule cong :premises (t90 t577))
% 0.49/0.86 (step t579 (cl (= (=> tptp.setadjoinSub2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t580 (cl (= (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t578 t579))
% 0.49/0.86 (step t581 (cl (= (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinSub true))) :rule cong :premises (t89 t580))
% 0.49/0.86 (step t582 (cl (= (=> tptp.setadjoinSub true) true)) :rule all_simplify)
% 0.49/0.86 (step t583 (cl (= (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t581 t582))
% 0.49/0.86 (step t584 (cl (= (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subsetTrans true))) :rule cong :premises (t88 t583))
% 0.49/0.86 (step t585 (cl (= (=> tptp.subsetTrans true) true)) :rule all_simplify)
% 0.49/0.86 (step t586 (cl (= (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t584 t585))
% 0.49/0.86 (step t587 (cl (= (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subsetRefl true))) :rule cong :premises (t87 t586))
% 0.49/0.86 (step t588 (cl (= (=> tptp.subsetRefl true) true)) :rule all_simplify)
% 0.49/0.86 (step t589 (cl (= (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t587 t588))
% 0.49/0.86 (step t590 (cl (= (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notequalI2 true))) :rule cong :premises (t86 t589))
% 0.49/0.86 (step t591 (cl (= (=> tptp.notequalI2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t592 (cl (= (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t590 t591))
% 0.49/0.86 (step t593 (cl (= (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notequalI1 true))) :rule cong :premises (t85 t592))
% 0.49/0.86 (step t594 (cl (= (=> tptp.notequalI1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t595 (cl (= (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t593 t594))
% 0.49/0.86 (step t596 (cl (= (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notsubsetI true))) :rule cong :premises (t84 t595))
% 0.49/0.86 (step t597 (cl (= (=> tptp.notsubsetI true) true)) :rule all_simplify)
% 0.49/0.86 (step t598 (cl (= (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t596 t597))
% 0.49/0.86 (step t599 (cl (= (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subsetE2 true))) :rule cong :premises (t83 t598))
% 0.49/0.86 (step t600 (cl (= (=> tptp.subsetE2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t601 (cl (= (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t599 t600))
% 0.49/0.86 (step t602 (cl (= (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subsetE true))) :rule cong :premises (t82 t601))
% 0.49/0.86 (step t603 (cl (= (=> tptp.subsetE true) true)) :rule all_simplify)
% 0.49/0.86 (step t604 (cl (= (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t602 t603))
% 0.49/0.86 (step t605 (cl (= (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptysetsubset true))) :rule cong :premises (t81 t604))
% 0.49/0.86 (step t606 (cl (= (=> tptp.emptysetsubset true) true)) :rule all_simplify)
% 0.49/0.86 (step t607 (cl (= (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t605 t606))
% 0.49/0.86 (step t608 (cl (= (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subsetI2 true))) :rule cong :premises (t80 t607))
% 0.49/0.86 (step t609 (cl (= (=> tptp.subsetI2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t610 (cl (= (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t608 t609))
% 0.49/0.86 (step t611 (cl (= (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.eqimpsubset1 true))) :rule cong :premises (t79 t610))
% 0.49/0.86 (step t612 (cl (= (=> tptp.eqimpsubset1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t613 (cl (= (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t611 t612))
% 0.49/0.86 (step t614 (cl (= (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.eqimpsubset2 true))) :rule cong :premises (t78 t613))
% 0.49/0.86 (step t615 (cl (= (=> tptp.eqimpsubset2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t616 (cl (= (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t614 t615))
% 0.49/0.86 (step t617 (cl (= (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subsetI1 true))) :rule cong :premises (t77 t616))
% 0.49/0.86 (step t618 (cl (= (=> tptp.subsetI1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t619 (cl (= (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t617 t618))
% 0.49/0.86 (step t620 (cl (= (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.dsetconstr__Cong true))) :rule cong :premises (t76 t619))
% 0.49/0.86 (step t621 (cl (= (=> tptp.dsetconstr__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t622 (cl (= (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t620 t621))
% 0.49/0.86 (step t623 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.descr__Cong true))) :rule cong :premises (t75 t622))
% 0.49/0.86 (step t624 (cl (= (=> tptp.descr__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t625 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t623 t624))
% 0.49/0.86 (step t626 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuEu true))) :rule cong :premises (t74 t625))
% 0.49/0.86 (step t627 (cl (= (=> tptp.exuEu true) true)) :rule all_simplify)
% 0.49/0.86 (step t628 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t626 t627))
% 0.49/0.86 (step t629 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.omega__Cong true))) :rule cong :premises (t73 t628))
% 0.49/0.86 (step t630 (cl (= (=> tptp.omega__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t631 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t629 t630))
% 0.49/0.86 (step t632 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunion__Cong true))) :rule cong :premises (t72 t631))
% 0.49/0.86 (step t633 (cl (= (=> tptp.setunion__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t634 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t632 t633))
% 0.49/0.86 (step t635 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powerset__Cong true))) :rule cong :premises (t71 t634))
% 0.49/0.86 (step t636 (cl (= (=> tptp.powerset__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t637 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t635 t636))
% 0.49/0.86 (step t638 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoin__Cong true))) :rule cong :premises (t70 t637))
% 0.49/0.86 (step t639 (cl (= (=> tptp.setadjoin__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t640 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t638 t639))
% 0.49/0.86 (step t641 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyset__Cong true))) :rule cong :premises (t69 t640))
% 0.49/0.86 (step t642 (cl (= (=> tptp.emptyset__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t643 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t641 t642))
% 0.49/0.86 (step t644 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exu__Cong true))) :rule cong :premises (t68 t643))
% 0.49/0.86 (step t645 (cl (= (=> tptp.exu__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t646 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t644 t645))
% 0.49/0.86 (step t647 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuE3u true))) :rule cong :premises (t67 t646))
% 0.49/0.86 (step t648 (cl (= (=> tptp.exuE3u true) true)) :rule all_simplify)
% 0.49/0.86 (step t649 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t647 t648))
% 0.49/0.86 (step t650 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.in__Cong true))) :rule cong :premises (t66 t649))
% 0.49/0.86 (step t651 (cl (= (=> tptp.in__Cong true) true)) :rule all_simplify)
% 0.49/0.86 (step t652 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t650 t651))
% 0.49/0.86 (step t653 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.inCongP true))) :rule cong :premises (t65 t652))
% 0.49/0.86 (step t654 (cl (= (=> tptp.inCongP true) true)) :rule all_simplify)
% 0.49/0.86 (step t655 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t653 t654))
% 0.49/0.86 (step t656 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuI2 true))) :rule cong :premises (t64 t655))
% 0.49/0.86 (step t657 (cl (= (=> tptp.exuI2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t658 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t656 t657))
% 0.49/0.86 (step t659 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuI3 true))) :rule cong :premises (t63 t658))
% 0.49/0.86 (step t660 (cl (= (=> tptp.exuI3 true) true)) :rule all_simplify)
% 0.49/0.86 (step t661 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t659 t660))
% 0.49/0.86 (step t662 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuI1 true))) :rule cong :premises (t62 t661))
% 0.49/0.86 (step t663 (cl (= (=> tptp.exuI1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t664 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t662 t663))
% 0.49/0.86 (step t665 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notdallE true))) :rule cong :premises (t61 t664))
% 0.49/0.86 (step t666 (cl (= (=> tptp.notdallE true) true)) :rule all_simplify)
% 0.49/0.86 (step t667 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t665 t666))
% 0.49/0.86 (step t668 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notdexE true))) :rule cong :premises (t60 t667))
% 0.49/0.86 (step t669 (cl (= (=> tptp.notdexE true) true)) :rule all_simplify)
% 0.49/0.86 (step t670 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t668 t669))
% 0.49/0.86 (step t671 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.prop2set2propI true))) :rule cong :premises (t59 t670))
% 0.49/0.86 (step t672 (cl (= (=> tptp.prop2set2propI true) true)) :rule all_simplify)
% 0.49/0.86 (step t673 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t671 t672))
% 0.49/0.86 (step t674 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.prop2setI true))) :rule cong :premises (t58 t673))
% 0.49/0.86 (step t675 (cl (= (=> tptp.prop2setI true) true)) :rule all_simplify)
% 0.49/0.86 (step t676 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t674 t675))
% 0.49/0.86 (step t677 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.quantDeMorgan4 true))) :rule cong :premises (t57 t676))
% 0.49/0.86 (step t678 (cl (= (=> tptp.quantDeMorgan4 true) true)) :rule all_simplify)
% 0.49/0.86 (step t679 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t677 t678))
% 0.49/0.86 (step t680 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.quantDeMorgan3 true))) :rule cong :premises (t56 t679))
% 0.49/0.86 (step t681 (cl (= (=> tptp.quantDeMorgan3 true) true)) :rule all_simplify)
% 0.49/0.86 (step t682 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t680 t681))
% 0.49/0.86 (step t683 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.quantDeMorgan2 true))) :rule cong :premises (t55 t682))
% 0.49/0.86 (step t684 (cl (= (=> tptp.quantDeMorgan2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t685 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t683 t684))
% 0.49/0.86 (step t686 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.quantDeMorgan1 true))) :rule cong :premises (t54 t685))
% 0.49/0.86 (step t687 (cl (= (=> tptp.quantDeMorgan1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t688 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t686 t687))
% 0.49/0.86 (step t689 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.vacuousDall true))) :rule cong :premises (t53 t688))
% 0.49/0.86 (step t690 (cl (= (=> tptp.vacuousDall true) true)) :rule all_simplify)
% 0.49/0.86 (step t691 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t689 t690))
% 0.49/0.86 (step t692 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyE1 true))) :rule cong :premises (t52 t691))
% 0.49/0.86 (step t693 (cl (= (=> tptp.emptyE1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t694 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t692 t693))
% 0.49/0.86 (step t695 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairsetIR true))) :rule cong :premises (t51 t694))
% 0.49/0.86 (step t696 (cl (= (=> tptp.upairsetIR true) true)) :rule all_simplify)
% 0.49/0.86 (step t697 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t695 t696))
% 0.49/0.86 (step t698 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairsetIL true))) :rule cong :premises (t50 t697))
% 0.49/0.86 (step t699 (cl (= (=> tptp.upairsetIL true) true)) :rule all_simplify)
% 0.49/0.86 (step t700 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t698 t699))
% 0.49/0.86 (step t701 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.upairsetE true))) :rule cong :premises (t49 t700))
% 0.49/0.86 (step t702 (cl (= (=> tptp.upairsetE true) true)) :rule all_simplify)
% 0.49/0.86 (step t703 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t701 t702))
% 0.49/0.86 (step t704 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.singletonsswitch true))) :rule cong :premises (t48 t703))
% 0.49/0.86 (step t705 (cl (= (=> tptp.singletonsswitch true) true)) :rule all_simplify)
% 0.49/0.86 (step t706 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t704 t705))
% 0.49/0.86 (step t707 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.eqinunit true))) :rule cong :premises (t47 t706))
% 0.49/0.86 (step t708 (cl (= (=> tptp.eqinunit true) true)) :rule all_simplify)
% 0.49/0.86 (step t709 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t707 t708))
% 0.49/0.86 (step t710 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notinsingleton true))) :rule cong :premises (t46 t709))
% 0.49/0.86 (step t711 (cl (= (=> tptp.notinsingleton true) true)) :rule all_simplify)
% 0.49/0.86 (step t712 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t710 t711))
% 0.49/0.86 (step t713 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.uniqinunit true))) :rule cong :premises (t45 t712))
% 0.49/0.86 (step t714 (cl (= (=> tptp.uniqinunit true) true)) :rule all_simplify)
% 0.49/0.86 (step t715 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t713 t714))
% 0.49/0.86 (step t716 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.nonemptyImpWitness true))) :rule cong :premises (t44 t715))
% 0.49/0.86 (step t717 (cl (= (=> tptp.nonemptyImpWitness true) true)) :rule all_simplify)
% 0.49/0.86 (step t718 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t716 t717))
% 0.49/0.86 (step t719 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuE2 true))) :rule cong :premises (t43 t718))
% 0.49/0.86 (step t720 (cl (= (=> tptp.exuE2 true) true)) :rule all_simplify)
% 0.49/0.86 (step t721 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t719 t720))
% 0.49/0.86 (step t722 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.subPowSU true))) :rule cong :premises (t42 t721))
% 0.49/0.86 (step t723 (cl (= (=> tptp.subPowSU true) true)) :rule all_simplify)
% 0.49/0.86 (step t724 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t722 t723))
% 0.49/0.86 (step t725 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionE true))) :rule cong :premises (t41 t724))
% 0.49/0.86 (step t726 (cl (= (=> tptp.setunionE true) true)) :rule all_simplify)
% 0.49/0.86 (step t727 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t725 t726))
% 0.49/0.86 (step t728 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionI true))) :rule cong :premises (t40 t727))
% 0.49/0.86 (step t729 (cl (= (=> tptp.setunionI true) true)) :rule all_simplify)
% 0.49/0.86 (step t730 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t728 t729))
% 0.49/0.86 (step t731 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetE true))) :rule cong :premises (t39 t730))
% 0.49/0.86 (step t732 (cl (= (=> tptp.powersetE true) true)) :rule all_simplify)
% 0.49/0.86 (step t733 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t731 t732))
% 0.49/0.86 (step t734 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyInPowerset true))) :rule cong :premises (t38 t733))
% 0.49/0.86 (step t735 (cl (= (=> tptp.emptyInPowerset true) true)) :rule all_simplify)
% 0.49/0.86 (step t736 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t734 t735))
% 0.49/0.86 (step t737 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyinPowerset true))) :rule cong :premises (t37 t736))
% 0.49/0.86 (step t738 (cl (= (=> tptp.emptyinPowerset true) true)) :rule all_simplify)
% 0.49/0.86 (step t739 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t737 t738))
% 0.49/0.86 (step t740 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetI true))) :rule cong :premises (t36 t739))
% 0.49/0.86 (step t741 (cl (= (=> tptp.powersetI true) true)) :rule all_simplify)
% 0.49/0.86 (step t742 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t740 t741))
% 0.49/0.86 (step t743 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setoftrueEq true))) :rule cong :premises (t35 t742))
% 0.49/0.86 (step t744 (cl (= (=> tptp.setoftrueEq true) true)) :rule all_simplify)
% 0.49/0.86 (step t745 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t743 t744))
% 0.49/0.86 (step t746 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinOr true))) :rule cong :premises (t34 t745))
% 0.49/0.86 (step t747 (cl (= (=> tptp.setadjoinOr true) true)) :rule all_simplify)
% 0.49/0.86 (step t748 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t746 t747))
% 0.49/0.86 (step t749 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinE true))) :rule cong :premises (t33 t748))
% 0.49/0.86 (step t750 (cl (= (=> tptp.setadjoinE true) true)) :rule all_simplify)
% 0.49/0.86 (step t751 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t749 t750))
% 0.49/0.86 (step t752 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinIR true))) :rule cong :premises (t32 t751))
% 0.49/0.86 (step t753 (cl (= (=> tptp.setadjoinIR true) true)) :rule all_simplify)
% 0.49/0.86 (step t754 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t752 t753))
% 0.49/0.86 (step t755 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyinunitempty true))) :rule cong :premises (t31 t754))
% 0.49/0.86 (step t756 (cl (= (=> tptp.emptyinunitempty true) true)) :rule all_simplify)
% 0.49/0.86 (step t757 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t755 t756))
% 0.49/0.86 (step t758 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinIL true))) :rule cong :premises (t30 t757))
% 0.49/0.86 (step t759 (cl (= (=> tptp.setadjoinIL true) true)) :rule all_simplify)
% 0.49/0.86 (step t760 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t758 t759))
% 0.49/0.86 (step t761 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.nonemptyI1 true))) :rule cong :premises (t29 t760))
% 0.49/0.86 (step t762 (cl (= (=> tptp.nonemptyI1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t763 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t761 t762))
% 0.49/0.86 (step t764 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.nonemptyI true))) :rule cong :premises (t28 t763))
% 0.49/0.86 (step t765 (cl (= (=> tptp.nonemptyI true) true)) :rule all_simplify)
% 0.49/0.86 (step t766 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t764 t765))
% 0.49/0.86 (step t767 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.nonemptyE1 true))) :rule cong :premises (t27 t766))
% 0.49/0.86 (step t768 (cl (= (=> tptp.nonemptyE1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t769 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t767 t768))
% 0.49/0.86 (step t770 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setbeta true))) :rule cong :premises (t26 t769))
% 0.49/0.86 (step t771 (cl (= (=> tptp.setbeta true) true)) :rule all_simplify)
% 0.49/0.86 (step t772 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t770 t771))
% 0.49/0.86 (step t773 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.noeltsimpempty true))) :rule cong :premises (t25 t772))
% 0.49/0.86 (step t774 (cl (= (=> tptp.noeltsimpempty true) true)) :rule all_simplify)
% 0.49/0.86 (step t775 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t773 t774))
% 0.49/0.86 (step t776 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptyI true))) :rule cong :premises (t24 t775))
% 0.49/0.86 (step t777 (cl (= (=> tptp.emptyI true) true)) :rule all_simplify)
% 0.49/0.86 (step t778 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t776 t777))
% 0.49/0.86 (step t779 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setext true))) :rule cong :premises (t23 t778))
% 0.49/0.86 (step t780 (cl (= (=> tptp.setext true) true)) :rule all_simplify)
% 0.49/0.86 (step t781 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t779 t780))
% 0.49/0.86 (step t782 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuE3e true))) :rule cong :premises (t22 t781))
% 0.49/0.86 (step t783 (cl (= (=> tptp.exuE3e true) true)) :rule all_simplify)
% 0.49/0.86 (step t784 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t782 t783))
% 0.49/0.86 (step t785 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.notinemptyset true))) :rule cong :premises (t21 t784))
% 0.49/0.86 (step t786 (cl (= (=> tptp.notinemptyset true) true)) :rule all_simplify)
% 0.49/0.86 (step t787 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t785 t786))
% 0.49/0.86 (step t788 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptysetimpfalse true))) :rule cong :premises (t20 t787))
% 0.49/0.86 (step t789 (cl (= (=> tptp.emptysetimpfalse true) true)) :rule all_simplify)
% 0.49/0.86 (step t790 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t788 t789))
% 0.49/0.86 (step t791 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptysetE true))) :rule cong :premises (t19 t790))
% 0.49/0.86 (step t792 (cl (= (=> tptp.emptysetE true) true)) :rule all_simplify)
% 0.49/0.86 (step t793 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t791 t792))
% 0.49/0.86 (step t794 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.prop2setE true))) :rule cong :premises (t18 t793))
% 0.49/0.86 (step t795 (cl (= (=> tptp.prop2setE true) true)) :rule all_simplify)
% 0.49/0.86 (step t796 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t794 t795))
% 0.49/0.86 (step t797 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.exuE1 true))) :rule cong :premises (t17 t796))
% 0.49/0.86 (step t798 (cl (= (=> tptp.exuE1 true) true)) :rule all_simplify)
% 0.49/0.86 (step t799 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t797 t798))
% 0.49/0.86 (step t800 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.dsetconstrER true))) :rule cong :premises (t16 t799))
% 0.49/0.86 (step t801 (cl (= (=> tptp.dsetconstrER true) true)) :rule all_simplify)
% 0.49/0.86 (step t802 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t800 t801))
% 0.49/0.86 (step t803 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.dsetconstrEL true))) :rule cong :premises (t15 t802))
% 0.49/0.86 (step t804 (cl (= (=> tptp.dsetconstrEL true) true)) :rule all_simplify)
% 0.49/0.86 (step t805 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t803 t804))
% 0.49/0.86 (step t806 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.dsetconstrI true))) :rule cong :premises (t14 t805))
% 0.49/0.86 (step t807 (cl (= (=> tptp.dsetconstrI true) true)) :rule all_simplify)
% 0.49/0.86 (step t808 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t806 t807))
% 0.49/0.86 (step t809 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.descrp true))) :rule cong :premises (t13 t808))
% 0.49/0.86 (step t810 (cl (= (=> tptp.descrp true) true)) :rule all_simplify)
% 0.49/0.86 (step t811 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t809 t810))
% 0.49/0.86 (step t812 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.wellorderingAx true))) :rule cong :premises (t12 t811))
% 0.49/0.86 (step t813 (cl (= (=> tptp.wellorderingAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t814 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t812 t813))
% 0.49/0.86 (step t815 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.foundationAx true))) :rule cong :premises (t11 t814))
% 0.49/0.86 (step t816 (cl (= (=> tptp.foundationAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t817 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t815 t816))
% 0.49/0.86 (step t818 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.replAx true))) :rule cong :premises (t10 t817))
% 0.49/0.86 (step t819 (cl (= (=> tptp.replAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t820 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t818 t819))
% 0.49/0.86 (step t821 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.omegaIndAx true))) :rule cong :premises (t9 t820))
% 0.49/0.86 (step t822 (cl (= (=> tptp.omegaIndAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t823 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t821 t822))
% 0.49/0.86 (step t824 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.omegaSAx true))) :rule cong :premises (t8 t823))
% 0.49/0.86 (step t825 (cl (= (=> tptp.omegaSAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t826 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t824 t825))
% 0.49/0.86 (step t827 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.omega0Ax true))) :rule cong :premises (t7 t826))
% 0.49/0.86 (step t828 (cl (= (=> tptp.omega0Ax true) true)) :rule all_simplify)
% 0.49/0.86 (step t829 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t827 t828))
% 0.49/0.86 (step t830 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setunionAx true))) :rule cong :premises (t6 t829))
% 0.49/0.86 (step t831 (cl (= (=> tptp.setunionAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t832 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t830 t831))
% 0.49/0.86 (step t833 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.powersetAx true))) :rule cong :premises (t5 t832))
% 0.49/0.86 (step t834 (cl (= (=> tptp.powersetAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t835 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t833 t834))
% 0.49/0.86 (step t836 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setadjoinAx true))) :rule cong :premises (t4 t835))
% 0.49/0.86 (step t837 (cl (= (=> tptp.setadjoinAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t838 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t836 t837))
% 0.49/0.86 (step t839 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.emptysetAx true))) :rule cong :premises (t3 t838))
% 0.49/0.86 (step t840 (cl (= (=> tptp.emptysetAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t841 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t839 t840))
% 0.49/0.86 (step t842 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (=> tptp.setextAx true))) :rule cong :premises (t2 t841))
% 0.49/0.86 (step t843 (cl (= (=> tptp.setextAx true) true)) :rule all_simplify)
% 0.49/0.86 (step t844 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) true)) :rule trans :premises (t842 t843))
% 0.49/0.86 (step t845 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (not true))) :rule cong :premises (t844))
% 0.49/0.86 (step t846 (cl (= (not true) false)) :rule all_simplify)
% 0.49/0.86 (step t847 (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 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) false)) :rule trans :premises (t845 t846))
% 0.49/0.87 (step t848 (cl false) :rule resolution :premises (t1 t847 a216))
% 0.49/0.87 (step t849 (cl (not false)) :rule false)
% 0.49/0.87 (step t850 (cl) :rule resolution :premises (t848 t849))
% 0.49/0.87
% 0.49/0.87 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.WNKjaM55nm/cvc5---1.0.5_16121.smt2
% 0.49/0.87 % cvc5---1.0.5 exiting
% 0.49/0.87 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------