TSTP Solution File: NUM586+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM586+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n017.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 : 600s
% DateTime : Mon Jul 18 14:43:53 EDT 2022
% Result : Theorem 244.37s 244.55s
% Output : Proof 244.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM586+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jul 7 07:57:15 EDT 2022
% 0.14/0.34 % CPUTime :
% 244.37/244.55 % SZS status Theorem
% 244.37/244.55 (* PROOF-FOUND *)
% 244.37/244.55 (* BEGIN-PROOF *)
% 244.37/244.55 % SZS output start Proof
% 244.37/244.55 1. (aElementOf0 (xi) (szNzAzT0)) (-. (aElementOf0 (xi) (szNzAzT0))) ### Axiom
% 244.37/244.55 2. (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))) ### Axiom
% 244.37/244.55 3. (-. (aSet0 T_0)) (aSet0 T_0) ### Axiom
% 244.37/244.55 4. ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk))))) (-. (aSet0 T_0)) ### ConjTree 3
% 244.37/244.55 5. ((aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk)))))) (-. (aSet0 T_0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ### Imply 2 4
% 244.37/244.55 6. (((aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk)))))) /\ (((((aSet0 T_0) /\ (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 T_0) = (xk))) => (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (aSet0 T_0)) ### And 5
% 244.37/244.55 7. (All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) (-. (aSet0 T_0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ### All 6
% 244.37/244.55 8. ((aFunction0 (sdtlpdtrp0 (xC) (xi))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) (xi))) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))))))))))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (aSet0 T_0)) ### ConjTree 7
% 244.37/244.55 9. ((aElementOf0 (xi) (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) (xi))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) (xi))) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))))))))))))) (-. (aSet0 T_0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (aElementOf0 (xi) (szNzAzT0)) ### Imply 1 8
% 244.37/244.55 10. (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (aSet0 T_0)) ### All 9
% 244.37/244.55 11. (aElementOf0 (xi) (szNzAzT0)) (-. (aElementOf0 (xi) (szNzAzT0))) ### Axiom
% 244.37/244.55 12. (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))) ### Axiom
% 244.37/244.55 13. (-. (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) ### Axiom
% 244.37/244.55 14. ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk))))) (-. (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) ### ConjTree 13
% 244.37/244.55 15. ((aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk)))))) (-. (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ### Imply 12 14
% 244.37/244.55 16. (((aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk)))))) /\ (((((aSet0 T_0) /\ (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 T_0) = (xk))) => (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) ### And 15
% 244.37/244.55 17. (All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) (-. (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ### All 16
% 244.37/244.55 18. ((aFunction0 (sdtlpdtrp0 (xC) (xi))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) (xi))) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))))))))))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) ### ConjTree 17
% 244.37/244.55 19. ((aElementOf0 (xi) (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) (xi))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) (xi))) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))))))))))))) (-. (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (aElementOf0 (xi) (szNzAzT0)) ### Imply 11 18
% 244.37/244.55 20. (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) ### All 19
% 244.37/244.55 21. (-. ((aSet0 T_0) /\ (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (aElementOf0 (xi) (szNzAzT0)) (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) ### NotAnd 10 20
% 244.37/244.56 22. (-. (((aSet0 T_0) /\ (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ### NotOr 21
% 244.37/244.56 23. (aElementOf0 (xi) (szNzAzT0)) (-. (aElementOf0 (xi) (szNzAzT0))) ### Axiom
% 244.37/244.56 24. (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (-. (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))) ### Axiom
% 244.37/244.56 25. ((sbrdtbr0 T_0) != (xk)) ((sbrdtbr0 T_0) = (xk)) ### Axiom
% 244.37/244.56 26. ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk))))) ((sbrdtbr0 T_0) != (xk)) ### ConjTree 25
% 244.37/244.56 27. ((aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk)))))) ((sbrdtbr0 T_0) != (xk)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ### Imply 24 26
% 244.37/244.56 28. (((aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 T_0) /\ ((All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 T_0) = (xk)))))) /\ (((((aSet0 T_0) /\ (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 T_0) = (xk))) => (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ((sbrdtbr0 T_0) != (xk)) ### And 27
% 244.37/244.56 29. (All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) ((sbrdtbr0 T_0) != (xk)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ### All 28
% 244.37/244.56 30. ((aFunction0 (sdtlpdtrp0 (xC) (xi))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) (xi))) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))))))))))))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ((sbrdtbr0 T_0) != (xk)) ### ConjTree 29
% 244.37/244.56 31. ((aElementOf0 (xi) (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) (xi))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi))))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) (xi))) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))))))))))))) ((sbrdtbr0 T_0) != (xk)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (aElementOf0 (xi) (szNzAzT0)) ### Imply 23 30
% 244.37/244.56 32. (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ((sbrdtbr0 T_0) != (xk)) ### All 31
% 244.37/244.56 33. (-. ((((aSet0 T_0) /\ (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 T_0) = (xk)))) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (aElementOf0 (xi) (szNzAzT0)) (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) ### NotAnd 22 32
% 244.40/244.57 34. (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => (((((aSet0 T_0) /\ (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 T_0) = (xk))) \/ (aElementOf0 T_0 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk))))))) (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ### ConjTree 33
% 244.40/244.57 35. ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) T_0) = (xx)) ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) T_0) != (xx)) ### Axiom
% 244.40/244.57 36. (-. ((((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => (((((aSet0 T_0) /\ (All W1, ((aElementOf0 W1 T_0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 T_0) = (xk))) \/ (aElementOf0 T_0 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk)))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) T_0) = (xx)))) ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) T_0) = (xx)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (aElementOf0 (xi) (szNzAzT0)) (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) ### NotAnd 34 35
% 244.40/244.57 37. (-. (Ex W0, ((((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => (((((aSet0 W0) /\ (All W1, ((aElementOf0 W1 W0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W0) = (xk))) \/ (aElementOf0 W0 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk)))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W0) = (xx))))) (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) T_0) = (xx)) ### NotExists 36
% 244.40/244.57 38. ((aFunction0 (xC)) /\ (((szDzozmdt0 (xC)) = (szNzAzT0)) /\ (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))))) ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) T_0) = (xx)) (aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) (aElementOf0 (xi) (szNzAzT0)) (-. (Ex W0, ((((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => (((((aSet0 W0) /\ (All W1, ((aElementOf0 W1 W0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W0) = (xk))) \/ (aElementOf0 W0 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk)))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W0) = (xx))))) ### ConjTree 37
% 244.40/244.57 39. ((aElementOf0 T_0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) T_0) = (xx))) (-. (Ex W0, ((((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => (((((aSet0 W0) /\ (All W1, ((aElementOf0 W1 W0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W0) = (xk))) \/ (aElementOf0 W0 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk)))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W0) = (xx))))) (aElementOf0 (xi) (szNzAzT0)) ((aFunction0 (xC)) /\ (((szDzozmdt0 (xC)) = (szNzAzT0)) /\ (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))))) ### And 38
% 244.40/244.57 40. (Ex W0, ((aElementOf0 W0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W0) = (xx)))) ((aFunction0 (xC)) /\ (((szDzozmdt0 (xC)) = (szNzAzT0)) /\ (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))))) (aElementOf0 (xi) (szNzAzT0)) (-. (Ex W0, ((((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => (((((aSet0 W0) /\ (All W1, ((aElementOf0 W1 W0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W0) = (xk))) \/ (aElementOf0 W0 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk)))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W0) = (xx))))) ### Exists 39
% 244.40/244.57 41. ((Ex W0, ((aElementOf0 W0 (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W0) = (xx)))) /\ (aElementOf0 (xx) (sdtlcdtrc0 (sdtlpdtrp0 (xC) (xi)) (szDzozmdt0 (sdtlpdtrp0 (xC) (xi)))))) (-. (Ex W0, ((((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))) => (((((aSet0 W0) /\ (All W1, ((aElementOf0 W1 W0) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) \/ (aSubsetOf0 W0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))) /\ ((sbrdtbr0 W0) = (xk))) \/ (aElementOf0 W0 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) (xk)))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xi)) W0) = (xx))))) (aElementOf0 (xi) (szNzAzT0)) ((aFunction0 (xC)) /\ (((szDzozmdt0 (xC)) = (szNzAzT0)) /\ (All W0, ((aElementOf0 W0 (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) W0)) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) W0)))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) W0)) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) W0) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))))))))))))))) ### And 40
% 244.40/244.57 % SZS output end Proof
% 244.40/244.57 (* END-PROOF *)
%------------------------------------------------------------------------------