TSTP Solution File: NUM630+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM630+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 : n024.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 14:44:18 EDT 2022
% Result : Theorem 9.55s 9.71s
% Output : Proof 9.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM630+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 04:33:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 9.55/9.71 % SZS status Theorem
% 9.55/9.71 (* PROOF-FOUND *)
% 9.55/9.71 (* BEGIN-PROOF *)
% 9.55/9.71 % SZS output start Proof
% 9.55/9.71 1. (aElementOf0 (xn) (szNzAzT0)) (-. (aElementOf0 (xn) (szNzAzT0))) ### Axiom
% 9.55/9.71 2. (aSet0 (xP)) (-. (aSet0 (xP))) ### Axiom
% 9.55/9.71 3. ((xP) != (xP)) ### NotEqual
% 9.55/9.71 4. ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) ((xD) != (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) ### Axiom
% 9.55/9.71 5. ((xk) != (xk)) ### NotEqual
% 9.55/9.71 6. ((slbdtsldtrb0 (xD) (xk)) != (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk))) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) ### NotEqual 4 5
% 9.55/9.71 7. (-. (aElementOf0 (xP) (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk)))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) ### P-NotP 3 6
% 9.55/9.71 8. (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xn))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))) => ((((All W2, ((aElementOf0 W2 (xP)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))) \/ (aSubsetOf0 (xP) (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))) /\ ((sbrdtbr0 (xP)) = (xk))) \/ (aElementOf0 (xP) (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk))))))) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ### ConjTree 7
% 9.55/9.71 9. ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP)) = (sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))) ### Sym(=)
% 9.55/9.71 10. ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((All W0, ((aElementOf0 W0 (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xP)) \/ (W0 = (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP)) = (sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) ### ConjTree 9
% 9.55/9.71 11. (((aSet0 (xP)) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xn))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))) => ((((All W2, ((aElementOf0 W2 (xP)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))) \/ (aSubsetOf0 (xP) (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))) /\ ((sbrdtbr0 (xP)) = (xk))) \/ (aElementOf0 (xP) (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((All W0, ((aElementOf0 W0 (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xP)) \/ (W0 = (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP)) = (sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))))) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) (aSet0 (xP)) ### DisjTree 2 8 10
% 9.55/9.71 12. (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xn))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))))) (aSet0 (xP)) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) ### All 11
% 9.55/9.71 13. ((aFunction0 (sdtlpdtrp0 (xC) (xn))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xn))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xn)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xn))))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) (xn))) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xn))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))))))))))))) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) (aSet0 (xP)) ### ConjTree 12
% 9.55/9.71 14. ((aElementOf0 (xn) (szNzAzT0)) => ((aFunction0 (sdtlpdtrp0 (xC) (xn))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xn))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((All W1, (((aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xn)))) => ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ ((sbrdtbr0 W1) = (xk)))))) /\ (((((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))) /\ ((sbrdtbr0 W1) = (xk))) => (aElementOf0 W1 (szDzozmdt0 (sdtlpdtrp0 (xC) (xn))))))) /\ (((szDzozmdt0 (sdtlpdtrp0 (xC) (xn))) = (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk))) /\ (All W1, (((aSet0 W1) /\ (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xn))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))) => ((((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))) \/ (aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))) /\ ((sbrdtbr0 W1) = (xk))) \/ (aElementOf0 W1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))) (xk))))))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) (sdtlpdtrp0 (xN) (xn))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((All W2, ((aElementOf0 W2 (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W2) /\ ((aElementOf0 W2 W1) \/ (W2 = (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) W1) = (sdtlpdtrp0 (xc) (sdtpldt0 W1 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))))))))))))) (aSet0 (xP)) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) (aElementOf0 (xn) (szNzAzT0)) ### Imply 1 13
% 9.55/9.71 15. (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 (xn) (szNzAzT0)) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) (aSet0 (xP)) ### All 14
% 9.55/9.71 16. ((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))))))))))))))))))))) (aSet0 (xP)) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) (aElementOf0 (xn) (szNzAzT0)) ### ConjTree 15
% 9.55/9.71 17. ((aSet0 (xP)) /\ ((All W0, ((aElementOf0 W0 (xQ)) => (sdtlseqdt0 (szmzizndt0 (xQ)) W0))) /\ ((All W0, ((aElementOf0 W0 (xP)) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xQ)) /\ (W0 != (szmzizndt0 (xQ))))))) /\ ((xP) = (sdtmndt0 (xQ) (szmzizndt0 (xQ))))))) (aElementOf0 (xn) (szNzAzT0)) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) ((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))))))))))))))))))))) ### ConjTree 16
% 9.55/9.71 18. ((aElementOf0 (xn) (szDzozmdt0 (xd))) /\ (((sdtlpdtrp0 (xd) (xn)) = (szDzizrdt0 (xd))) /\ ((aElementOf0 (xn) (sdtlbdtrb0 (xd) (szDzizrdt0 (xd)))) /\ ((aElementOf0 (xn) (szNzAzT0)) /\ ((sdtlpdtrp0 (xe) (xn)) = (xp)))))) ((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))))))))))))))))))))) ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) ((aSet0 (xP)) /\ ((All W0, ((aElementOf0 W0 (xQ)) => (sdtlseqdt0 (szmzizndt0 (xQ)) W0))) /\ ((All W0, ((aElementOf0 W0 (xP)) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xQ)) /\ (W0 != (szmzizndt0 (xQ))))))) /\ ((xP) = (sdtmndt0 (xQ) (szmzizndt0 (xQ))))))) ### ConjTree 17
% 9.55/9.71 19. ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((aSet0 (xD)) /\ ((All W0, ((aElementOf0 W0 (xD)) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) /\ (W0 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) ((aSet0 (xP)) /\ ((All W0, ((aElementOf0 W0 (xQ)) => (sdtlseqdt0 (szmzizndt0 (xQ)) W0))) /\ ((All W0, ((aElementOf0 W0 (xP)) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xQ)) /\ (W0 != (szmzizndt0 (xQ))))))) /\ ((xP) = (sdtmndt0 (xQ) (szmzizndt0 (xQ))))))) ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))) ((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 (xn) (szDzozmdt0 (xd))) /\ (((sdtlpdtrp0 (xd) (xn)) = (szDzizrdt0 (xd))) /\ ((aElementOf0 (xn) (sdtlbdtrb0 (xd) (szDzizrdt0 (xd)))) /\ ((aElementOf0 (xn) (szNzAzT0)) /\ ((sdtlpdtrp0 (xe) (xn)) = (xp)))))) ### ConjTree 18
% 9.55/9.71 20. ((All W0, ((aElementOf0 W0 (xP)) => (aElementOf0 W0 (xD)))) /\ ((aSubsetOf0 (xP) (xD)) /\ (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))))) ((aElementOf0 (xn) (szDzozmdt0 (xd))) /\ (((sdtlpdtrp0 (xd) (xn)) = (szDzizrdt0 (xd))) /\ ((aElementOf0 (xn) (sdtlbdtrb0 (xd) (szDzizrdt0 (xd)))) /\ ((aElementOf0 (xn) (szNzAzT0)) /\ ((sdtlpdtrp0 (xe) (xn)) = (xp)))))) ((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 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) != (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP))) ((aSet0 (xP)) /\ ((All W0, ((aElementOf0 W0 (xQ)) => (sdtlseqdt0 (szmzizndt0 (xQ)) W0))) /\ ((All W0, ((aElementOf0 W0 (xP)) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xQ)) /\ (W0 != (szmzizndt0 (xQ))))))) /\ ((xP) = (sdtmndt0 (xQ) (szmzizndt0 (xQ))))))) ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((aSet0 (xD)) /\ ((All W0, ((aElementOf0 W0 (xD)) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) /\ (W0 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) ### ConjTree 19
% 9.55/9.71 21. (-. ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) => (((aSet0 (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) /\ (All W0, ((aElementOf0 W0 (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xP)) \/ (W0 = (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))))))) => ((sdtlpdtrp0 (xc) (sdtpldt0 (xP) (szmzizndt0 (sdtlpdtrp0 (xN) (xn))))) = (sdtlpdtrp0 (sdtlpdtrp0 (xC) (xn)) (xP)))))) ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xn))) W0))) /\ ((aSet0 (xD)) /\ ((All W0, ((aElementOf0 W0 (xD)) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xn))) /\ (W0 != (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) /\ ((xD) = (sdtmndt0 (sdtlpdtrp0 (xN) (xn)) (szmzizndt0 (sdtlpdtrp0 (xN) (xn)))))))) ((aSet0 (xP)) /\ ((All W0, ((aElementOf0 W0 (xQ)) => (sdtlseqdt0 (szmzizndt0 (xQ)) W0))) /\ ((All W0, ((aElementOf0 W0 (xP)) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xQ)) /\ (W0 != (szmzizndt0 (xQ))))))) /\ ((xP) = (sdtmndt0 (xQ) (szmzizndt0 (xQ))))))) ((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 (xn) (szDzozmdt0 (xd))) /\ (((sdtlpdtrp0 (xd) (xn)) = (szDzizrdt0 (xd))) /\ ((aElementOf0 (xn) (sdtlbdtrb0 (xd) (szDzizrdt0 (xd)))) /\ ((aElementOf0 (xn) (szNzAzT0)) /\ ((sdtlpdtrp0 (xe) (xn)) = (xp)))))) ((All W0, ((aElementOf0 W0 (xP)) => (aElementOf0 W0 (xD)))) /\ ((aSubsetOf0 (xP) (xD)) /\ (aElementOf0 (xP) (slbdtsldtrb0 (xD) (xk))))) ### ConjTree 20
% 9.55/9.72 % SZS output end Proof
% 9.55/9.72 (* END-PROOF *)
%------------------------------------------------------------------------------