%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM586+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:29 AM UTC 2025
% Result : Theorem 0.21s 0.48s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM586+3 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 01:33:01 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 tff(aElementOf0_type, type, (
% 0.21/0.48 aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.48 tff(szDzozmdt0_type, type, (
% 0.21/0.48 szDzozmdt0: $i > $i)).
% 0.21/0.48 tff(sdtlpdtrp0_type, type, (
% 0.21/0.48 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.21/0.48 tff(xi_type, type, (
% 0.21/0.48 xi: $i)).
% 0.21/0.48 tff(xC_type, type, (
% 0.21/0.48 xC: $i)).
% 0.21/0.48 tff(tptp_fun_W0_32_type, type, (
% 0.21/0.48 tptp_fun_W0_32: $i)).
% 0.21/0.48 tff(slbdtsldtrb0_type, type, (
% 0.21/0.48 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.21/0.48 tff(xk_type, type, (
% 0.21/0.48 xk: $i)).
% 0.21/0.48 tff(sdtmndt0_type, type, (
% 0.21/0.48 sdtmndt0: ( $i * $i ) > $i)).
% 0.21/0.48 tff(szmzizndt0_type, type, (
% 0.21/0.48 szmzizndt0: $i > $i)).
% 0.21/0.48 tff(xN_type, type, (
% 0.21/0.48 xN: $i)).
% 0.21/0.48 tff(tptp_fun_W2_31_type, type, (
% 0.21/0.48 tptp_fun_W2_31: ( $i * $i ) > $i)).
% 0.21/0.48 tff(aSet0_type, type, (
% 0.21/0.48 aSet0: $i > $o)).
% 0.21/0.48 tff(aSubsetOf0_type, type, (
% 0.21/0.48 aSubsetOf0: ( $i * $i ) > $o)).
% 0.21/0.48 tff(sbrdtbr0_type, type, (
% 0.21/0.48 sbrdtbr0: $i > $i)).
% 0.21/0.48 tff(sdtpldt0_type, type, (
% 0.21/0.48 sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.48 tff(aElement0_type, type, (
% 0.21/0.48 aElement0: $i > $o)).
% 0.21/0.48 tff(sdtlseqdt0_type, type, (
% 0.21/0.48 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.21/0.48 tff(xc_type, type, (
% 0.21/0.48 xc: $i)).
% 0.21/0.48 tff(aFunction0_type, type, (
% 0.21/0.48 aFunction0: $i > $o)).
% 0.21/0.48 tff(szNzAzT0_type, type, (
% 0.21/0.48 szNzAzT0: $i)).
% 0.21/0.48 tff(tptp_fun_W1_33_type, type, (
% 0.21/0.48 tptp_fun_W1_33: $i > $i)).
% 0.21/0.48 tff(xx_type, type, (
% 0.21/0.48 xx: $i)).
% 0.21/0.48 tff(sdtlcdtrc0_type, type, (
% 0.21/0.48 sdtlcdtrc0: ( $i * $i ) > $i)).
% 0.21/0.48 tff(1,plain,
% 0.21/0.48 (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(2,axiom,(aElementOf0(xi, szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4200')).
% 0.21/0.48 tff(3,plain,
% 0.21/0.48 (aElementOf0(xi, szNzAzT0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.48 tff(4,plain,
% 0.21/0.48 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.50 tff(8,plain,
% 0.21/0.50 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(9,plain,
% 0.21/0.50 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.50 tff(10,plain,
% 0.21/0.50 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[9, 7])).
% 0.21/0.50 tff(11,plain,
% 0.21/0.50 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(12,plain,
% 0.21/0.50 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.51 tff(13,plain,
% 0.21/0.51 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), 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)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(14,plain,
% 0.21/0.51 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), 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)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.51 tff(15,plain,
% 0.21/0.51 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(16,plain,
% 0.21/0.51 (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) <=> ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) <=> ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))))), ((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))), ((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), quant_intro(proof_bind(^[W1: $i] : rewrite(((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))))) <=> (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), (![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))))) <=> ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), ((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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)))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), ((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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)))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))))), (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)))), (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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))))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)))))) <=> (aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))), trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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))))))))), rewrite(((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))))), (![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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))))))) <=> ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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))))))))), ((((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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)))))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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))) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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))) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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))))))))), ((((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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)))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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(W0, szNzAzT0) => (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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))))))))))), rewrite((aElementOf0(W0, szNzAzT0) => (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))))))),
% 0.36/0.54 inference(bind,[status(th)],[])).
% 0.36/0.54 tff(17,plain,
% 0.36/0.54 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))))),
% 0.36/0.54 inference(quant_intro,[status(thm)],[16])).
% 0.36/0.54 tff(18,axiom,((aFunction0(xC) & (szDzozmdt0(xC) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4151')).
% 0.36/0.54 tff(19,plain,
% 0.36/0.54 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (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) & ![W2: $i] : (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))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (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)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (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)))))))))),
% 0.36/0.54 inference(and_elim,[status(thm)],[18])).
% 0.36/0.54 tff(20,plain,
% 0.36/0.54 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.36/0.54 tff(21,plain,
% 0.36/0.54 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, 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)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.36/0.54 tff(22,plain,(
% 0.36/0.54 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), 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)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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)))))))))),
% 0.36/0.54 inference(skolemize,[status(sab)],[21])).
% 0.36/0.54 tff(23,plain,
% 0.36/0.54 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~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))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (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(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.38/0.55 tff(24,plain,
% 0.38/0.55 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[23, 12])).
% 0.38/0.55 tff(25,plain,
% 0.38/0.55 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[24, 10])).
% 0.38/0.55 tff(26,plain,
% 0.38/0.55 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[25, 5])).
% 0.38/0.55 tff(27,plain,
% 0.38/0.55 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(28,plain,
% 0.38/0.55 (((~aElementOf0(xi, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))) <=> ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))))))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(29,plain,
% 0.38/0.56 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))))))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[28])).
% 0.38/0.56 tff(30,plain,
% 0.38/0.56 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))))))),
% 0.38/0.57 inference(transitivity,[status(thm)],[29, 27])).
% 0.38/0.57 tff(31,plain,
% 0.38/0.57 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(32,plain,
% 0.38/0.57 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.38/0.57 tff(33,plain,
% 0.38/0.57 (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[32, 26, 3])).
% 0.38/0.57 tff(34,plain,
% 0.38/0.57 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))))) | (szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(35,plain,
% 0.38/0.57 (szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.38/0.57 tff(36,plain,
% 0.38/0.57 (aElementOf0(W0!32, szDzozmdt0(sdtlpdtrp0(xC, xi))) <=> aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[35])).
% 0.38/0.57 tff(37,plain,
% 0.38/0.57 (aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) <=> aElementOf0(W0!32, szDzozmdt0(sdtlpdtrp0(xC, xi)))),
% 0.38/0.57 inference(symmetry,[status(thm)],[36])).
% 0.38/0.57 tff(38,plain,
% 0.38/0.57 ((~aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) <=> (~aElementOf0(W0!32, szDzozmdt0(sdtlpdtrp0(xC, xi))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[37])).
% 0.38/0.57 tff(39,plain,
% 0.38/0.57 (^[W0: $i] : rewrite(((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))) <=> ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(40,plain,
% 0.38/0.58 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))) <=> ![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[39])).
% 0.38/0.58 tff(41,plain,
% 0.38/0.58 (^[W0: $i] : refl(((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))) <=> ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(42,plain,
% 0.38/0.58 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))) <=> ![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[41])).
% 0.38/0.58 tff(43,plain,
% 0.38/0.58 (^[W0: $i] : rewrite(((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))) <=> ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(44,plain,
% 0.38/0.58 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))) <=> ![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[43])).
% 0.38/0.58 tff(45,plain,
% 0.38/0.58 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))) <=> ![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.58 inference(transitivity,[status(thm)],[44, 42])).
% 0.38/0.58 tff(46,plain,
% 0.38/0.58 (^[W0: $i] : rewrite(((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) <=> ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(47,plain,
% 0.38/0.58 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) <=> ![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[46])).
% 0.38/0.58 tff(48,plain,
% 0.38/0.58 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) <=> ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))), rewrite((aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) <=> (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))), rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))), (((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) <=> ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))), rewrite(((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) <=> ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))), (((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) <=> ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))), ((((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))) <=> (((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))))), rewrite((((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))) <=> ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))), ((((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))) <=> ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.59 inference(bind,[status(th)],[])).
% 0.38/0.59 tff(49,plain,
% 0.38/0.59 (![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))) <=> ![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))),
% 0.38/0.59 inference(quant_intro,[status(thm)],[48])).
% 0.38/0.59 tff(50,plain,
% 0.38/0.59 ((~?[W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))) <=> (~?[W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(51,plain,
% 0.38/0.59 ((~?[W0: $i] : (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) => ((((aSet0(W0) & ![W1: $i] : (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))) <=> (~?[W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(52,axiom,(~?[W0: $i] : (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) => ((((aSet0(W0) & ![W1: $i] : (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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.38/0.59 tff(53,plain,
% 0.38/0.59 (~?[W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.38/0.59 tff(54,plain,
% 0.38/0.59 (~?[W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.38/0.59 tff(55,plain,
% 0.38/0.59 (~?[W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.38/0.59 tff(56,plain,
% 0.38/0.59 (~?[W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[55, 50])).
% 0.38/0.59 tff(57,plain,
% 0.38/0.59 (^[W0: $i] : nnf_neg(nnf_neg(refl($oeq((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))), (~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))))), nnf_neg(nnf_neg(refl($oeq((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))), (~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))), nnf_neg(refl($oeq((~aSet0(W0)), (~aSet0(W0)))), sk($oeq((~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))), (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))), $oeq((~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))), ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))), $oeq((~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))), ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))), refl($oeq((~(sbrdtbr0(W0) = xk)), (~(sbrdtbr0(W0) = xk)))), $oeq((~((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk))), (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))))), nnf_neg(monotonicity(refl($oeq(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))), nnf_pos(proof_bind(^[W1: $i] : refl($oeq((aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))), (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))), $oeq(![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))), ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))), $oeq((aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))), (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))), $oeq((~(~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))), (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))), nnf_neg(monotonicity(refl($oeq(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)), aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)))), nnf_pos(proof_bind(^[W1: $i] : refl($oeq(((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)), ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))), $oeq(![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)), ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))), $oeq((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))), (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))), $oeq((~(~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))), (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))), $oeq((~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))), ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))), refl($oeq((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)), (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)))), $oeq((~((aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | ((aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(W0) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))), (((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)))))),
% 0.38/0.60 inference(bind,[status(th)],[])).
% 0.38/0.60 tff(58,plain,(
% 0.38/0.60 ![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(sbrdtbr0(W0) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)))),
% 0.38/0.60 inference(nnf-neg,[status(sab)],[56, 57])).
% 0.38/0.60 tff(59,plain,
% 0.38/0.60 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | ((~aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & ((~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, xi)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[58, 49])).
% 0.38/0.60 tff(60,plain,
% 0.38/0.60 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[59, 47])).
% 0.38/0.60 tff(61,plain,
% 0.38/0.60 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[60, 45])).
% 0.38/0.60 tff(62,plain,
% 0.38/0.60 (![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[61, 40])).
% 0.38/0.60 tff(63,plain,
% 0.38/0.60 (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(sdtlpdtrp0(xC, xi))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) <=> ?[W0: $i] : (aElementOf0(W0, szDzozmdt0(sdtlpdtrp0(xC, xi))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(64,axiom,(?[W0: $i] : (aElementOf0(W0, szDzozmdt0(sdtlpdtrp0(xC, xi))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) & aElementOf0(xx, sdtlcdtrc0(sdtlpdtrp0(xC, xi), szDzozmdt0(sdtlpdtrp0(xC, xi))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4200_02')).
% 0.38/0.60 tff(65,plain,
% 0.38/0.60 (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(sdtlpdtrp0(xC, xi))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))),
% 0.38/0.60 inference(and_elim,[status(thm)],[64])).
% 0.38/0.60 tff(66,plain,
% 0.38/0.60 (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(sdtlpdtrp0(xC, xi))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[65, 63])).
% 0.38/0.60 tff(67,plain,(
% 0.38/0.60 aElementOf0(W0!32, szDzozmdt0(sdtlpdtrp0(xC, xi))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)),
% 0.38/0.60 inference(skolemize,[status(sab)],[66])).
% 0.38/0.60 tff(68,plain,
% 0.38/0.60 (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx),
% 0.38/0.60 inference(and_elim,[status(thm)],[67])).
% 0.38/0.60 tff(69,plain,
% 0.38/0.60 (((~![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) | ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~((~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) <=> ((~![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~((~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(70,plain,
% 0.38/0.60 (((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~(aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~(aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1)))))) <=> ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~((~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(71,plain,
% 0.38/0.60 (((~![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) | ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~(aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~(aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) <=> ((~![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) | ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~((~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[70])).
% 0.38/0.60 tff(72,plain,
% 0.38/0.60 (((~![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) | ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~(aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~(aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) <=> ((~![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~((~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))),
% 0.38/0.61 inference(transitivity,[status(thm)],[71, 69])).
% 0.38/0.61 tff(73,plain,
% 0.38/0.61 ((~![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) | ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~(aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~(aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(74,plain,
% 0.38/0.61 ((~![W0: $i] : ((~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0) = xx)) | (~(aElementOf0(W0, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_33(W0), W0)) | aElementOf0(tptp_fun_W1_33(W0), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!32) = xx)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~((~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.38/0.61 tff(75,plain,
% 0.38/0.61 (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~((~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[74, 68, 62])).
% 0.38/0.61 tff(76,plain,
% 0.38/0.61 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~((~(sbrdtbr0(W0!32) = xk)) | (~((~((~aSet0(W0!32)) | (~((~aElementOf0(tptp_fun_W1_33(W0!32), W0!32)) | aElementOf0(tptp_fun_W1_33(W0!32), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | aSubsetOf0(W0!32, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)))),
% 0.38/0.62 inference(tautology,[status(thm)],[])).
% 0.38/0.62 tff(77,plain,
% 0.38/0.62 (~aElementOf0(W0!32, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.38/0.62 tff(78,plain,
% 0.38/0.62 (~aElementOf0(W0!32, szDzozmdt0(sdtlpdtrp0(xC, xi)))),
% 0.38/0.62 inference(modus_ponens,[status(thm)],[77, 38])).
% 0.38/0.62 tff(79,plain,
% 0.38/0.62 (aElementOf0(W0!32, szDzozmdt0(sdtlpdtrp0(xC, xi)))),
% 0.38/0.62 inference(and_elim,[status(thm)],[67])).
% 0.38/0.62 tff(80,plain,
% 0.38/0.62 ($false),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.38/0.62 % SZS output end Proof
% 0.38/0.62 % E exiting
%------------------------------------------------------------------------------