%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM585+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 1.05s 1.22s
% Output : Proof 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM585+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.19/0.33 % Computer : n005.cluster.edu
% 0.19/0.33 % Model : x86_64 x86_64
% 0.19/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.33 % Memory : 8042.1875MB
% 0.19/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.33 % CPULimit : 300
% 0.19/0.33 % WCLimit : 300
% 0.19/0.33 % DateTime : Fri Jun 20 01:31:20 EDT 2025
% 0.19/0.33 % CPUTime :
% 1.05/1.22 % SZS status Theorem
% 1.05/1.22 % SZS output start Proof
% 1.05/1.22 tff(aElementOf0_type, type, (
% 1.05/1.22 aElementOf0: ( $i * $i ) > $o)).
% 1.05/1.22 tff(szDzozmdt0_type, type, (
% 1.05/1.22 szDzozmdt0: $i > $i)).
% 1.05/1.22 tff(xc_type, type, (
% 1.05/1.22 xc: $i)).
% 1.05/1.22 tff(sdtpldt0_type, type, (
% 1.05/1.22 sdtpldt0: ( $i * $i ) > $i)).
% 1.05/1.22 tff(szmzizndt0_type, type, (
% 1.05/1.22 szmzizndt0: $i > $i)).
% 1.05/1.22 tff(sdtlpdtrp0_type, type, (
% 1.05/1.22 sdtlpdtrp0: ( $i * $i ) > $i)).
% 1.05/1.22 tff(tptp_fun_W0_32_type, type, (
% 1.05/1.22 tptp_fun_W0_32: $i)).
% 1.05/1.22 tff(xN_type, type, (
% 1.05/1.22 xN: $i)).
% 1.05/1.22 tff(tptp_fun_W2_34_type, type, (
% 1.05/1.22 tptp_fun_W2_34: $i > $i)).
% 1.05/1.22 tff(tptp_fun_W1_33_type, type, (
% 1.05/1.22 tptp_fun_W1_33: $i)).
% 1.05/1.22 tff(xC_type, type, (
% 1.05/1.22 xC: $i)).
% 1.05/1.22 tff(sdtlcdtrc0_type, type, (
% 1.05/1.22 sdtlcdtrc0: ( $i * $i ) > $i)).
% 1.05/1.22 tff(aSet0_type, type, (
% 1.05/1.22 aSet0: $i > $o)).
% 1.05/1.22 tff(xT_type, type, (
% 1.05/1.22 xT: $i)).
% 1.05/1.22 tff(szNzAzT0_type, type, (
% 1.05/1.22 szNzAzT0: $i)).
% 1.05/1.22 tff(aSubsetOf0_type, type, (
% 1.05/1.22 aSubsetOf0: ( $i * $i ) > $o)).
% 1.05/1.22 tff(aElement0_type, type, (
% 1.05/1.22 aElement0: $i > $o)).
% 1.05/1.22 tff(sdtlseqdt0_type, type, (
% 1.05/1.22 sdtlseqdt0: ( $i * $i ) > $o)).
% 1.05/1.22 tff(sdtmndt0_type, type, (
% 1.05/1.22 sdtmndt0: ( $i * $i ) > $i)).
% 1.05/1.22 tff(xk_type, type, (
% 1.05/1.22 xk: $i)).
% 1.05/1.22 tff(sbrdtbr0_type, type, (
% 1.05/1.22 sbrdtbr0: $i > $i)).
% 1.05/1.22 tff(tptp_fun_W2_31_type, type, (
% 1.05/1.22 tptp_fun_W2_31: ( $i * $i ) > $i)).
% 1.05/1.22 tff(slbdtsldtrb0_type, type, (
% 1.05/1.22 slbdtsldtrb0: ( $i * $i ) > $i)).
% 1.05/1.22 tff(aFunction0_type, type, (
% 1.05/1.22 aFunction0: $i > $o)).
% 1.05/1.22 tff(tptp_fun_W1_20_type, type, (
% 1.05/1.22 tptp_fun_W1_20: $i > $i)).
% 1.05/1.22 tff(xK_type, type, (
% 1.05/1.22 xK: $i)).
% 1.05/1.22 tff(xS_type, type, (
% 1.05/1.22 xS: $i)).
% 1.05/1.22 tff(tptp_fun_W1_19_type, type, (
% 1.05/1.22 tptp_fun_W1_19: $i > $i)).
% 1.05/1.22 tff(1,plain,
% 1.05/1.22 (^[W1: $i] : refl((~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))))),
% 1.05/1.22 inference(bind,[status(th)],[])).
% 1.05/1.22 tff(2,plain,
% 1.05/1.22 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.05/1.22 inference(quant_intro,[status(thm)],[1])).
% 1.05/1.22 tff(3,plain,
% 1.05/1.22 (^[W1: $i] : rewrite((~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))))),
% 1.05/1.22 inference(bind,[status(th)],[])).
% 1.05/1.22 tff(4,plain,
% 1.05/1.22 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.05/1.22 inference(quant_intro,[status(thm)],[3])).
% 1.05/1.22 tff(5,plain,
% 1.05/1.22 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.05/1.22 inference(transitivity,[status(thm)],[4, 2])).
% 1.05/1.22 tff(6,plain,
% 1.05/1.22 (^[W1: $i] : trans(monotonicity(rewrite(((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) <=> ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))), rewrite((aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))) <=> (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))), ((((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) <=> (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))), rewrite((((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) <=> (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))), ((((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) <=> (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))))),
% 1.05/1.22 inference(bind,[status(th)],[])).
% 1.05/1.22 tff(7,plain,
% 1.05/1.22 (![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.05/1.22 inference(quant_intro,[status(thm)],[6])).
% 1.05/1.22 tff(8,plain,
% 1.05/1.22 (((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & aElementOf0(W0!32, szNzAzT0) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & aElementOf0(W0!32, szNzAzT0) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(9,plain,
% 1.05/1.22 ((aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))) <=> (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(10,plain,
% 1.05/1.22 (((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & aElementOf0(W0!32, szNzAzT0) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & aElementOf0(W0!32, szNzAzT0) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[9])).
% 1.05/1.22 tff(11,plain,
% 1.05/1.22 (((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & aElementOf0(W0!32, szNzAzT0) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & aElementOf0(W0!32, szNzAzT0) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))),
% 1.05/1.23 inference(transitivity,[status(thm)],[10, 8])).
% 1.05/1.23 tff(12,plain,
% 1.05/1.23 ((~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))) <=> (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(13,plain,
% 1.05/1.23 ((~![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) => (![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) => aElementOf0(W1, xT)) | aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT))))) <=> (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(14,axiom,(~![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) => (![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) => aElementOf0(W1, xT)) | aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.05/1.23 tff(15,plain,
% 1.05/1.23 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.05/1.23 tff(16,plain,
% 1.05/1.23 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[15, 12])).
% 1.05/1.23 tff(17,plain,
% 1.05/1.23 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.05/1.23 tff(18,plain,
% 1.05/1.23 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[17, 12])).
% 1.05/1.23 tff(19,plain,
% 1.05/1.23 ((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & aElementOf0(W0!32, szNzAzT0) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[18, 11])).
% 1.05/1.23 tff(20,plain,
% 1.05/1.23 (![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))),
% 1.05/1.23 inference(and_elim,[status(thm)],[19])).
% 1.05/1.23 tff(21,plain,
% 1.05/1.23 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[20, 7])).
% 1.05/1.23 tff(22,plain,
% 1.05/1.23 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[21, 5])).
% 1.07/1.23 tff(23,plain,
% 1.07/1.23 (((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33))))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(24,plain,
% 1.07/1.23 ((~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33))))))) <=> (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(25,plain,
% 1.07/1.23 (((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33))))))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[24])).
% 1.07/1.23 tff(26,plain,
% 1.07/1.23 (((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33))))))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[25, 23])).
% 1.07/1.23 tff(27,plain,
% 1.07/1.23 ((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(28,plain,
% 1.07/1.23 ((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.07/1.23 tff(29,plain,
% 1.07/1.23 (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33))))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[28, 22])).
% 1.07/1.23 tff(30,plain,
% 1.07/1.23 (((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))) | ((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))),
% 1.07/1.23 inference(tautology,[status(thm)],[])).
% 1.07/1.23 tff(31,plain,
% 1.07/1.23 ((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.07/1.23 tff(32,plain,
% 1.07/1.23 (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))),
% 1.07/1.23 inference(and_elim,[status(thm)],[19])).
% 1.07/1.23 tff(33,plain,
% 1.07/1.23 (aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))),
% 1.07/1.23 inference(or_elim,[status(thm)],[32])).
% 1.07/1.23 tff(34,plain,
% 1.07/1.23 ((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))))),
% 1.07/1.23 inference(tautology,[status(thm)],[])).
% 1.07/1.23 tff(35,plain,
% 1.07/1.23 ((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))))) | (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[34, 33])).
% 1.07/1.23 tff(36,plain,
% 1.07/1.23 (~((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[35, 31])).
% 1.07/1.23 tff(37,plain,
% 1.07/1.23 (((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)),
% 1.07/1.23 inference(tautology,[status(thm)],[])).
% 1.07/1.23 tff(38,plain,
% 1.07/1.23 (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[37, 36])).
% 1.07/1.23 tff(39,plain,
% 1.07/1.23 (aElementOf0(W0!32, szNzAzT0)),
% 1.07/1.23 inference(and_elim,[status(thm)],[19])).
% 1.07/1.23 tff(40,plain,
% 1.07/1.23 (^[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)))))))))))))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(41,plain,
% 1.07/1.23 (![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))))))))))))))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[40])).
% 1.07/1.24 tff(42,plain,
% 1.07/1.24 (^[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))))))))))))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(43,plain,
% 1.07/1.24 (![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)))))))))))))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[42])).
% 1.07/1.24 tff(44,plain,
% 1.07/1.24 (^[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))))))))))))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(45,plain,
% 1.07/1.24 (![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)))))))))))))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[44])).
% 1.07/1.24 tff(46,plain,
% 1.07/1.24 (![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)))))))))))))),
% 1.07/1.24 inference(transitivity,[status(thm)],[45, 43])).
% 1.07/1.24 tff(47,plain,
% 1.07/1.24 (^[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))))))))))))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(48,plain,
% 1.07/1.24 (![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)))))))))))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[47])).
% 1.07/1.25 tff(49,plain,
% 1.07/1.25 (^[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)))))))))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(50,plain,
% 1.07/1.25 (![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))))))))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[49])).
% 1.07/1.25 tff(51,plain,
% 1.07/1.25 (![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)))))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(52,plain,
% 1.07/1.25 (^[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)))))))))))),
% 1.07/1.27 inference(bind,[status(th)],[])).
% 1.07/1.27 tff(53,plain,
% 1.07/1.27 (![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)))))))))),
% 1.07/1.27 inference(quant_intro,[status(thm)],[52])).
% 1.07/1.27 tff(54,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')).
% 1.07/1.27 tff(55,plain,
% 1.07/1.27 (![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)))))))))),
% 1.07/1.27 inference(and_elim,[status(thm)],[54])).
% 1.07/1.27 tff(56,plain,
% 1.07/1.27 (![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)))))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[55, 53])).
% 1.07/1.27 tff(57,plain,
% 1.07/1.27 (![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)))))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[56, 51])).
% 1.07/1.27 tff(58,plain,(
% 1.07/1.27 ![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)))))))))),
% 1.07/1.27 inference(skolemize,[status(sab)],[57])).
% 1.07/1.27 tff(59,plain,
% 1.07/1.27 (![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))))))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[58, 50])).
% 1.07/1.27 tff(60,plain,
% 1.07/1.27 (![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)))))))))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[59, 48])).
% 1.07/1.28 tff(61,plain,
% 1.07/1.28 (![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)))))))))))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[60, 46])).
% 1.07/1.28 tff(62,plain,
% 1.07/1.28 (![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))))))))))))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[61, 41])).
% 1.07/1.28 tff(63,plain,
% 1.07/1.28 (((~![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(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))))) <=> ((~![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(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(64,plain,
% 1.07/1.28 (((~aElementOf0(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))) <=> ((~aElementOf0(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(65,plain,
% 1.07/1.28 (((~![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(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) <=> ((~![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(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))))))),
% 1.07/1.29 inference(monotonicity,[status(thm)],[64])).
% 1.07/1.29 tff(66,plain,
% 1.07/1.29 (((~![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(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) <=> ((~![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(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))))),
% 1.07/1.29 inference(transitivity,[status(thm)],[65, 63])).
% 1.07/1.29 tff(67,plain,
% 1.07/1.29 ((~![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(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.07/1.29 inference(quant_inst,[status(thm)],[])).
% 1.07/1.29 tff(68,plain,
% 1.07/1.29 ((~![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(W0!32, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))))),
% 1.07/1.29 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.07/1.29 tff(69,plain,
% 1.07/1.29 (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[68, 62, 39])).
% 1.07/1.29 tff(70,plain,
% 1.07/1.29 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))) | ![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(71,plain,
% 1.07/1.29 (![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.07/1.30 tff(72,plain,
% 1.07/1.30 (((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~((~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~((~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.07/1.30 inference(rewrite,[status(thm)],[])).
% 1.07/1.30 tff(73,plain,
% 1.07/1.30 ((~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))) <=> (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~((~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.07/1.30 inference(rewrite,[status(thm)],[])).
% 1.07/1.30 tff(74,plain,
% 1.07/1.30 (((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~((~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.07/1.30 inference(monotonicity,[status(thm)],[73])).
% 1.07/1.30 tff(75,plain,
% 1.07/1.30 (((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~((~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.07/1.30 inference(transitivity,[status(thm)],[74, 72])).
% 1.07/1.30 tff(76,plain,
% 1.07/1.30 ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.07/1.30 inference(quant_inst,[status(thm)],[])).
% 1.07/1.30 tff(77,plain,
% 1.07/1.30 ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~((~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.07/1.30 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.07/1.30 tff(78,plain,
% 1.07/1.30 (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~((~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[77, 71])).
% 1.07/1.30 tff(79,plain,
% 1.07/1.30 (((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~((~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | ((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(80,plain,
% 1.07/1.30 ((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[79, 78])).
% 1.07/1.30 tff(81,plain,
% 1.07/1.30 (((~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(82,plain,
% 1.07/1.30 (aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[81, 36])).
% 1.07/1.30 tff(83,plain,
% 1.07/1.30 ((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(84,plain,
% 1.07/1.30 ((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[83, 82])).
% 1.07/1.30 tff(85,plain,
% 1.07/1.30 (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[84, 80])).
% 1.07/1.30 tff(86,plain,
% 1.07/1.30 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aSet0(tptp_fun_W2_34(W1!33))),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(87,plain,
% 1.07/1.30 (aSet0(tptp_fun_W2_34(W1!33))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[86, 85])).
% 1.07/1.30 tff(88,plain,
% 1.07/1.30 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(89,plain,
% 1.07/1.30 (sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[88, 85])).
% 1.07/1.30 tff(90,plain,
% 1.07/1.30 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(91,plain,
% 1.07/1.30 (aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[90, 85])).
% 1.07/1.30 tff(92,plain,
% 1.07/1.30 ((aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(93,plain,
% 1.07/1.30 (aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.07/1.30 tff(94,plain,
% 1.07/1.30 ((~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(95,plain,
% 1.07/1.30 (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[94, 93, 89])).
% 1.07/1.30 tff(96,plain,
% 1.07/1.30 (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | ((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))),
% 1.07/1.30 inference(tautology,[status(thm)],[])).
% 1.07/1.30 tff(97,plain,
% 1.07/1.30 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.07/1.30 inference(unit_resolution,[status(thm)],[96, 95])).
% 1.07/1.30 tff(98,plain,
% 1.07/1.30 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))) | ![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.07/1.31 inference(tautology,[status(thm)],[])).
% 1.07/1.31 tff(99,plain,
% 1.07/1.31 (![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.07/1.31 inference(unit_resolution,[status(thm)],[98, 69])).
% 1.07/1.31 tff(100,plain,
% 1.07/1.31 (((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.07/1.31 inference(rewrite,[status(thm)],[])).
% 1.07/1.31 tff(101,plain,
% 1.07/1.31 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) <=> ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.07/1.31 inference(rewrite,[status(thm)],[])).
% 1.07/1.31 tff(102,plain,
% 1.07/1.31 (((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.07/1.31 inference(monotonicity,[status(thm)],[101])).
% 1.07/1.31 tff(103,plain,
% 1.07/1.31 (((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[102, 100])).
% 1.15/1.32 tff(104,plain,
% 1.15/1.32 ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(105,plain,
% 1.15/1.32 ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.15/1.32 tff(106,plain,
% 1.15/1.32 ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[105, 99])).
% 1.15/1.32 tff(107,plain,
% 1.15/1.32 (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[106, 97, 87])).
% 1.15/1.32 tff(108,plain,
% 1.15/1.32 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))),
% 1.15/1.32 inference(tautology,[status(thm)],[])).
% 1.15/1.32 tff(109,plain,
% 1.15/1.32 (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[108, 107])).
% 1.15/1.32 tff(110,plain,
% 1.15/1.32 (sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33))),
% 1.15/1.32 inference(symmetry,[status(thm)],[109])).
% 1.15/1.32 tff(111,plain,
% 1.15/1.32 (sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33),
% 1.15/1.32 inference(transitivity,[status(thm)],[110, 38])).
% 1.15/1.32 tff(112,plain,
% 1.15/1.32 (^[W0: $i] : refl((~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(113,plain,
% 1.15/1.32 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[112])).
% 1.15/1.32 tff(114,plain,
% 1.15/1.32 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(115,plain,
% 1.15/1.32 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[114])).
% 1.15/1.32 tff(116,plain,
% 1.15/1.32 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[115, 113])).
% 1.15/1.32 tff(117,plain,
% 1.15/1.32 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) <=> ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))), rewrite((aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))) <=> (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))), ((((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0))))) <=> (((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))), rewrite((((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))), ((((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(118,plain,
% 1.15/1.32 (![W0: $i] : (((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[117])).
% 1.15/1.32 tff(119,plain,
% 1.15/1.32 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0))) <=> ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(120,axiom,((((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))) & aSubsetOf0(sdtlcdtrc0(xc, szDzozmdt0(xc)), xT)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3453')).
% 1.15/1.32 tff(121,plain,
% 1.15/1.32 (((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))),
% 1.15/1.32 inference(and_elim,[status(thm)],[120])).
% 1.15/1.32 tff(122,plain,
% 1.15/1.32 ((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 1.15/1.32 inference(and_elim,[status(thm)],[121])).
% 1.15/1.32 tff(123,plain,
% 1.15/1.32 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 1.15/1.32 inference(and_elim,[status(thm)],[122])).
% 1.15/1.32 tff(124,plain,
% 1.15/1.32 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[123, 119])).
% 1.15/1.32 tff(125,plain,(
% 1.15/1.32 ![W0: $i] : (((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))))),
% 1.15/1.32 inference(skolemize,[status(sab)],[124])).
% 1.15/1.32 tff(126,plain,
% 1.15/1.32 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[125, 118])).
% 1.15/1.32 tff(127,plain,
% 1.15/1.32 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[126, 116])).
% 1.15/1.32 tff(128,plain,
% 1.15/1.32 (((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | (~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | (~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(129,plain,
% 1.15/1.32 ((~((~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))))) <=> (~((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | (~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33))))))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(130,plain,
% 1.15/1.32 (((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | (~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[129])).
% 1.15/1.32 tff(131,plain,
% 1.15/1.32 (((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | (~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[130, 128])).
% 1.15/1.32 tff(132,plain,
% 1.15/1.32 ((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))))))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(133,plain,
% 1.15/1.32 ((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | (~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33))))))))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.15/1.32 tff(134,plain,
% 1.15/1.32 (~((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | (~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[133, 127])).
% 1.15/1.32 tff(135,plain,
% 1.15/1.32 (((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | (~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33))))))) | (aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))),
% 1.15/1.32 inference(tautology,[status(thm)],[])).
% 1.15/1.32 tff(136,plain,
% 1.15/1.32 (aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[135, 134])).
% 1.15/1.32 tff(137,plain,
% 1.15/1.32 (~aElementOf0(W1!33, xT)),
% 1.15/1.32 inference(or_elim,[status(thm)],[32])).
% 1.15/1.32 tff(138,plain,
% 1.15/1.32 (^[W0: $i] : refl(((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(139,plain,
% 1.15/1.32 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[138])).
% 1.15/1.32 tff(140,plain,
% 1.15/1.32 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(141,plain,
% 1.15/1.32 (^[W0: $i] : rewrite((aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(142,plain,
% 1.15/1.32 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[141])).
% 1.15/1.32 tff(143,plain,
% 1.15/1.32 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))),
% 1.15/1.32 inference(and_elim,[status(thm)],[121])).
% 1.15/1.32 tff(144,plain,
% 1.15/1.32 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.15/1.32 tff(145,plain,
% 1.15/1.32 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[144, 140])).
% 1.15/1.32 tff(146,plain,(
% 1.15/1.32 ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.15/1.32 inference(skolemize,[status(sab)],[145])).
% 1.15/1.32 tff(147,plain,
% 1.15/1.32 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[146, 139])).
% 1.15/1.32 tff(148,plain,
% 1.15/1.32 (((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | ((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W1!33, xT))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | (~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W1!33, xT))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(149,plain,
% 1.15/1.32 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | ((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W1!33, xT))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(150,plain,
% 1.15/1.32 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | (~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W1!33, xT)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.15/1.32 tff(151,plain,
% 1.15/1.32 (~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[150, 147, 137])).
% 1.15/1.32 tff(152,plain,
% 1.15/1.32 ((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))),
% 1.15/1.32 inference(tautology,[status(thm)],[])).
% 1.15/1.32 tff(153,plain,
% 1.15/1.32 ((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[152, 151])).
% 1.15/1.32 tff(154,plain,
% 1.15/1.32 (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[153, 136])).
% 1.15/1.32 tff(155,plain,
% 1.15/1.32 (((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))) | ((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(156,plain,
% 1.15/1.33 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))) | ((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33)))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(157,plain,
% 1.15/1.33 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.15/1.33 tff(158,plain,
% 1.15/1.33 (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[157, 154, 111])).
% 1.15/1.33 tff(159,plain,
% 1.15/1.33 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))) <=> (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(160,plain,
% 1.15/1.33 (![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[159])).
% 1.15/1.33 tff(161,plain,
% 1.15/1.33 (^[W0: $i] : refl((~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))) <=> (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(162,plain,
% 1.15/1.33 (![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[161])).
% 1.15/1.33 tff(163,plain,
% 1.15/1.33 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))) <=> (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(164,plain,
% 1.15/1.33 (![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[163])).
% 1.15/1.33 tff(165,plain,
% 1.15/1.33 (![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))),
% 1.15/1.33 inference(transitivity,[status(thm)],[164, 162])).
% 1.15/1.33 tff(166,plain,
% 1.15/1.33 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) <=> ((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))), trans(monotonicity(rewrite(((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) <=> (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))), ((aElementOf0(W0, szDzozmdt0(xc)) | ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK))) <=> (aElementOf0(W0, szDzozmdt0(xc)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))) | (~(sbrdtbr0(W0) = xK))))), rewrite((aElementOf0(W0, szDzozmdt0(xc)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))) | (~(sbrdtbr0(W0) = xK))) <=> (aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))), ((aElementOf0(W0, szDzozmdt0(xc)) | ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK))) <=> (aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))), ((((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & (aElementOf0(W0, szDzozmdt0(xc)) | ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK)))) <=> (((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK))))) & (aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))))), rewrite((((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK))))) & (aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))))))) <=> (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))), ((((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & (aElementOf0(W0, szDzozmdt0(xc)) | ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK)))) <=> (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(167,plain,
% 1.15/1.33 (![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & (aElementOf0(W0, szDzozmdt0(xc)) | ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK)))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[166])).
% 1.15/1.33 tff(168,plain,
% 1.15/1.33 (^[W0: $i] : rewrite((((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc)))) <=> (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & (aElementOf0(W0, szDzozmdt0(xc)) | ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK)))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(169,plain,
% 1.15/1.33 (![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc)))) <=> ![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & (aElementOf0(W0, szDzozmdt0(xc)) | ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK))))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[168])).
% 1.15/1.33 tff(170,plain,
% 1.15/1.33 (![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc)))) <=> ![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(171,plain,
% 1.15/1.33 (^[W0: $i] : rewrite(((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc)))) <=> (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc)))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(172,plain,
% 1.15/1.33 (![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc)))) <=> ![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc))))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[171])).
% 1.15/1.33 tff(173,plain,
% 1.15/1.33 (((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 1.15/1.33 inference(and_elim,[status(thm)],[122])).
% 1.15/1.33 tff(174,plain,
% 1.15/1.33 ((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))),
% 1.15/1.33 inference(and_elim,[status(thm)],[173])).
% 1.15/1.33 tff(175,plain,
% 1.15/1.33 (aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))),
% 1.15/1.33 inference(and_elim,[status(thm)],[174])).
% 1.15/1.33 tff(176,plain,
% 1.15/1.33 (![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))),
% 1.15/1.33 inference(and_elim,[status(thm)],[175])).
% 1.15/1.33 tff(177,plain,
% 1.15/1.33 (![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.15/1.33 tff(178,plain,
% 1.15/1.33 (![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[177, 170])).
% 1.15/1.33 tff(179,plain,(
% 1.15/1.33 ![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & ((((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK))) | aElementOf0(W0, szDzozmdt0(xc))))),
% 1.15/1.33 inference(skolemize,[status(sab)],[178])).
% 1.15/1.33 tff(180,plain,
% 1.15/1.33 (![W0: $i] : (((~aElementOf0(W0, szDzozmdt0(xc))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xK))) & (aElementOf0(W0, szDzozmdt0(xc)) | ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS))))) | (~(sbrdtbr0(W0) = xK))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[179, 169])).
% 1.15/1.33 tff(181,plain,
% 1.15/1.33 (![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[180, 167])).
% 1.15/1.33 tff(182,plain,
% 1.15/1.33 (![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))) | (~(sbrdtbr0(W0) = xK)))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[181, 165])).
% 1.15/1.33 tff(183,plain,
% 1.15/1.33 (![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[182, 160])).
% 1.15/1.33 tff(184,plain,
% 1.15/1.33 (((~![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))) | (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))) | (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)))))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(185,plain,
% 1.15/1.33 ((~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~(aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))))))) <=> (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(186,plain,
% 1.15/1.33 (((~![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))) | (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~(aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS)))))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))) | (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)))))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[185])).
% 1.15/1.33 tff(187,plain,
% 1.15/1.33 (((~![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))) | (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~(aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS)))))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))) | (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)))))))),
% 1.15/1.33 inference(transitivity,[status(thm)],[186, 184])).
% 1.15/1.33 tff(188,plain,
% 1.15/1.33 ((~![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))) | (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~(aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS)))))))))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(189,plain,
% 1.15/1.34 ((~![W0: $i] : (~((~((~aElementOf0(W0, szDzozmdt0(xc))) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, xS)) | (~(sbrdtbr0(W0) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))))) | (~(aElementOf0(W0, szDzozmdt0(xc)) | (~(sbrdtbr0(W0) = xK)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_19(W0), W0)) | aElementOf0(tptp_fun_W1_19(W0), xS)))))))))))) | (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))))))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.15/1.34 tff(190,plain,
% 1.15/1.34 (~((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)))))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[189, 183])).
% 1.15/1.34 tff(191,plain,
% 1.15/1.34 (((~((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, xS))))))) | (~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))))) | ((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)))),
% 1.15/1.34 inference(tautology,[status(thm)],[])).
% 1.15/1.34 tff(192,plain,
% 1.15/1.34 ((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[191, 190])).
% 1.15/1.34 tff(193,plain,
% 1.15/1.34 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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))))))))))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(194,plain,
% 1.15/1.34 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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)))))))))))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[193])).
% 1.15/1.34 tff(195,plain,
% 1.15/1.34 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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))))))))))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(196,plain,
% 1.15/1.34 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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)))))))))))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[195])).
% 1.15/1.34 tff(197,plain,
% 1.15/1.34 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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))))))))))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(198,plain,
% 1.15/1.34 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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)))))))))))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[197])).
% 1.15/1.34 tff(199,plain,
% 1.15/1.34 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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)))))))))))),
% 1.15/1.34 inference(transitivity,[status(thm)],[198, 196])).
% 1.15/1.34 tff(200,plain,
% 1.15/1.34 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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)) & (((~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)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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))))))))))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(201,plain,
% 1.15/1.35 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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)) & (((~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)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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)))))))))))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[200])).
% 1.15/1.35 tff(202,plain,
% 1.15/1.35 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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)) & (((~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))))))))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(203,plain,
% 1.15/1.35 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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)) & (((~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)))))))))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[202])).
% 1.15/1.35 tff(204,plain,
% 1.15/1.35 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(205,plain,
% 1.15/1.35 (^[W0: $i] : trans(monotonicity(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(trans(monotonicity(trans(monotonicity(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))) & aSet0(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))) & aSet0(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))) & aSet0(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)) & aSet0(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))) & aSet0(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)) & aSet0(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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), quant_intro(proof_bind(^[W2: $i] : rewrite((aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS)) <=> ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)))), (![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS)) <=> ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)))), (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)))), (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))), ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS))), ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)))), (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, 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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, 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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, 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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, 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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, 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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))), ((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))), (((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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))), 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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))), (((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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))), ((aElementOf0(W0, szNzAzT0) => ![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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> (aElementOf0(W0, szNzAzT0) => ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))))), rewrite((aElementOf0(W0, szNzAzT0) => ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))), ((aElementOf0(W0, szNzAzT0) => ![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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))))),
% 1.15/1.36 inference(bind,[status(th)],[])).
% 1.15/1.36 tff(206,plain,
% 1.15/1.36 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.15/1.36 inference(quant_intro,[status(thm)],[205])).
% 1.15/1.36 tff(207,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![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))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3965')).
% 1.15/1.36 tff(208,plain,
% 1.15/1.36 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.15/1.36 tff(209,plain,
% 1.15/1.36 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.15/1.36 tff(210,plain,(
% 1.15/1.36 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.15/1.36 inference(skolemize,[status(sab)],[209])).
% 1.15/1.36 tff(211,plain,
% 1.15/1.36 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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)) & (((~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)))))))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.15/1.36 tff(212,plain,
% 1.15/1.36 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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)))))))))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[211, 201])).
% 1.15/1.36 tff(213,plain,
% 1.15/1.36 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, 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))) | (~((~(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)))))))))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[212, 199])).
% 1.15/1.36 tff(214,plain,
% 1.15/1.36 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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)))))))))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[213, 194])).
% 1.15/1.36 tff(215,plain,
% 1.15/1.36 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(216,plain,
% 1.15/1.37 (((~aElementOf0(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) <=> ((~aElementOf0(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(217,plain,
% 1.15/1.37 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[216])).
% 1.15/1.37 tff(218,plain,
% 1.15/1.37 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.15/1.37 inference(transitivity,[status(thm)],[217, 215])).
% 1.15/1.37 tff(219,plain,
% 1.15/1.37 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(220,plain,
% 1.15/1.37 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) | (~![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))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))) | (~(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(W0!32, szNzAzT0)) | ![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.15/1.37 tff(221,plain,
% 1.15/1.37 (![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[220, 214, 39])).
% 1.15/1.37 tff(222,plain,
% 1.15/1.37 (((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(223,plain,
% 1.15/1.38 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) <=> ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(224,plain,
% 1.15/1.38 (((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[223])).
% 1.15/1.38 tff(225,plain,
% 1.15/1.38 (((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.22/1.38 inference(transitivity,[status(thm)],[224, 222])).
% 1.22/1.38 tff(226,plain,
% 1.22/1.38 ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.22/1.38 inference(quant_inst,[status(thm)],[])).
% 1.22/1.38 tff(227,plain,
% 1.22/1.38 ((~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)))))))) | (~((~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.22/1.39 tff(228,plain,
% 1.22/1.39 ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[227, 221])).
% 1.22/1.39 tff(229,plain,
% 1.22/1.39 (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[228, 97, 87])).
% 1.22/1.39 tff(230,plain,
% 1.22/1.39 (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(231,plain,
% 1.22/1.39 (aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[230, 229])).
% 1.22/1.39 tff(232,plain,
% 1.22/1.39 ((aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS)))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(233,plain,
% 1.22/1.39 (aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[232, 231])).
% 1.22/1.39 tff(234,plain,
% 1.22/1.39 (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS)) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), slbdtsldtrb0(xS, xK))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, xS))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) <=> aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(235,plain,
% 1.22/1.39 (sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[234, 229])).
% 1.22/1.39 tff(236,plain,
% 1.22/1.39 ((~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(237,plain,
% 1.22/1.39 ((~((~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = xK)) | (~(aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xS) | (~((~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~((~aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W1_19(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))), xS))))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc)))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[236, 235, 233])).
% 1.22/1.39 tff(238,plain,
% 1.22/1.39 ($false),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[237, 192, 158])).
% 1.22/1.39 % SZS output end Proof
% 1.22/1.40 % E exiting
%------------------------------------------------------------------------------