%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM581+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:21:28 AM UTC 2025
% Result : Theorem 0.69s 0.86s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM581+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 01:32:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.69/0.86 % SZS status Theorem
% 0.69/0.86 % SZS output start Proof
% 0.69/0.86 tff(aElementOf0_type, type, (
% 0.69/0.86 aElementOf0: ( $i * $i ) > $o)).
% 0.69/0.86 tff(sdtlpdtrp0_type, type, (
% 0.69/0.86 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.69/0.86 tff(sz00_type, type, (
% 0.69/0.86 sz00: $i)).
% 0.69/0.86 tff(xN_type, type, (
% 0.69/0.86 xN: $i)).
% 0.69/0.86 tff(szmzizndt0_type, type, (
% 0.69/0.86 szmzizndt0: $i > $i)).
% 0.69/0.86 tff(xi_type, type, (
% 0.69/0.86 xi: $i)).
% 0.69/0.86 tff(xS_type, type, (
% 0.69/0.86 xS: $i)).
% 0.69/0.86 tff(tptp_fun_W0_31_type, type, (
% 0.69/0.86 tptp_fun_W0_31: $i)).
% 0.69/0.86 tff(szNzAzT0_type, type, (
% 0.69/0.86 szNzAzT0: $i)).
% 0.69/0.86 tff(szDzozmdt0_type, type, (
% 0.69/0.86 szDzozmdt0: $i > $i)).
% 0.69/0.86 tff(aFunction0_type, type, (
% 0.69/0.86 aFunction0: $i > $o)).
% 0.69/0.86 tff(isCountable0_type, type, (
% 0.69/0.86 isCountable0: $i > $o)).
% 0.69/0.86 tff(szszuzczcdt0_type, type, (
% 0.69/0.86 szszuzczcdt0: $i > $i)).
% 0.69/0.86 tff(aSubsetOf0_type, type, (
% 0.69/0.86 aSubsetOf0: ( $i * $i ) > $o)).
% 0.69/0.86 tff(sdtmndt0_type, type, (
% 0.69/0.86 sdtmndt0: ( $i * $i ) > $i)).
% 0.69/0.86 tff(aSet0_type, type, (
% 0.69/0.86 aSet0: $i > $o)).
% 0.69/0.86 tff(aElement0_type, type, (
% 0.69/0.86 aElement0: $i > $o)).
% 0.69/0.86 tff(sdtlseqdt0_type, type, (
% 0.69/0.86 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.69/0.86 tff(xQ_type, type, (
% 0.69/0.86 xQ: $i)).
% 0.69/0.86 tff(sdtpldt0_type, type, (
% 0.69/0.86 sdtpldt0: ( $i * $i ) > $i)).
% 0.69/0.86 tff(xK_type, type, (
% 0.69/0.86 xK: $i)).
% 0.69/0.86 tff(sbrdtbr0_type, type, (
% 0.69/0.86 sbrdtbr0: $i > $i)).
% 0.69/0.86 tff(tptp_fun_W1_29_type, type, (
% 0.69/0.86 tptp_fun_W1_29: $i > $i)).
% 0.69/0.86 tff(tptp_fun_W2_1_type, type, (
% 0.69/0.86 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.69/0.86 tff(xk_type, type, (
% 0.69/0.86 xk: $i)).
% 0.69/0.86 tff(slbdtsldtrb0_type, type, (
% 0.69/0.86 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.69/0.86 tff(1,plain,
% 0.69/0.86 ((sdtlpdtrp0(xN, sz00) = xS) <=> (sdtlpdtrp0(xN, sz00) = xS)),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(2,axiom,(((aFunction0(xN) & (szDzozmdt0(xN) = szNzAzT0)) & (sdtlpdtrp0(xN, sz00) = xS)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3623')).
% 0.69/0.86 tff(3,plain,
% 0.69/0.86 ((aFunction0(xN) & (szDzozmdt0(xN) = szNzAzT0)) & (sdtlpdtrp0(xN, sz00) = xS)),
% 0.69/0.86 inference(and_elim,[status(thm)],[2])).
% 0.69/0.86 tff(4,plain,
% 0.69/0.86 (sdtlpdtrp0(xN, sz00) = xS),
% 0.69/0.86 inference(and_elim,[status(thm)],[3])).
% 0.69/0.86 tff(5,plain,
% 0.69/0.86 (sdtlpdtrp0(xN, sz00) = xS),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.69/0.86 tff(6,plain,
% 0.69/0.86 (^[W0: $i] : refl((~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(7,plain,
% 0.69/0.86 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[6])).
% 0.69/0.86 tff(8,plain,
% 0.69/0.86 (^[W0: $i] : trans(trans(monotonicity(rewrite((aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))), ((aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))))), rewrite((aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))), ((aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))))), rewrite((~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))), ((aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(9,plain,
% 0.69/0.86 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[8])).
% 0.69/0.86 tff(10,plain,
% 0.69/0.86 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(11,axiom,((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) = xK)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4007')).
% 0.69/0.86 tff(12,plain,
% 0.69/0.86 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(and_elim,[status(thm)],[11])).
% 0.69/0.86 tff(13,plain,
% 0.69/0.86 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(and_elim,[status(thm)],[12])).
% 0.69/0.86 tff(14,plain,
% 0.69/0.86 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.69/0.86 tff(15,plain,(
% 0.69/0.86 ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(skolemize,[status(sab)],[14])).
% 0.69/0.86 tff(16,plain,
% 0.69/0.86 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.69/0.86 tff(17,plain,
% 0.69/0.86 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[16, 7])).
% 0.69/0.86 tff(18,plain,
% 0.69/0.86 ((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~(((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(19,plain,
% 0.69/0.86 (~(((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.69/0.86 tff(20,plain,
% 0.69/0.86 ((~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(21,plain,
% 0.69/0.86 ((~((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) => ((aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) => (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) => aElementOf0(W0, xS)) | aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS))))) <=> (~(aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS)) | (~(aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))))))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(22,axiom,(~((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) => ((aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) => (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) => aElementOf0(W0, xS)) | aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.69/0.86 tff(23,plain,
% 0.69/0.86 (~(aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS)) | (~(aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0)))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.69/0.86 tff(24,plain,
% 0.69/0.86 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.69/0.86 inference(or_elim,[status(thm)],[23])).
% 0.69/0.86 tff(25,plain,
% 0.69/0.86 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.69/0.86 tff(26,plain,
% 0.69/0.86 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.69/0.86 tff(27,plain,
% 0.69/0.86 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.69/0.86 tff(28,plain,(
% 0.69/0.86 ~((~aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0!31, xS))),
% 0.69/0.86 inference(skolemize,[status(sab)],[27])).
% 0.69/0.86 tff(29,plain,
% 0.69/0.86 (aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.69/0.86 inference(or_elim,[status(thm)],[28])).
% 0.69/0.86 tff(30,plain,
% 0.69/0.86 ((((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.69/0.86 inference(tautology,[status(thm)],[])).
% 0.69/0.86 tff(31,plain,
% 0.69/0.86 ((((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.69/0.86 tff(32,plain,
% 0.69/0.86 (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[31, 19])).
% 0.69/0.86 tff(33,plain,
% 0.69/0.86 (((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.69/0.86 inference(tautology,[status(thm)],[])).
% 0.69/0.86 tff(34,plain,
% 0.69/0.86 (aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.69/0.86 tff(35,plain,
% 0.69/0.86 (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(36,axiom,(aElementOf0(xi, szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3989')).
% 0.69/0.86 tff(37,plain,
% 0.69/0.86 (aElementOf0(xi, szNzAzT0)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.69/0.86 tff(38,plain,
% 0.69/0.86 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(39,plain,
% 0.69/0.86 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[38])).
% 0.69/0.86 tff(40,plain,
% 0.69/0.86 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(41,plain,
% 0.69/0.86 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[40])).
% 0.69/0.86 tff(42,plain,
% 0.69/0.86 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(43,plain,
% 0.69/0.86 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[42])).
% 0.69/0.86 tff(44,plain,
% 0.69/0.86 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.69/0.86 inference(transitivity,[status(thm)],[43, 41])).
% 0.69/0.86 tff(45,plain,
% 0.69/0.86 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(46,plain,
% 0.69/0.86 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[45])).
% 0.69/0.86 tff(47,plain,
% 0.69/0.86 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(48,plain,
% 0.69/0.86 (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))), (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) <=> ((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)))), rewrite(((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0))), (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)))), ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) <=> ((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))))), rewrite(((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))), ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))), ((aElementOf0(W0, szNzAzT0) => (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> (aElementOf0(W0, szNzAzT0) => (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))))), rewrite((aElementOf0(W0, szNzAzT0) => (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))), ((aElementOf0(W0, szNzAzT0) => (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(49,plain,
% 0.69/0.86 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[48])).
% 0.69/0.87 tff(50,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3671')).
% 0.69/0.87 tff(51,plain,
% 0.69/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.69/0.87 tff(52,plain,
% 0.69/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.69/0.87 tff(53,plain,(
% 0.69/0.87 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.69/0.87 inference(skolemize,[status(sab)],[52])).
% 0.69/0.87 tff(54,plain,
% 0.69/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.69/0.87 tff(55,plain,
% 0.69/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.69/0.87 tff(56,plain,
% 0.69/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[55, 39])).
% 0.69/0.87 tff(57,plain,
% 0.69/0.87 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)))))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(58,plain,
% 0.69/0.87 (((~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0)))))) <=> ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)))))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(59,plain,
% 0.69/0.87 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0))))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[58])).
% 0.69/0.87 tff(60,plain,
% 0.69/0.87 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)))))),
% 0.69/0.87 inference(transitivity,[status(thm)],[59, 57])).
% 0.69/0.87 tff(61,plain,
% 0.69/0.87 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))))))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(62,plain,
% 0.69/0.87 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, W0))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.69/0.87 tff(63,plain,
% 0.69/0.87 (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[62, 56, 37])).
% 0.69/0.87 tff(64,plain,
% 0.69/0.87 (((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0))) | isCountable0(sdtlpdtrp0(xN, xi))),
% 0.69/0.87 inference(tautology,[status(thm)],[])).
% 0.69/0.87 tff(65,plain,
% 0.69/0.87 (isCountable0(sdtlpdtrp0(xN, xi))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.69/0.87 tff(66,plain,
% 0.69/0.87 (((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)),
% 0.69/0.87 inference(tautology,[status(thm)],[])).
% 0.69/0.87 tff(67,plain,
% 0.69/0.87 (aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.69/0.87 tff(68,plain,
% 0.69/0.87 ((aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0))),
% 0.69/0.87 inference(tautology,[status(thm)],[])).
% 0.69/0.87 tff(69,plain,
% 0.69/0.87 (aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0)))))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.69/0.87 tff(70,plain,
% 0.69/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(71,plain,
% 0.69/0.87 (^[W0: $i] : trans(monotonicity(rewrite((~((~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))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) <=> (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite((~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) <=> (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))), (((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))))), rewrite(((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), (((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(72,plain,
% 0.72/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[71])).
% 0.72/0.87 tff(73,plain,
% 0.72/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.72/0.87 inference(transitivity,[status(thm)],[72, 70])).
% 0.72/0.87 tff(74,plain,
% 0.72/0.87 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(75,plain,
% 0.72/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[74])).
% 0.72/0.87 tff(76,plain,
% 0.72/0.87 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(77,plain,
% 0.72/0.87 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[76])).
% 0.72/0.88 tff(78,plain,
% 0.72/0.88 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))))),
% 0.72/0.88 inference(transitivity,[status(thm)],[77, 75])).
% 0.72/0.88 tff(79,plain,
% 0.72/0.88 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(trans(monotonicity(rewrite((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = 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)))))) <=> (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), rewrite((aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = 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))))))), ((aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = 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)))))))), rewrite((~(((~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)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), 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)))))) <=> (~(((~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, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = 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)))))))), ((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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), rewrite((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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))), rewrite(((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) <=> (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0)))))))), (((~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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(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))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))), 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))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))))), (((~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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(80,plain,
% 0.72/0.88 (![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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[79])).
% 0.72/0.88 tff(81,plain,
% 0.72/0.88 (^[W0: $i] : trans(monotonicity(rewrite((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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))), rewrite((((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))), 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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(82,plain,
% 0.72/0.88 (![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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[81])).
% 0.72/0.88 tff(83,plain,
% 0.72/0.88 (![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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(84,plain,
% 0.72/0.88 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) <=> ((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (((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))))) <=> ((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(((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))))) <=> (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)))))), (((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))))) <=> (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)))))))), ((((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))))))) <=> ((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(((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))))))) <=> (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)))))))), ((((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))))))) <=> (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))))))))), (((((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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), rewrite(((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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), (![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))), rewrite(((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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite(((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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), rewrite(((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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), (((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))) <=> (((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))), rewrite((((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))) <=> ((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), (((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))) <=> ((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))), ((aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) <=> (aElementOf0(W0, szNzAzT0) => ((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))), rewrite((aElementOf0(W0, szNzAzT0) => ((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, 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)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))), ((aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(85,plain,
% 0.72/0.89 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[84])).
% 0.72/0.89 tff(86,plain,
% 0.72/0.89 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, 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))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))),
% 0.72/0.89 inference(and_elim,[status(thm)],[2])).
% 0.72/0.89 tff(87,plain,
% 0.72/0.89 (![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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.72/0.89 tff(88,plain,
% 0.72/0.89 (![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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.72/0.89 tff(89,plain,(
% 0.72/0.89 ![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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))),
% 0.72/0.89 inference(skolemize,[status(sab)],[88])).
% 0.72/0.89 tff(90,plain,
% 0.72/0.89 (![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] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.72/0.90 tff(91,plain,
% 0.72/0.90 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.72/0.90 tff(92,plain,
% 0.72/0.90 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, 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] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[91, 78])).
% 0.72/0.90 tff(93,plain,
% 0.72/0.90 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[92, 73])).
% 0.72/0.90 tff(94,plain,
% 0.72/0.90 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))))))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(95,plain,
% 0.72/0.90 (((~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) <=> ((~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))))))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(96,plain,
% 0.72/0.90 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)))))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[95])).
% 0.72/0.90 tff(97,plain,
% 0.72/0.90 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))))))),
% 0.72/0.90 inference(transitivity,[status(thm)],[96, 94])).
% 0.72/0.90 tff(98,plain,
% 0.72/0.90 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(99,plain,
% 0.72/0.90 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![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, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.72/0.90 tff(100,plain,
% 0.72/0.90 ((~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[99, 93, 37])).
% 0.72/0.90 tff(101,plain,
% 0.72/0.90 (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[100, 69, 65])).
% 0.72/0.90 tff(102,plain,
% 0.72/0.90 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)))) | ![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.72/0.90 inference(tautology,[status(thm)],[])).
% 0.72/0.90 tff(103,plain,
% 0.72/0.90 (![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.72/0.90 tff(104,plain,
% 0.72/0.90 ((~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~(((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(105,plain,
% 0.72/0.90 (~(((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.72/0.90 tff(106,plain,
% 0.72/0.90 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(107,plain,
% 0.72/0.90 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[106])).
% 0.72/0.90 tff(108,plain,
% 0.72/0.90 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(109,plain,
% 0.72/0.90 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(110,plain,
% 0.72/0.91 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[109])).
% 0.72/0.91 tff(111,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mZeroLess')).
% 0.72/0.91 tff(112,plain,
% 0.72/0.91 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.72/0.91 tff(113,plain,
% 0.72/0.91 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.72/0.91 tff(114,plain,(
% 0.72/0.91 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 0.72/0.91 inference(skolemize,[status(sab)],[113])).
% 0.72/0.91 tff(115,plain,
% 0.72/0.91 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.72/0.91 tff(116,plain,
% 0.72/0.91 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))) | ((~aElementOf0(xi, szNzAzT0)) | sdtlseqdt0(sz00, xi))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))) | (~aElementOf0(xi, szNzAzT0)) | sdtlseqdt0(sz00, xi))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(117,plain,
% 0.72/0.91 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))) | ((~aElementOf0(xi, szNzAzT0)) | sdtlseqdt0(sz00, xi))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(118,plain,
% 0.72/0.91 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))) | (~aElementOf0(xi, szNzAzT0)) | sdtlseqdt0(sz00, xi)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.72/0.91 tff(119,plain,
% 0.72/0.91 (sdtlseqdt0(sz00, xi)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[118, 115, 37])).
% 0.72/0.91 tff(120,plain,
% 0.72/0.91 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))))))), (((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))))))))), rewrite(((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))), (((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(121,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[120])).
% 0.72/0.91 tff(122,plain,
% 0.72/0.91 (^[W0: $i, W1: $i] : refl(((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(123,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[122])).
% 0.72/0.91 tff(124,plain,
% 0.72/0.91 (^[W0: $i, W1: $i] : rewrite(((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(125,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[124])).
% 0.72/0.91 tff(126,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 0.72/0.91 inference(transitivity,[status(thm)],[125, 123])).
% 0.72/0.91 tff(127,plain,
% 0.72/0.91 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) <=> (~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> (~(~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))))), rewrite((~(~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), rewrite((![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> (((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))), rewrite((((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(128,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[127])).
% 0.72/0.91 tff(129,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(130,plain,
% 0.72/0.91 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))), ((sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> (sdtlseqdt0(W1, W0) => (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), rewrite((sdtlseqdt0(W1, W0) => (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))), ((sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))), rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(131,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[130])).
% 0.72/0.91 tff(132,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3754')).
% 0.72/0.91 tff(133,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.72/0.91 tff(134,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.72/0.91 tff(135,plain,(
% 0.72/0.91 ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 0.72/0.91 inference(skolemize,[status(sab)],[134])).
% 0.72/0.91 tff(136,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.72/0.91 tff(137,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.72/0.91 tff(138,plain,
% 0.72/0.91 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[137, 121])).
% 0.72/0.91 tff(139,plain,
% 0.72/0.91 (aElementOf0(sz00, szNzAzT0) <=> aElementOf0(sz00, szNzAzT0)),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(140,axiom,(aElementOf0(sz00, szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mZeroNum')).
% 0.72/0.91 tff(141,plain,
% 0.72/0.91 (aElementOf0(sz00, szNzAzT0)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.72/0.91 tff(142,plain,
% 0.72/0.91 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(xi, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(xi, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(143,plain,
% 0.72/0.91 (((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(xi, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(144,plain,
% 0.72/0.91 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) <=> (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(145,plain,
% 0.72/0.91 (((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[144])).
% 0.72/0.91 tff(146,plain,
% 0.72/0.91 ((~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) <=> (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[145])).
% 0.72/0.91 tff(147,plain,
% 0.72/0.91 (((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[146])).
% 0.72/0.91 tff(148,plain,
% 0.72/0.91 (((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(xi, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 0.72/0.91 inference(transitivity,[status(thm)],[147, 143])).
% 0.72/0.91 tff(149,plain,
% 0.72/0.91 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(xi, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[148])).
% 0.72/0.91 tff(150,plain,
% 0.72/0.91 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(xi, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 0.72/0.91 inference(transitivity,[status(thm)],[149, 142])).
% 0.72/0.91 tff(151,plain,
% 0.72/0.91 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(152,plain,
% 0.72/0.91 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(xi, szNzAzT0)) | (~sdtlseqdt0(sz00, xi)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.72/0.91 tff(153,plain,
% 0.72/0.91 (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[152, 141, 138, 37, 119])).
% 0.72/0.91 tff(154,plain,
% 0.72/0.91 (((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))) | ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))),
% 0.72/0.91 inference(tautology,[status(thm)],[])).
% 0.72/0.91 tff(155,plain,
% 0.72/0.91 (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.72/0.91 tff(156,plain,
% 0.72/0.91 (aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)) <=> aElementOf0(W0!31, xS)),
% 0.72/0.91 inference(monotonicity,[status(thm)],[5])).
% 0.72/0.91 tff(157,plain,
% 0.72/0.91 (aElementOf0(W0!31, xS) <=> aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 0.72/0.91 inference(symmetry,[status(thm)],[156])).
% 0.72/0.91 tff(158,plain,
% 0.72/0.91 ((~aElementOf0(W0!31, xS)) <=> (~aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[157])).
% 0.72/0.91 tff(159,plain,
% 0.72/0.91 (~aElementOf0(W0!31, xS)),
% 0.72/0.91 inference(or_elim,[status(thm)],[28])).
% 0.72/0.91 tff(160,plain,
% 0.72/0.91 (~aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.72/0.91 tff(161,plain,
% 0.72/0.91 (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(162,plain,
% 0.72/0.91 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(163,plain,
% 0.72/0.91 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.72/0.91 tff(164,plain,
% 0.72/0.91 (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[163, 160, 155])).
% 0.72/0.91 tff(165,plain,
% 0.72/0.91 (((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 0.72/0.91 inference(tautology,[status(thm)],[])).
% 0.72/0.91 tff(166,plain,
% 0.72/0.91 ((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.72/0.91 tff(167,plain,
% 0.72/0.91 ((((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.72/0.91 inference(tautology,[status(thm)],[])).
% 0.72/0.91 tff(168,plain,
% 0.72/0.91 (~aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[167, 166, 105])).
% 0.72/0.91 tff(169,plain,
% 0.72/0.91 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(170,axiom,((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & (sbrdtbr0(xQ) = xk)) & aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3989_02')).
% 0.72/0.92 tff(171,plain,
% 0.72/0.92 (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & (sbrdtbr0(xQ) = xk)),
% 0.72/0.92 inference(and_elim,[status(thm)],[170])).
% 0.72/0.92 tff(172,plain,
% 0.72/0.92 ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.72/0.92 inference(and_elim,[status(thm)],[171])).
% 0.72/0.92 tff(173,plain,
% 0.72/0.92 (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.72/0.92 inference(and_elim,[status(thm)],[172])).
% 0.72/0.92 tff(174,plain,
% 0.72/0.92 ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)),
% 0.72/0.92 inference(and_elim,[status(thm)],[173])).
% 0.72/0.92 tff(175,plain,
% 0.72/0.92 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.72/0.92 inference(and_elim,[status(thm)],[174])).
% 0.72/0.92 tff(176,plain,
% 0.72/0.92 ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.72/0.92 inference(and_elim,[status(thm)],[175])).
% 0.72/0.92 tff(177,plain,
% 0.72/0.92 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.72/0.92 inference(and_elim,[status(thm)],[176])).
% 0.72/0.92 tff(178,plain,
% 0.72/0.92 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[177, 169])).
% 0.72/0.92 tff(179,plain,
% 0.72/0.92 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(180,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[179])).
% 0.72/0.92 tff(181,plain,
% 0.72/0.92 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(182,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[181])).
% 0.72/0.92 tff(183,plain,
% 0.72/0.92 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(184,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[183])).
% 0.72/0.92 tff(185,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.72/0.92 inference(transitivity,[status(thm)],[184, 182])).
% 0.72/0.92 tff(186,plain,
% 0.72/0.92 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(187,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[186])).
% 0.72/0.92 tff(188,plain,
% 0.72/0.92 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(189,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[188])).
% 0.72/0.92 tff(190,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(191,plain,
% 0.72/0.92 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(192,plain,
% 0.72/0.92 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[191])).
% 0.72/0.92 tff(193,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefSub')).
% 0.72/0.92 tff(194,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.72/0.92 tff(195,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.72/0.92 tff(196,plain,(
% 0.72/0.92 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.72/0.92 inference(skolemize,[status(sab)],[195])).
% 0.72/0.92 tff(197,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.72/0.92 tff(198,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[197, 187])).
% 0.72/0.92 tff(199,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[198, 185])).
% 0.72/0.92 tff(200,plain,
% 0.72/0.92 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[199, 180])).
% 0.72/0.92 tff(201,plain,
% 0.72/0.92 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(202,plain,
% 0.72/0.92 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) <=> ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(203,plain,
% 0.72/0.92 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[202])).
% 0.72/0.92 tff(204,plain,
% 0.72/0.92 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 0.72/0.92 inference(transitivity,[status(thm)],[203, 201])).
% 0.72/0.92 tff(205,plain,
% 0.72/0.92 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(206,plain,
% 0.72/0.92 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.72/0.92 tff(207,plain,
% 0.72/0.92 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[206, 200, 178])).
% 0.72/0.92 tff(208,plain,
% 0.72/0.92 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(209,plain,
% 0.72/0.92 ((~((~((~aSet0(xQ)) | aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) <=> (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(210,plain,
% 0.72/0.92 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~((~aSet0(xQ)) | aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[209])).
% 0.72/0.92 tff(211,plain,
% 0.72/0.92 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~((~aSet0(xQ)) | aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 0.72/0.93 inference(transitivity,[status(thm)],[210, 208])).
% 0.72/0.93 tff(212,plain,
% 0.72/0.93 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~((~aSet0(xQ)) | aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(213,plain,
% 0.72/0.93 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.72/0.93 tff(214,plain,
% 0.72/0.93 (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[213, 207])).
% 0.72/0.93 tff(215,plain,
% 0.72/0.93 (((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | ((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 0.78/0.93 inference(tautology,[status(thm)],[])).
% 0.78/0.93 tff(216,plain,
% 0.78/0.93 ((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.78/0.93 tff(217,plain,
% 0.78/0.93 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(218,plain,
% 0.78/0.93 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.78/0.93 inference(and_elim,[status(thm)],[172])).
% 0.78/0.93 tff(219,plain,
% 0.78/0.93 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.78/0.93 tff(220,plain,
% 0.78/0.93 ((~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.78/0.93 inference(tautology,[status(thm)],[])).
% 0.78/0.93 tff(221,plain,
% 0.78/0.93 ((~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.78/0.93 tff(222,plain,
% 0.78/0.93 (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[221, 216])).
% 0.78/0.93 tff(223,plain,
% 0.78/0.93 (((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | ![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.78/0.93 inference(tautology,[status(thm)],[])).
% 0.78/0.93 tff(224,plain,
% 0.78/0.93 (![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.78/0.93 tff(225,plain,
% 0.78/0.93 (((~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | ((~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(226,plain,
% 0.78/0.93 ((~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | ((~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(227,plain,
% 0.78/0.93 ((~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.78/0.93 tff(228,plain,
% 0.78/0.93 ((~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[227, 224])).
% 0.78/0.93 tff(229,plain,
% 0.78/0.93 (~aElementOf0(W0!31, xQ)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[228, 168])).
% 0.78/0.93 tff(230,plain,
% 0.78/0.93 ((~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 0.78/0.93 inference(tautology,[status(thm)],[])).
% 0.78/0.93 tff(231,plain,
% 0.78/0.93 (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[230, 229, 34])).
% 0.78/0.93 tff(232,plain,
% 0.78/0.93 (szmzizndt0(sdtlpdtrp0(xN, xi)) = W0!31),
% 0.78/0.93 inference(symmetry,[status(thm)],[231])).
% 0.78/0.93 tff(233,plain,
% 0.78/0.93 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)) <=> aElementOf0(W0!31, xS)),
% 0.78/0.93 inference(monotonicity,[status(thm)],[232, 5])).
% 0.78/0.93 tff(234,plain,
% 0.78/0.93 (aElementOf0(W0!31, xS) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00))),
% 0.78/0.93 inference(symmetry,[status(thm)],[233])).
% 0.78/0.93 tff(235,plain,
% 0.78/0.93 ((~aElementOf0(W0!31, xS)) <=> (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)))),
% 0.78/0.93 inference(monotonicity,[status(thm)],[234])).
% 0.78/0.93 tff(236,plain,
% 0.78/0.93 (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[159, 235])).
% 0.78/0.93 tff(237,plain,
% 0.78/0.93 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(238,plain,
% 0.78/0.93 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))),
% 0.78/0.93 inference(and_elim,[status(thm)],[176])).
% 0.78/0.93 tff(239,plain,
% 0.78/0.93 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 0.78/0.93 inference(and_elim,[status(thm)],[238])).
% 0.78/0.93 tff(240,plain,
% 0.78/0.93 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[239, 237])).
% 0.78/0.93 tff(241,plain,
% 0.78/0.93 (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(242,plain,
% 0.78/0.93 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(243,plain,
% 0.78/0.93 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.78/0.93 tff(244,plain,
% 0.78/0.93 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[243, 240, 155])).
% 0.78/0.93 tff(245,plain,
% 0.78/0.93 ($false),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[244, 236])).
% 0.78/0.93 % SZS output end Proof
% 0.78/0.94 % E exiting
%------------------------------------------------------------------------------