%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM583+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:28 AM UTC 2025
% Result : Theorem 0.71s 0.87s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM583+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 01:32:46 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.71/0.87 % SZS status Theorem
% 0.71/0.87 % SZS output start Proof
% 0.71/0.87 tff(aElementOf0_type, type, (
% 0.71/0.87 aElementOf0: ( $i * $i ) > $o)).
% 0.71/0.87 tff(xS_type, type, (
% 0.71/0.87 xS: $i)).
% 0.71/0.87 tff(tptp_fun_W0_31_type, type, (
% 0.71/0.87 tptp_fun_W0_31: $i)).
% 0.71/0.87 tff(szmzizndt0_type, type, (
% 0.71/0.87 szmzizndt0: $i > $i)).
% 0.71/0.87 tff(sdtlpdtrp0_type, type, (
% 0.71/0.87 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.71/0.87 tff(xi_type, type, (
% 0.71/0.87 xi: $i)).
% 0.71/0.87 tff(xN_type, type, (
% 0.71/0.87 xN: $i)).
% 0.71/0.87 tff(xQ_type, type, (
% 0.71/0.87 xQ: $i)).
% 0.71/0.87 tff(aElement0_type, type, (
% 0.71/0.87 aElement0: $i > $o)).
% 0.71/0.87 tff(sdtpldt0_type, type, (
% 0.71/0.87 sdtpldt0: ( $i * $i ) > $i)).
% 0.71/0.87 tff(aSet0_type, type, (
% 0.71/0.87 aSet0: $i > $o)).
% 0.71/0.87 tff(sdtlseqdt0_type, type, (
% 0.71/0.87 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.71/0.87 tff(xK_type, type, (
% 0.71/0.87 xK: $i)).
% 0.71/0.87 tff(sbrdtbr0_type, type, (
% 0.71/0.87 sbrdtbr0: $i > $i)).
% 0.71/0.87 tff(aSubsetOf0_type, type, (
% 0.71/0.87 aSubsetOf0: ( $i * $i ) > $o)).
% 0.71/0.87 tff(sdtmndt0_type, type, (
% 0.71/0.87 sdtmndt0: ( $i * $i ) > $i)).
% 0.71/0.87 tff(tptp_fun_W2_1_type, type, (
% 0.71/0.87 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.71/0.87 tff(xk_type, type, (
% 0.71/0.87 xk: $i)).
% 0.71/0.87 tff(slbdtsldtrb0_type, type, (
% 0.71/0.87 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.71/0.87 tff(szszuzczcdt0_type, type, (
% 0.71/0.87 szszuzczcdt0: $i > $i)).
% 0.71/0.87 tff(isCountable0_type, type, (
% 0.71/0.87 isCountable0: $i > $o)).
% 0.71/0.87 tff(szNzAzT0_type, type, (
% 0.71/0.87 szNzAzT0: $i)).
% 0.71/0.87 tff(tptp_fun_W1_29_type, type, (
% 0.71/0.87 tptp_fun_W1_29: $i > $i)).
% 0.71/0.87 tff(sz00_type, type, (
% 0.71/0.87 sz00: $i)).
% 0.71/0.87 tff(szDzozmdt0_type, type, (
% 0.71/0.87 szDzozmdt0: $i > $i)).
% 0.71/0.87 tff(aFunction0_type, type, (
% 0.71/0.87 aFunction0: $i > $o)).
% 0.71/0.87 tff(1,plain,
% 0.71/0.87 (^[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)))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(2,plain,
% 0.71/0.87 (![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))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1])).
% 0.71/0.87 tff(3,plain,
% 0.71/0.87 (^[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))))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(4,plain,
% 0.71/0.87 (![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))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[3])).
% 0.71/0.87 tff(5,plain,
% 0.71/0.87 (![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))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(6,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')).
% 0.71/0.87 tff(7,plain,
% 0.71/0.87 (((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))))))),
% 0.71/0.87 inference(and_elim,[status(thm)],[6])).
% 0.71/0.87 tff(8,plain,
% 0.71/0.87 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.71/0.87 inference(and_elim,[status(thm)],[7])).
% 0.71/0.87 tff(9,plain,
% 0.71/0.87 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.71/0.87 tff(10,plain,(
% 0.71/0.87 ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.71/0.87 inference(skolemize,[status(sab)],[9])).
% 0.71/0.87 tff(11,plain,
% 0.71/0.87 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.71/0.87 tff(12,plain,
% 0.71/0.87 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.71/0.87 tff(13,plain,
% 0.71/0.87 ((~![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))))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(14,plain,
% 0.71/0.87 (~(((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.71/0.87 tff(15,plain,
% 0.71/0.87 ((~![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)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(16,plain,
% 0.71/0.87 ((~((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))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(17,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__')).
% 0.71/0.88 tff(18,plain,
% 0.71/0.88 (~(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)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.71/0.88 tff(19,plain,
% 0.71/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.71/0.88 inference(or_elim,[status(thm)],[18])).
% 0.71/0.88 tff(20,plain,
% 0.71/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.71/0.88 tff(21,plain,
% 0.71/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.71/0.88 tff(22,plain,
% 0.71/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.71/0.88 tff(23,plain,(
% 0.71/0.88 ~((~aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0!31, xS))),
% 0.71/0.88 inference(skolemize,[status(sab)],[22])).
% 0.71/0.88 tff(24,plain,
% 0.71/0.88 (aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.71/0.88 inference(or_elim,[status(thm)],[23])).
% 0.71/0.88 tff(25,plain,
% 0.71/0.88 ((((~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)))))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(26,plain,
% 0.71/0.88 ((((~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)))))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.71/0.88 tff(27,plain,
% 0.71/0.88 (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[26, 14])).
% 0.71/0.88 tff(28,plain,
% 0.71/0.88 (((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(29,plain,
% 0.71/0.88 (aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.71/0.88 tff(30,plain,
% 0.71/0.88 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(31,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')).
% 0.71/0.88 tff(32,plain,
% 0.71/0.88 (((((((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)),
% 0.71/0.88 inference(and_elim,[status(thm)],[31])).
% 0.71/0.88 tff(33,plain,
% 0.71/0.88 ((((((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))))),
% 0.71/0.88 inference(and_elim,[status(thm)],[32])).
% 0.71/0.88 tff(34,plain,
% 0.71/0.88 (((((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)))))),
% 0.71/0.88 inference(and_elim,[status(thm)],[33])).
% 0.71/0.88 tff(35,plain,
% 0.71/0.88 ((((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)),
% 0.71/0.88 inference(and_elim,[status(thm)],[34])).
% 0.71/0.88 tff(36,plain,
% 0.71/0.88 (((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))))))),
% 0.71/0.88 inference(and_elim,[status(thm)],[35])).
% 0.71/0.88 tff(37,plain,
% 0.71/0.88 ((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))))),
% 0.71/0.88 inference(and_elim,[status(thm)],[36])).
% 0.71/0.88 tff(38,plain,
% 0.71/0.88 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.71/0.88 inference(and_elim,[status(thm)],[37])).
% 0.71/0.88 tff(39,plain,
% 0.71/0.88 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[38, 30])).
% 0.71/0.88 tff(40,plain,
% 0.71/0.88 (^[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)))))))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(41,plain,
% 0.71/0.88 (![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))))))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[40])).
% 0.71/0.88 tff(42,plain,
% 0.71/0.88 (^[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)))))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(43,plain,
% 0.71/0.88 (![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))))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[42])).
% 0.71/0.88 tff(44,plain,
% 0.71/0.88 (^[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)))))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(45,plain,
% 0.71/0.88 (![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))))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[44])).
% 0.71/0.88 tff(46,plain,
% 0.71/0.88 (![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))))))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[45, 43])).
% 0.71/0.88 tff(47,plain,
% 0.71/0.88 (^[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)))))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(48,plain,
% 0.71/0.88 (![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))))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[47])).
% 0.71/0.88 tff(49,plain,
% 0.71/0.88 (^[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)))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(50,plain,
% 0.71/0.88 (![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))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[49])).
% 0.71/0.88 tff(51,plain,
% 0.71/0.88 (![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)))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(52,plain,
% 0.71/0.88 (^[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)))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(53,plain,
% 0.71/0.88 (![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)))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[52])).
% 0.71/0.88 tff(54,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')).
% 0.71/0.88 tff(55,plain,
% 0.71/0.88 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.71/0.88 tff(56,plain,
% 0.71/0.88 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.71/0.88 tff(57,plain,(
% 0.71/0.88 ![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)))))))),
% 0.71/0.88 inference(skolemize,[status(sab)],[56])).
% 0.71/0.88 tff(58,plain,
% 0.71/0.88 (![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))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.71/0.88 tff(59,plain,
% 0.71/0.88 (![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))))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.71/0.88 tff(60,plain,
% 0.71/0.88 (![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))))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[59, 46])).
% 0.71/0.88 tff(61,plain,
% 0.71/0.88 (![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))))))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[60, 41])).
% 0.71/0.88 tff(62,plain,
% 0.71/0.88 (((~![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)))))))))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(63,plain,
% 0.71/0.88 (((~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)))))))))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(64,plain,
% 0.71/0.88 (((~![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))))))))))))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[63])).
% 0.71/0.88 tff(65,plain,
% 0.71/0.88 (((~![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)))))))))))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[64, 62])).
% 0.71/0.88 tff(66,plain,
% 0.71/0.88 ((~![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)))))))))))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(67,plain,
% 0.71/0.88 ((~![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))))))))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.71/0.88 tff(68,plain,
% 0.71/0.88 (![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))))))))))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[67, 61, 39])).
% 0.71/0.88 tff(69,plain,
% 0.71/0.88 (((~![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)))))))))))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(70,plain,
% 0.71/0.89 ((~((~((~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))))))))))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(71,plain,
% 0.71/0.89 (((~![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)))))))))))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[70])).
% 0.71/0.89 tff(72,plain,
% 0.71/0.89 (((~![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)))))))))))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[71, 69])).
% 0.71/0.89 tff(73,plain,
% 0.71/0.89 ((~![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))))))))))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(74,plain,
% 0.71/0.89 ((~![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))))))))))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.71/0.89 tff(75,plain,
% 0.71/0.89 (~((~(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)))))))))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[74, 68])).
% 0.71/0.89 tff(76,plain,
% 0.71/0.89 (((~(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)))))))))),
% 0.71/0.89 inference(tautology,[status(thm)],[])).
% 0.71/0.89 tff(77,plain,
% 0.71/0.89 ((~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))))))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.71/0.89 tff(78,plain,
% 0.71/0.89 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(79,plain,
% 0.71/0.89 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.71/0.89 inference(and_elim,[status(thm)],[33])).
% 0.71/0.89 tff(80,plain,
% 0.71/0.89 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.71/0.89 tff(81,plain,
% 0.71/0.89 ((~((~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))))))))),
% 0.71/0.89 inference(tautology,[status(thm)],[])).
% 0.71/0.89 tff(82,plain,
% 0.71/0.89 ((~((~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))))))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.71/0.89 tff(83,plain,
% 0.71/0.89 (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[82, 77])).
% 0.71/0.89 tff(84,plain,
% 0.71/0.89 (((~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)))))),
% 0.71/0.89 inference(tautology,[status(thm)],[])).
% 0.71/0.89 tff(85,plain,
% 0.71/0.89 (![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.71/0.89 tff(86,plain,
% 0.71/0.89 (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(87,axiom,(aElementOf0(xi, szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3989')).
% 0.71/0.89 tff(88,plain,
% 0.71/0.89 (aElementOf0(xi, szNzAzT0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.71/0.89 tff(89,plain,
% 0.71/0.89 (^[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)))))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(90,plain,
% 0.71/0.89 (![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))))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[89])).
% 0.71/0.89 tff(91,plain,
% 0.71/0.89 (^[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)))))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(92,plain,
% 0.71/0.89 (![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))))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[91])).
% 0.71/0.89 tff(93,plain,
% 0.71/0.89 (^[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)))))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(94,plain,
% 0.71/0.89 (![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))))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[93])).
% 0.71/0.89 tff(95,plain,
% 0.71/0.89 (![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))))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[94, 92])).
% 0.71/0.89 tff(96,plain,
% 0.71/0.89 (^[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)))))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(97,plain,
% 0.71/0.89 (![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)))) <=> ![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))))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[96])).
% 0.71/0.89 tff(98,plain,
% 0.71/0.89 (![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)))) <=> ![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))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(99,plain,
% 0.71/0.89 (^[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))))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(100,plain,
% 0.71/0.89 (![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)))) <=> ![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))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[99])).
% 0.71/0.89 tff(101,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')).
% 0.71/0.89 tff(102,plain,
% 0.71/0.89 (![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))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.71/0.89 tff(103,plain,
% 0.71/0.89 (![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))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.71/0.89 tff(104,plain,(
% 0.71/0.89 ![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))))),
% 0.71/0.89 inference(skolemize,[status(sab)],[103])).
% 0.71/0.89 tff(105,plain,
% 0.71/0.89 (![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))))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.71/0.89 tff(106,plain,
% 0.71/0.89 (![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))))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.71/0.89 tff(107,plain,
% 0.71/0.89 (![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))))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[106, 90])).
% 0.71/0.89 tff(108,plain,
% 0.71/0.89 (((~![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)))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(109,plain,
% 0.71/0.89 (((~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)))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(110,plain,
% 0.71/0.89 (((~![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))))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[109])).
% 0.71/0.90 tff(111,plain,
% 0.71/0.90 (((~![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)))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[110, 108])).
% 0.71/0.90 tff(112,plain,
% 0.71/0.90 ((~![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))))))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(113,plain,
% 0.71/0.90 ((~![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))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.71/0.90 tff(114,plain,
% 0.71/0.90 (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[113, 107, 88])).
% 0.71/0.90 tff(115,plain,
% 0.71/0.90 (((~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))),
% 0.71/0.90 inference(tautology,[status(thm)],[])).
% 0.71/0.90 tff(116,plain,
% 0.71/0.90 (isCountable0(sdtlpdtrp0(xN, xi))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.71/0.90 tff(117,plain,
% 0.71/0.90 (((~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)),
% 0.71/0.90 inference(tautology,[status(thm)],[])).
% 0.71/0.90 tff(118,plain,
% 0.71/0.90 (aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.71/0.90 tff(119,plain,
% 0.71/0.90 ((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))),
% 0.71/0.90 inference(tautology,[status(thm)],[])).
% 0.71/0.90 tff(120,plain,
% 0.71/0.90 (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)))))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.71/0.90 tff(121,plain,
% 0.71/0.90 (![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))))))))) <=> ![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)))))))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(122,plain,
% 0.71/0.90 (^[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)))))))))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(123,plain,
% 0.71/0.90 (![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)))))))) <=> ![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)))))))))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[122])).
% 0.71/0.90 tff(124,plain,
% 0.71/0.90 (![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)))))))) <=> ![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)))))))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[123, 121])).
% 0.71/0.90 tff(125,plain,
% 0.71/0.90 (^[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)))))))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(126,plain,
% 0.71/0.90 (![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)))))))) <=> ![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))))))))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[125])).
% 0.71/0.90 tff(127,plain,
% 0.71/0.90 (^[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)))))))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(128,plain,
% 0.71/0.90 (![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)))))))) <=> ![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))))))))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[127])).
% 0.71/0.90 tff(129,plain,
% 0.71/0.90 (![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)))))))) <=> ![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))))))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[128, 126])).
% 0.71/0.90 tff(130,plain,
% 0.71/0.90 (^[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))))))))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(131,plain,
% 0.74/0.91 (![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))))))))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[130])).
% 0.74/0.91 tff(132,plain,
% 0.74/0.91 (^[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))))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(133,plain,
% 0.74/0.91 (![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))))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[132])).
% 0.74/0.91 tff(134,plain,
% 0.74/0.91 (![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)))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(135,plain,
% 0.74/0.91 (^[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)))))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(136,plain,
% 0.74/0.92 (![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)))))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[135])).
% 0.74/0.92 tff(137,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')).
% 0.74/0.92 tff(138,plain,
% 0.74/0.92 (![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))))))),
% 0.74/0.92 inference(and_elim,[status(thm)],[137])).
% 0.74/0.92 tff(139,plain,
% 0.74/0.92 (![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)))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[138, 136])).
% 0.74/0.92 tff(140,plain,
% 0.74/0.92 (![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)))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[139, 134])).
% 0.74/0.92 tff(141,plain,(
% 0.74/0.92 ![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)))))),
% 0.74/0.92 inference(skolemize,[status(sab)],[140])).
% 0.74/0.92 tff(142,plain,
% 0.74/0.92 (![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))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[141, 133])).
% 0.74/0.92 tff(143,plain,
% 0.74/0.92 (![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))))))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[142, 131])).
% 0.74/0.92 tff(144,plain,
% 0.74/0.92 (![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))))))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[143, 129])).
% 0.74/0.92 tff(145,plain,
% 0.74/0.92 (![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)))))))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[144, 124])).
% 0.74/0.92 tff(146,plain,
% 0.74/0.92 (((~![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))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(147,plain,
% 0.74/0.93 (((~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))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(148,plain,
% 0.74/0.93 (((~![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)))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[147])).
% 0.74/0.93 tff(149,plain,
% 0.74/0.93 (((~![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))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[148, 146])).
% 0.74/0.93 tff(150,plain,
% 0.74/0.93 ((~![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)))))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(151,plain,
% 0.74/0.93 ((~![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)))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.74/0.93 tff(152,plain,
% 0.74/0.93 ((~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)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[151, 145, 88])).
% 0.74/0.93 tff(153,plain,
% 0.74/0.93 (~((~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))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[152, 120, 116])).
% 0.74/0.93 tff(154,plain,
% 0.74/0.93 (((~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))))))),
% 0.74/0.93 inference(tautology,[status(thm)],[])).
% 0.74/0.93 tff(155,plain,
% 0.74/0.93 (![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.74/0.93 tff(156,plain,
% 0.74/0.93 ((~![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))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(157,plain,
% 0.74/0.93 (~(((~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)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.74/0.93 tff(158,plain,
% 0.74/0.93 (~aElementOf0(W0!31, xS)),
% 0.74/0.93 inference(or_elim,[status(thm)],[23])).
% 0.74/0.93 tff(159,plain,
% 0.74/0.93 (^[W0: $i] : refl(((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(160,plain,
% 0.77/0.93 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[159])).
% 0.77/0.93 tff(161,plain,
% 0.77/0.93 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(162,plain,
% 0.77/0.93 (^[W0: $i] : rewrite((aElementOf0(W0, sdtlpdtrp0(xN, xi)) => aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(163,plain,
% 0.77/0.93 (![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[162])).
% 0.77/0.93 tff(164,axiom,(![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => aElementOf0(W0, xS)) & aSubsetOf0(sdtlpdtrp0(xN, xi), xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4037')).
% 0.77/0.93 tff(165,plain,
% 0.77/0.93 (![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => aElementOf0(W0, xS))),
% 0.77/0.93 inference(and_elim,[status(thm)],[164])).
% 0.77/0.93 tff(166,plain,
% 0.77/0.93 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[165, 163])).
% 0.77/0.93 tff(167,plain,
% 0.77/0.93 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[166, 161])).
% 0.77/0.93 tff(168,plain,(
% 0.77/0.93 ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 0.77/0.93 inference(skolemize,[status(sab)],[167])).
% 0.77/0.93 tff(169,plain,
% 0.77/0.93 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[168, 160])).
% 0.77/0.93 tff(170,plain,
% 0.77/0.93 (((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))) | ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, xS))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, xS))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(171,plain,
% 0.77/0.93 ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))) | ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, xS))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(172,plain,
% 0.77/0.93 ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, xS)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.77/0.93 tff(173,plain,
% 0.77/0.93 (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[172, 169, 158])).
% 0.77/0.93 tff(174,plain,
% 0.77/0.93 (((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 0.77/0.93 inference(tautology,[status(thm)],[])).
% 0.77/0.93 tff(175,plain,
% 0.77/0.93 ((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.77/0.93 tff(176,plain,
% 0.77/0.93 ((((~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)))))),
% 0.77/0.93 inference(tautology,[status(thm)],[])).
% 0.77/0.93 tff(177,plain,
% 0.77/0.93 ((((~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))))) | (~aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.77/0.94 tff(178,plain,
% 0.77/0.94 (~aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[177, 157])).
% 0.77/0.94 tff(179,plain,
% 0.77/0.94 (((~![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)))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(180,plain,
% 0.77/0.94 ((~![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)))))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(181,plain,
% 0.77/0.94 ((~![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))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.77/0.94 tff(182,plain,
% 0.77/0.94 (~aElementOf0(W0!31, xQ)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[181, 178, 85])).
% 0.77/0.94 tff(183,plain,
% 0.77/0.94 ((~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 0.77/0.94 inference(tautology,[status(thm)],[])).
% 0.77/0.94 tff(184,plain,
% 0.77/0.94 (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[183, 182, 29])).
% 0.77/0.94 tff(185,plain,
% 0.77/0.94 (aElementOf0(W0!31, xS) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), xS)),
% 0.77/0.94 inference(monotonicity,[status(thm)],[184])).
% 0.77/0.94 tff(186,plain,
% 0.77/0.94 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), xS) <=> aElementOf0(W0!31, xS)),
% 0.77/0.94 inference(symmetry,[status(thm)],[185])).
% 0.77/0.94 tff(187,plain,
% 0.77/0.94 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(188,plain,
% 0.77/0.94 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))),
% 0.77/0.94 inference(and_elim,[status(thm)],[37])).
% 0.77/0.94 tff(189,plain,
% 0.77/0.94 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 0.77/0.94 inference(and_elim,[status(thm)],[188])).
% 0.77/0.94 tff(190,plain,
% 0.77/0.94 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[189, 187])).
% 0.77/0.94 tff(191,plain,
% 0.77/0.94 (((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), xS))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), xS))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(192,plain,
% 0.77/0.94 ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), xS))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(193,plain,
% 0.77/0.94 ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), xS)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.77/0.94 tff(194,plain,
% 0.77/0.94 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), xS)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[193, 190, 169])).
% 0.77/0.94 tff(195,plain,
% 0.77/0.94 (aElementOf0(W0!31, xS)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[194, 186])).
% 0.77/0.94 tff(196,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[158, 195])).
% 0.77/0.94 % SZS output end Proof
% 0.77/0.94 % E exiting
%------------------------------------------------------------------------------