%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM590+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:21:30 AM UTC 2025
% Result : Theorem 0.46s 0.64s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM590+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:32:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.46/0.64 % SZS status Theorem
% 0.46/0.64 % SZS output start Proof
% 0.46/0.64 tff(aElementOf0_type, type, (
% 0.46/0.64 aElementOf0: ( $i * $i ) > $o)).
% 0.46/0.64 tff(sdtlpdtrp0_type, type, (
% 0.46/0.64 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.46/0.64 tff(xi_type, type, (
% 0.46/0.64 xi: $i)).
% 0.46/0.64 tff(xN_type, type, (
% 0.46/0.64 xN: $i)).
% 0.46/0.64 tff(tptp_fun_W0_34_type, type, (
% 0.46/0.64 tptp_fun_W0_34: $i)).
% 0.46/0.64 tff(szmzizndt0_type, type, (
% 0.46/0.64 szmzizndt0: $i > $i)).
% 0.46/0.64 tff(aElement0_type, type, (
% 0.46/0.64 aElement0: $i > $o)).
% 0.46/0.64 tff(xY_type, type, (
% 0.46/0.64 xY: $i)).
% 0.46/0.64 tff(aSet0_type, type, (
% 0.46/0.64 aSet0: $i > $o)).
% 0.46/0.64 tff(sdtlseqdt0_type, type, (
% 0.46/0.64 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.46/0.64 tff(sdtmndt0_type, type, (
% 0.46/0.64 sdtmndt0: ( $i * $i ) > $i)).
% 0.46/0.64 tff(xC_type, type, (
% 0.46/0.64 xC: $i)).
% 0.46/0.64 tff(xd_type, type, (
% 0.46/0.64 xd: $i)).
% 0.46/0.64 tff(szNzAzT0_type, type, (
% 0.46/0.64 szNzAzT0: $i)).
% 0.46/0.64 tff(aSubsetOf0_type, type, (
% 0.46/0.64 aSubsetOf0: ( $i * $i ) > $o)).
% 0.46/0.64 tff(isCountable0_type, type, (
% 0.46/0.64 isCountable0: $i > $o)).
% 0.46/0.64 tff(1,plain,
% 0.46/0.64 (^[W0: $i] : refl((~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY))))),
% 0.46/0.64 inference(bind,[status(th)],[])).
% 0.46/0.64 tff(2,plain,
% 0.46/0.64 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY)))),
% 0.46/0.64 inference(quant_intro,[status(thm)],[1])).
% 0.46/0.64 tff(3,plain,
% 0.46/0.64 (^[W0: $i] : trans(trans(monotonicity(rewrite((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))), ((aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (aElementOf0(W0, xY) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))), rewrite((aElementOf0(W0, xY) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY)))), ((aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY))))), rewrite((~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY)))), ((aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY)))))),
% 0.46/0.64 inference(bind,[status(th)],[])).
% 0.46/0.64 tff(4,plain,
% 0.46/0.64 (![W0: $i] : (aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY)))),
% 0.46/0.64 inference(quant_intro,[status(thm)],[3])).
% 0.46/0.64 tff(5,plain,
% 0.46/0.64 (![W0: $i] : (aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ![W0: $i] : (aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.46/0.64 inference(rewrite,[status(thm)],[])).
% 0.46/0.64 tff(6,plain,
% 0.46/0.64 (^[W0: $i] : rewrite((aElementOf0(W0, xY) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 0.46/0.64 inference(bind,[status(th)],[])).
% 0.46/0.64 tff(7,plain,
% 0.46/0.64 (![W0: $i] : (aElementOf0(W0, xY) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ![W0: $i] : (aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.46/0.64 inference(quant_intro,[status(thm)],[6])).
% 0.46/0.64 tff(8,axiom,(((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(xY)) & ![W0: $i] : (aElementOf0(W0, xY) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (xY = sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & (xd = sdtlpdtrp0(xC, xi))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4448_02')).
% 0.46/0.64 tff(9,plain,
% 0.46/0.64 ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(xY)) & ![W0: $i] : (aElementOf0(W0, xY) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (xY = sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.46/0.64 inference(and_elim,[status(thm)],[8])).
% 0.46/0.64 tff(10,plain,
% 0.46/0.64 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(xY)) & ![W0: $i] : (aElementOf0(W0, xY) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.46/0.64 inference(and_elim,[status(thm)],[9])).
% 0.46/0.64 tff(11,plain,
% 0.46/0.64 (![W0: $i] : (aElementOf0(W0, xY) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.46/0.64 inference(and_elim,[status(thm)],[10])).
% 0.46/0.64 tff(12,plain,
% 0.46/0.64 (![W0: $i] : (aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.46/0.64 tff(13,plain,
% 0.46/0.64 (![W0: $i] : (aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.46/0.64 tff(14,plain,(
% 0.46/0.64 ![W0: $i] : (aElementOf0(W0, xY) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.46/0.64 inference(skolemize,[status(sab)],[13])).
% 0.46/0.64 tff(15,plain,
% 0.46/0.64 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY)))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.46/0.64 tff(16,plain,
% 0.46/0.64 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY)))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.46/0.64 tff(17,plain,
% 0.46/0.64 ((~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0, xY)))) | (~(((~aElement0(W0!34)) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | (W0!34 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0!34, xY)))),
% 0.46/0.64 inference(quant_inst,[status(thm)],[])).
% 0.46/0.64 tff(18,plain,
% 0.46/0.64 (~(((~aElement0(W0!34)) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | (W0!34 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0!34, xY))),
% 0.46/0.64 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.46/0.64 tff(19,plain,
% 0.46/0.64 ((~![W0: $i] : ((~aElementOf0(W0, xY)) | aElementOf0(W0, szNzAzT0))) <=> (~![W0: $i] : ((~aElementOf0(W0, xY)) | aElementOf0(W0, szNzAzT0)))),
% 0.46/0.64 inference(rewrite,[status(thm)],[])).
% 0.46/0.64 tff(20,plain,
% 0.46/0.64 ((~![W0: $i] : (aElementOf0(W0, xY) => aElementOf0(W0, szNzAzT0))) <=> (~![W0: $i] : ((~aElementOf0(W0, xY)) | aElementOf0(W0, szNzAzT0)))),
% 0.46/0.64 inference(rewrite,[status(thm)],[])).
% 0.46/0.64 tff(21,axiom,(~(![W0: $i] : (aElementOf0(W0, xY) => aElementOf0(W0, szNzAzT0)) | aSubsetOf0(xY, szNzAzT0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.46/0.64 tff(22,plain,
% 0.46/0.64 (~![W0: $i] : (aElementOf0(W0, xY) => aElementOf0(W0, szNzAzT0))),
% 0.46/0.64 inference(or_elim,[status(thm)],[21])).
% 0.46/0.64 tff(23,plain,
% 0.46/0.64 (~![W0: $i] : ((~aElementOf0(W0, xY)) | aElementOf0(W0, szNzAzT0))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.46/0.64 tff(24,plain,
% 0.46/0.64 (~![W0: $i] : ((~aElementOf0(W0, xY)) | aElementOf0(W0, szNzAzT0))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.46/0.64 tff(25,plain,
% 0.46/0.64 (~![W0: $i] : ((~aElementOf0(W0, xY)) | aElementOf0(W0, szNzAzT0))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.46/0.64 tff(26,plain,
% 0.46/0.64 (~![W0: $i] : ((~aElementOf0(W0, xY)) | aElementOf0(W0, szNzAzT0))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.46/0.64 tff(27,plain,(
% 0.46/0.64 ~((~aElementOf0(W0!34, xY)) | aElementOf0(W0!34, szNzAzT0))),
% 0.46/0.64 inference(skolemize,[status(sab)],[26])).
% 0.46/0.64 tff(28,plain,
% 0.46/0.64 (aElementOf0(W0!34, xY)),
% 0.46/0.64 inference(or_elim,[status(thm)],[27])).
% 0.46/0.64 tff(29,plain,
% 0.46/0.64 ((((~aElement0(W0!34)) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | (W0!34 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0!34, xY)) | (~((~aElement0(W0!34)) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | (W0!34 = szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(W0!34, xY))),
% 0.46/0.64 inference(tautology,[status(thm)],[])).
% 0.46/0.64 tff(30,plain,
% 0.46/0.64 ((((~aElement0(W0!34)) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | (W0!34 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W0!34, xY)) | (~((~aElement0(W0!34)) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | (W0!34 = szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.46/0.64 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.46/0.64 tff(31,plain,
% 0.46/0.64 (~((~aElement0(W0!34)) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | (W0!34 = szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.46/0.64 inference(unit_resolution,[status(thm)],[30, 18])).
% 0.46/0.64 tff(32,plain,
% 0.46/0.64 (((~aElement0(W0!34)) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | (W0!34 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(W0!34, sdtlpdtrp0(xN, xi))),
% 0.46/0.64 inference(tautology,[status(thm)],[])).
% 0.46/0.64 tff(33,plain,
% 0.46/0.64 (aElementOf0(W0!34, sdtlpdtrp0(xN, xi))),
% 0.46/0.64 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.46/0.64 tff(34,plain,
% 0.46/0.64 (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 0.46/0.64 inference(rewrite,[status(thm)],[])).
% 0.46/0.64 tff(35,axiom,(aElementOf0(xi, szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4448')).
% 0.46/0.64 tff(36,plain,
% 0.46/0.64 (aElementOf0(xi, szNzAzT0)),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.46/0.64 tff(37,plain,
% 0.46/0.64 (^[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)))))))),
% 0.46/0.64 inference(bind,[status(th)],[])).
% 0.46/0.64 tff(38,plain,
% 0.46/0.64 (![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))))))),
% 0.46/0.64 inference(quant_intro,[status(thm)],[37])).
% 0.46/0.64 tff(39,plain,
% 0.46/0.64 (^[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)))))))),
% 0.46/0.64 inference(bind,[status(th)],[])).
% 0.46/0.64 tff(40,plain,
% 0.46/0.64 (![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))))))),
% 0.46/0.64 inference(quant_intro,[status(thm)],[39])).
% 0.46/0.64 tff(41,plain,
% 0.46/0.64 (^[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)))))))),
% 0.46/0.64 inference(bind,[status(th)],[])).
% 0.46/0.64 tff(42,plain,
% 0.46/0.64 (![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))))))),
% 0.46/0.64 inference(quant_intro,[status(thm)],[41])).
% 0.46/0.64 tff(43,plain,
% 0.46/0.64 (![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))))))),
% 0.46/0.64 inference(transitivity,[status(thm)],[42, 40])).
% 0.46/0.64 tff(44,plain,
% 0.46/0.64 (^[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)))))))),
% 0.46/0.64 inference(bind,[status(th)],[])).
% 0.46/0.64 tff(45,plain,
% 0.46/0.64 (![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))))))),
% 0.46/0.64 inference(quant_intro,[status(thm)],[44])).
% 0.46/0.64 tff(46,plain,
% 0.46/0.64 (![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))))),
% 0.46/0.64 inference(rewrite,[status(thm)],[])).
% 0.46/0.64 tff(47,plain,
% 0.46/0.64 (^[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))))))),
% 0.46/0.64 inference(bind,[status(th)],[])).
% 0.46/0.64 tff(48,plain,
% 0.46/0.64 (![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))))),
% 0.46/0.65 inference(quant_intro,[status(thm)],[47])).
% 0.46/0.65 tff(49,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')).
% 0.46/0.65 tff(50,plain,
% 0.46/0.65 (![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))))),
% 0.46/0.65 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.46/0.65 tff(51,plain,
% 0.46/0.65 (![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))))),
% 0.46/0.65 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.46/0.65 tff(52,plain,(
% 0.46/0.65 ![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))))),
% 0.46/0.65 inference(skolemize,[status(sab)],[51])).
% 0.46/0.65 tff(53,plain,
% 0.46/0.65 (![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))))))),
% 0.46/0.65 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.46/0.65 tff(54,plain,
% 0.46/0.65 (![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))))))),
% 0.46/0.65 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.46/0.65 tff(55,plain,
% 0.46/0.65 (![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))))))),
% 0.46/0.65 inference(modus_ponens,[status(thm)],[54, 38])).
% 0.46/0.65 tff(56,plain,
% 0.46/0.65 (((~![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))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~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))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))))))),
% 0.46/0.65 inference(rewrite,[status(thm)],[])).
% 0.46/0.65 tff(57,plain,
% 0.46/0.65 (((~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))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))))))),
% 0.46/0.65 inference(rewrite,[status(thm)],[])).
% 0.46/0.65 tff(58,plain,
% 0.46/0.65 (((~![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))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0)))))))),
% 0.46/0.65 inference(monotonicity,[status(thm)],[57])).
% 0.46/0.65 tff(59,plain,
% 0.46/0.65 (((~![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))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))))))),
% 0.46/0.65 inference(transitivity,[status(thm)],[58, 56])).
% 0.46/0.65 tff(60,plain,
% 0.46/0.65 ((~![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))))))),
% 0.46/0.65 inference(quant_inst,[status(thm)],[])).
% 0.46/0.65 tff(61,plain,
% 0.46/0.65 ((~![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))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0)))))),
% 0.46/0.65 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.46/0.65 tff(62,plain,
% 0.46/0.65 (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))))),
% 0.46/0.65 inference(unit_resolution,[status(thm)],[61, 55, 36])).
% 0.46/0.65 tff(63,plain,
% 0.46/0.65 (((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0)))) | ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))),
% 0.46/0.65 inference(tautology,[status(thm)],[])).
% 0.46/0.65 tff(64,plain,
% 0.46/0.65 (![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))),
% 0.46/0.65 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.46/0.65 tff(65,plain,
% 0.46/0.65 (~aElementOf0(W0!34, szNzAzT0)),
% 0.46/0.65 inference(or_elim,[status(thm)],[27])).
% 0.46/0.65 tff(66,plain,
% 0.46/0.65 (((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | ((~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!34, szNzAzT0))) <=> ((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!34, szNzAzT0))),
% 0.46/0.65 inference(rewrite,[status(thm)],[])).
% 0.46/0.65 tff(67,plain,
% 0.46/0.65 ((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | ((~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!34, szNzAzT0))),
% 0.46/0.65 inference(quant_inst,[status(thm)],[])).
% 0.46/0.65 tff(68,plain,
% 0.46/0.65 ((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szNzAzT0))) | (~aElementOf0(W0!34, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!34, szNzAzT0)),
% 0.46/0.65 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.46/0.65 tff(69,plain,
% 0.46/0.65 ($false),
% 0.46/0.65 inference(unit_resolution,[status(thm)],[68, 65, 64, 33])).
% 0.46/0.65 % SZS output end Proof
% 0.46/0.66 % E exiting
%------------------------------------------------------------------------------