%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM577+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:21:27 AM UTC 2025
% Result : Theorem 125.45s 125.69s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM577+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.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 01:33:34 EDT 2025
% 0.13/0.35 % CPUTime :
% 125.45/125.69 % SZS status Theorem
% 125.45/125.69 % SZS output start Proof
% 125.45/125.69 tff(aElementOf0_type, type, (
% 125.45/125.69 aElementOf0: ( $i * $i ) > $o)).
% 125.45/125.69 tff(sdtlpdtrp0_type, type, (
% 125.45/125.69 sdtlpdtrp0: ( $i * $i ) > $i)).
% 125.45/125.69 tff(szszuzczcdt0_type, type, (
% 125.45/125.69 szszuzczcdt0: $i > $i)).
% 125.45/125.69 tff(xn_type, type, (
% 125.45/125.69 xn: $i)).
% 125.45/125.69 tff(xN_type, type, (
% 125.45/125.69 xN: $i)).
% 125.45/125.69 tff(tptp_fun_W0_30_type, type, (
% 125.45/125.69 tptp_fun_W0_30: $i)).
% 125.45/125.69 tff(sdtmndt0_type, type, (
% 125.45/125.69 sdtmndt0: ( $i * $i ) > $i)).
% 125.45/125.69 tff(szmzizndt0_type, type, (
% 125.45/125.69 szmzizndt0: $i > $i)).
% 125.45/125.69 tff(aSet0_type, type, (
% 125.45/125.69 aSet0: $i > $o)).
% 125.45/125.69 tff(aSubsetOf0_type, type, (
% 125.45/125.69 aSubsetOf0: ( $i * $i ) > $o)).
% 125.45/125.69 tff(tptp_fun_W2_1_type, type, (
% 125.45/125.69 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 125.45/125.69 tff(isCountable0_type, type, (
% 125.45/125.69 isCountable0: $i > $o)).
% 125.45/125.69 tff(sdtlseqdt0_type, type, (
% 125.45/125.69 sdtlseqdt0: ( $i * $i ) > $o)).
% 125.45/125.69 tff(aElement0_type, type, (
% 125.45/125.69 aElement0: $i > $o)).
% 125.45/125.69 tff(szNzAzT0_type, type, (
% 125.45/125.69 szNzAzT0: $i)).
% 125.45/125.69 tff(xm_type, type, (
% 125.45/125.69 xm: $i)).
% 125.45/125.69 tff(tptp_fun_W1_29_type, type, (
% 125.45/125.69 tptp_fun_W1_29: $i > $i)).
% 125.45/125.69 tff(xS_type, type, (
% 125.45/125.69 xS: $i)).
% 125.45/125.69 tff(sz00_type, type, (
% 125.45/125.69 sz00: $i)).
% 125.45/125.69 tff(szDzozmdt0_type, type, (
% 125.45/125.69 szDzozmdt0: $i > $i)).
% 125.45/125.69 tff(aFunction0_type, type, (
% 125.45/125.69 aFunction0: $i > $o)).
% 125.45/125.69 tff(1,plain,
% 125.45/125.69 (aElementOf0(xn, szNzAzT0) <=> aElementOf0(xn, szNzAzT0)),
% 125.45/125.69 inference(rewrite,[status(thm)],[])).
% 125.45/125.69 tff(2,axiom,(aElementOf0(xn, szNzAzT0) & aElementOf0(xm, szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3904')).
% 125.45/125.69 tff(3,plain,
% 125.45/125.69 (aElementOf0(xn, szNzAzT0)),
% 125.45/125.69 inference(and_elim,[status(thm)],[2])).
% 125.45/125.69 tff(4,plain,
% 125.45/125.69 (aElementOf0(xn, szNzAzT0)),
% 125.45/125.69 inference(modus_ponens,[status(thm)],[3, 1])).
% 125.45/125.69 tff(5,plain,
% 125.45/125.69 (^[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)))))))),
% 125.45/125.69 inference(bind,[status(th)],[])).
% 125.45/125.69 tff(6,plain,
% 125.45/125.69 (![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))))))),
% 125.45/125.69 inference(quant_intro,[status(thm)],[5])).
% 125.45/125.69 tff(7,plain,
% 125.45/125.69 (^[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)))))))),
% 125.45/125.69 inference(bind,[status(th)],[])).
% 125.45/125.69 tff(8,plain,
% 125.45/125.69 (![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))))))),
% 125.45/125.69 inference(quant_intro,[status(thm)],[7])).
% 125.45/125.69 tff(9,plain,
% 125.45/125.69 (^[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)))))))),
% 125.45/125.69 inference(bind,[status(th)],[])).
% 125.45/125.69 tff(10,plain,
% 125.45/125.69 (![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))))))),
% 125.45/125.69 inference(quant_intro,[status(thm)],[9])).
% 125.45/125.69 tff(11,plain,
% 125.45/125.69 (![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))))))),
% 125.45/125.69 inference(transitivity,[status(thm)],[10, 8])).
% 125.45/125.69 tff(12,plain,
% 125.45/125.69 (^[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)))))))),
% 125.45/125.69 inference(bind,[status(th)],[])).
% 125.45/125.69 tff(13,plain,
% 125.45/125.69 (![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))))))),
% 125.45/125.69 inference(quant_intro,[status(thm)],[12])).
% 125.45/125.69 tff(14,plain,
% 125.45/125.69 (![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))))),
% 125.45/125.69 inference(rewrite,[status(thm)],[])).
% 125.45/125.69 tff(15,plain,
% 125.45/125.69 (^[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))))))),
% 125.45/125.69 inference(bind,[status(th)],[])).
% 125.45/125.69 tff(16,plain,
% 125.45/125.69 (![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))))),
% 125.45/125.69 inference(quant_intro,[status(thm)],[15])).
% 125.45/125.69 tff(17,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/sandbox/benchmark/theBenchmark.p','m__3671')).
% 125.45/125.69 tff(18,plain,
% 125.45/125.69 (![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))))),
% 125.45/125.69 inference(modus_ponens,[status(thm)],[17, 16])).
% 125.45/125.69 tff(19,plain,
% 125.45/125.69 (![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))))),
% 125.45/125.70 inference(modus_ponens,[status(thm)],[18, 14])).
% 125.45/125.70 tff(20,plain,(
% 125.45/125.70 ![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))))),
% 125.45/125.70 inference(skolemize,[status(sab)],[19])).
% 125.45/125.70 tff(21,plain,
% 125.45/125.70 (![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))))))),
% 125.45/125.70 inference(modus_ponens,[status(thm)],[20, 13])).
% 125.45/125.70 tff(22,plain,
% 125.45/125.70 (![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))))))),
% 125.45/125.70 inference(modus_ponens,[status(thm)],[21, 11])).
% 125.45/125.70 tff(23,plain,
% 125.45/125.70 (![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))))))),
% 125.45/125.70 inference(modus_ponens,[status(thm)],[22, 6])).
% 125.45/125.70 tff(24,plain,
% 125.45/125.70 (((~![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(xn, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), 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(xn, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)))))),
% 125.45/125.70 inference(rewrite,[status(thm)],[])).
% 125.45/125.70 tff(25,plain,
% 125.45/125.70 (((~aElementOf0(xn, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0)))))) <=> ((~aElementOf0(xn, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)))))),
% 125.45/125.70 inference(rewrite,[status(thm)],[])).
% 125.45/125.70 tff(26,plain,
% 125.45/125.70 (((~![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(xn, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | 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(xn, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0))))))),
% 125.45/125.70 inference(monotonicity,[status(thm)],[25])).
% 125.45/125.70 tff(27,plain,
% 125.45/125.70 (((~![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(xn, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | 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(xn, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)))))),
% 125.45/125.70 inference(transitivity,[status(thm)],[26, 24])).
% 125.45/125.70 tff(28,plain,
% 125.45/125.70 ((~![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(xn, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))))))),
% 125.45/125.70 inference(quant_inst,[status(thm)],[])).
% 125.45/125.70 tff(29,plain,
% 125.45/125.70 ((~![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(xn, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0))))),
% 125.45/125.70 inference(modus_ponens,[status(thm)],[28, 27])).
% 125.45/125.70 tff(30,plain,
% 125.45/125.70 (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)))),
% 125.45/125.70 inference(unit_resolution,[status(thm)],[29, 23, 4])).
% 125.45/125.70 tff(31,plain,
% 125.45/125.70 (((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0))) | isCountable0(sdtlpdtrp0(xN, xn))),
% 125.45/125.70 inference(tautology,[status(thm)],[])).
% 125.45/125.70 tff(32,plain,
% 125.45/125.70 (isCountable0(sdtlpdtrp0(xN, xn))),
% 125.45/125.70 inference(unit_resolution,[status(thm)],[31, 30])).
% 125.45/125.70 tff(33,plain,
% 125.45/125.70 (((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~aSet0(sdtlpdtrp0(xN, xn))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)),
% 125.45/125.70 inference(tautology,[status(thm)],[])).
% 125.45/125.70 tff(34,plain,
% 125.45/125.70 (aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0)),
% 125.45/125.70 inference(unit_resolution,[status(thm)],[33, 30])).
% 125.45/125.70 tff(35,plain,
% 125.45/125.70 ((aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0))),
% 125.45/125.70 inference(tautology,[status(thm)],[])).
% 125.45/125.70 tff(36,plain,
% 125.45/125.70 (aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0)))))),
% 125.45/125.70 inference(unit_resolution,[status(thm)],[35, 34])).
% 125.45/125.70 tff(37,plain,
% 125.45/125.70 (![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)))))))))),
% 125.45/125.70 inference(rewrite,[status(thm)],[])).
% 125.45/125.70 tff(38,plain,
% 125.45/125.70 (^[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)))))))))))),
% 125.45/125.70 inference(bind,[status(th)],[])).
% 125.45/125.70 tff(39,plain,
% 125.45/125.70 (![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)))))))))),
% 125.45/125.70 inference(quant_intro,[status(thm)],[38])).
% 125.45/125.70 tff(40,plain,
% 125.45/125.70 (![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)))))))))),
% 125.45/125.70 inference(transitivity,[status(thm)],[39, 37])).
% 125.45/125.70 tff(41,plain,
% 125.45/125.70 (^[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)))))))))),
% 125.45/125.70 inference(bind,[status(th)],[])).
% 125.45/125.70 tff(42,plain,
% 125.45/125.70 (![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))))))))),
% 125.45/125.70 inference(quant_intro,[status(thm)],[41])).
% 125.45/125.70 tff(43,plain,
% 125.45/125.70 (^[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)))))))))),
% 125.45/125.70 inference(bind,[status(th)],[])).
% 125.45/125.70 tff(44,plain,
% 125.45/125.70 (![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))))))))),
% 125.45/125.70 inference(quant_intro,[status(thm)],[43])).
% 125.45/125.70 tff(45,plain,
% 125.45/125.70 (![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))))))))),
% 125.55/125.71 inference(transitivity,[status(thm)],[44, 42])).
% 125.55/125.71 tff(46,plain,
% 125.55/125.71 (^[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))))))))))),
% 125.55/125.71 inference(bind,[status(th)],[])).
% 125.55/125.71 tff(47,plain,
% 125.55/125.71 (![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))))))))),
% 125.55/125.71 inference(quant_intro,[status(thm)],[46])).
% 125.55/125.71 tff(48,plain,
% 125.55/125.71 (^[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))))))),
% 125.55/125.71 inference(bind,[status(th)],[])).
% 125.55/125.71 tff(49,plain,
% 125.55/125.71 (![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))))),
% 125.55/125.71 inference(quant_intro,[status(thm)],[48])).
% 125.55/125.71 tff(50,plain,
% 125.55/125.71 (![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)))))),
% 125.55/125.71 inference(rewrite,[status(thm)],[])).
% 125.55/125.71 tff(51,plain,
% 125.55/125.71 (^[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)))))))),
% 125.55/125.73 inference(bind,[status(th)],[])).
% 125.55/125.73 tff(52,plain,
% 125.55/125.73 (![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)))))),
% 125.55/125.73 inference(quant_intro,[status(thm)],[51])).
% 125.55/125.73 tff(53,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/sandbox/benchmark/theBenchmark.p','m__3623')).
% 125.55/125.73 tff(54,plain,
% 125.55/125.73 (![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))))))),
% 125.55/125.73 inference(and_elim,[status(thm)],[53])).
% 125.55/125.73 tff(55,plain,
% 125.55/125.73 (![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)))))),
% 125.55/125.73 inference(modus_ponens,[status(thm)],[54, 52])).
% 125.55/125.73 tff(56,plain,
% 125.55/125.73 (![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)))))),
% 125.55/125.73 inference(modus_ponens,[status(thm)],[55, 50])).
% 125.55/125.73 tff(57,plain,(
% 125.55/125.73 ![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)))))),
% 125.55/125.73 inference(skolemize,[status(sab)],[56])).
% 125.55/125.73 tff(58,plain,
% 125.55/125.73 (![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))))),
% 125.55/125.73 inference(modus_ponens,[status(thm)],[57, 49])).
% 125.55/125.73 tff(59,plain,
% 125.55/125.73 (![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))))))))),
% 125.55/125.73 inference(modus_ponens,[status(thm)],[58, 47])).
% 125.55/125.73 tff(60,plain,
% 125.55/125.73 (![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))))))))),
% 125.55/125.73 inference(modus_ponens,[status(thm)],[59, 45])).
% 125.55/125.73 tff(61,plain,
% 125.55/125.73 (![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)))))))))),
% 125.55/125.73 inference(modus_ponens,[status(thm)],[60, 40])).
% 125.55/125.73 tff(62,plain,
% 125.55/125.73 (((~![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(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))) <=> ((~![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(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))),
% 125.55/125.73 inference(rewrite,[status(thm)],[])).
% 125.55/125.73 tff(63,plain,
% 125.55/125.73 (((~aElementOf0(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))) <=> ((~aElementOf0(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))),
% 125.55/125.73 inference(rewrite,[status(thm)],[])).
% 125.55/125.73 tff(64,plain,
% 125.55/125.73 (((~![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(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))) <=> ((~![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(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))),
% 125.55/125.73 inference(monotonicity,[status(thm)],[63])).
% 125.55/125.73 tff(65,plain,
% 125.55/125.73 (((~![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(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))) <=> ((~![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(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))),
% 125.55/125.73 inference(transitivity,[status(thm)],[64, 62])).
% 125.55/125.73 tff(66,plain,
% 125.55/125.73 ((~![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(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))),
% 125.55/125.74 inference(quant_inst,[status(thm)],[])).
% 125.55/125.74 tff(67,plain,
% 125.55/125.74 ((~![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(xn, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn))))))),
% 125.55/125.74 inference(modus_ponens,[status(thm)],[66, 65])).
% 125.55/125.74 tff(68,plain,
% 125.55/125.74 ((~isCountable0(sdtlpdtrp0(xN, xn))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xn), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xn))) | (~((~aElementOf0(tptp_fun_W1_29(xn), sdtlpdtrp0(xN, xn))) | aElementOf0(tptp_fun_W1_29(xn), szNzAzT0))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn))))))),
% 125.55/125.74 inference(unit_resolution,[status(thm)],[67, 61, 4])).
% 125.55/125.74 tff(69,plain,
% 125.55/125.74 (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))))),
% 125.55/125.74 inference(unit_resolution,[status(thm)],[68, 36, 32])).
% 125.55/125.74 tff(70,plain,
% 125.55/125.74 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn))))) | aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.74 inference(tautology,[status(thm)],[])).
% 125.55/125.74 tff(71,plain,
% 125.55/125.74 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.74 inference(unit_resolution,[status(thm)],[70, 69])).
% 125.55/125.74 tff(72,plain,
% 125.55/125.74 (^[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)))))))))))),
% 125.55/125.74 inference(bind,[status(th)],[])).
% 125.55/125.74 tff(73,plain,
% 125.55/125.74 (![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))))))))))),
% 125.55/125.74 inference(quant_intro,[status(thm)],[72])).
% 125.55/125.74 tff(74,plain,
% 125.55/125.74 (^[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)))))))))),
% 125.55/125.74 inference(bind,[status(th)],[])).
% 125.55/125.74 tff(75,plain,
% 125.55/125.74 (![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))))))))),
% 125.55/125.74 inference(quant_intro,[status(thm)],[74])).
% 125.55/125.74 tff(76,plain,
% 125.55/125.74 (^[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)))))))))),
% 125.55/125.74 inference(bind,[status(th)],[])).
% 125.55/125.74 tff(77,plain,
% 125.55/125.74 (![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))))))))),
% 125.55/125.74 inference(quant_intro,[status(thm)],[76])).
% 125.55/125.74 tff(78,plain,
% 125.55/125.74 (![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))))))))),
% 125.55/125.74 inference(transitivity,[status(thm)],[77, 75])).
% 125.55/125.74 tff(79,plain,
% 125.55/125.74 (^[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)))))))))),
% 125.55/125.74 inference(bind,[status(th)],[])).
% 125.55/125.74 tff(80,plain,
% 125.55/125.74 (![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))))))))),
% 125.55/125.74 inference(quant_intro,[status(thm)],[79])).
% 125.55/125.74 tff(81,plain,
% 125.55/125.74 (^[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)))))))),
% 125.55/125.74 inference(bind,[status(th)],[])).
% 125.55/125.74 tff(82,plain,
% 125.55/125.74 (![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))))))),
% 125.55/125.74 inference(quant_intro,[status(thm)],[81])).
% 125.55/125.74 tff(83,plain,
% 125.55/125.74 (![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)))))),
% 125.55/125.74 inference(rewrite,[status(thm)],[])).
% 125.55/125.74 tff(84,plain,
% 125.55/125.74 (^[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)))))))),
% 125.55/125.74 inference(bind,[status(th)],[])).
% 125.55/125.74 tff(85,plain,
% 125.55/125.74 (![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)))))),
% 125.55/125.74 inference(quant_intro,[status(thm)],[84])).
% 125.55/125.74 tff(86,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSub')).
% 125.55/125.74 tff(87,plain,
% 125.55/125.74 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 125.55/125.74 inference(modus_ponens,[status(thm)],[86, 85])).
% 125.55/125.74 tff(88,plain,
% 125.55/125.74 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 125.55/125.74 inference(modus_ponens,[status(thm)],[87, 83])).
% 125.55/125.74 tff(89,plain,(
% 125.55/125.74 ![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)))))))),
% 125.55/125.74 inference(skolemize,[status(sab)],[88])).
% 125.55/125.74 tff(90,plain,
% 125.55/125.74 (![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))))))),
% 125.55/125.74 inference(modus_ponens,[status(thm)],[89, 82])).
% 125.55/125.74 tff(91,plain,
% 125.55/125.74 (![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))))))))),
% 125.55/125.74 inference(modus_ponens,[status(thm)],[90, 80])).
% 125.55/125.74 tff(92,plain,
% 125.55/125.74 (![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))))))))),
% 125.55/125.74 inference(modus_ponens,[status(thm)],[91, 78])).
% 125.55/125.74 tff(93,plain,
% 125.55/125.74 (![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))))))))))),
% 125.55/125.74 inference(modus_ponens,[status(thm)],[92, 73])).
% 125.55/125.74 tff(94,plain,
% 125.55/125.74 (((~![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, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))) <=> ((~![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, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))),
% 125.55/125.74 inference(rewrite,[status(thm)],[])).
% 125.55/125.74 tff(95,plain,
% 125.55/125.74 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) <=> ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))),
% 125.55/125.74 inference(rewrite,[status(thm)],[])).
% 125.55/125.74 tff(96,plain,
% 125.55/125.74 (((~![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, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))) <=> ((~![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, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))))),
% 125.55/125.74 inference(monotonicity,[status(thm)],[95])).
% 125.55/125.74 tff(97,plain,
% 125.55/125.74 (((~![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, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))) <=> ((~![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, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))),
% 125.55/125.74 inference(transitivity,[status(thm)],[96, 94])).
% 125.55/125.74 tff(98,plain,
% 125.55/125.74 ((~![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, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))),
% 125.55/125.74 inference(quant_inst,[status(thm)],[])).
% 125.55/125.74 tff(99,plain,
% 125.55/125.74 ((~![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, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))),
% 125.55/125.74 inference(modus_ponens,[status(thm)],[98, 97])).
% 125.55/125.74 tff(100,plain,
% 125.55/125.74 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))),
% 125.55/125.74 inference(unit_resolution,[status(thm)],[99, 93, 71])).
% 125.55/125.74 tff(101,plain,
% 125.55/125.74 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) | (~((~(aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) | (~((~(aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))),
% 125.55/125.75 inference(rewrite,[status(thm)],[])).
% 125.55/125.75 tff(102,plain,
% 125.55/125.75 ((~((~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))) <=> (~((~(aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))),
% 125.55/125.75 inference(rewrite,[status(thm)],[])).
% 125.55/125.75 tff(103,plain,
% 125.55/125.75 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) | (~((~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) | (~((~(aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))),
% 125.55/125.75 inference(monotonicity,[status(thm)],[102])).
% 125.55/125.75 tff(104,plain,
% 125.55/125.75 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) | (~((~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) | (~((~(aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))))),
% 125.55/125.75 inference(transitivity,[status(thm)],[103, 101])).
% 125.55/125.75 tff(105,plain,
% 125.55/125.75 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) | (~((~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))),
% 125.55/125.75 inference(quant_inst,[status(thm)],[])).
% 125.55/125.75 tff(106,plain,
% 125.55/125.75 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))) | (~((~(aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))))),
% 125.55/125.75 inference(modus_ponens,[status(thm)],[105, 104])).
% 125.55/125.75 tff(107,plain,
% 125.55/125.75 (~((~(aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))))),
% 125.55/125.75 inference(unit_resolution,[status(thm)],[106, 100])).
% 125.55/125.75 tff(108,plain,
% 125.55/125.75 (((~(aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~((~aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))))) | ((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))),
% 125.55/125.75 inference(tautology,[status(thm)],[])).
% 125.55/125.75 tff(109,plain,
% 125.55/125.75 ((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))),
% 125.55/125.75 inference(unit_resolution,[status(thm)],[108, 107])).
% 125.55/125.75 tff(110,plain,
% 125.55/125.75 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn))))) | aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.75 inference(tautology,[status(thm)],[])).
% 125.55/125.75 tff(111,plain,
% 125.55/125.75 (aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.75 inference(unit_resolution,[status(thm)],[110, 69])).
% 125.55/125.75 tff(112,plain,
% 125.55/125.75 ((~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))),
% 125.55/125.75 inference(tautology,[status(thm)],[])).
% 125.55/125.75 tff(113,plain,
% 125.55/125.75 ((~((~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))))) | (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))))),
% 125.55/125.75 inference(unit_resolution,[status(thm)],[112, 111])).
% 125.55/125.75 tff(114,plain,
% 125.55/125.75 (~((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))))),
% 125.55/125.75 inference(unit_resolution,[status(thm)],[113, 109])).
% 125.55/125.75 tff(115,plain,
% 125.55/125.75 (((~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.75 inference(tautology,[status(thm)],[])).
% 125.55/125.75 tff(116,plain,
% 125.55/125.75 (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.75 inference(unit_resolution,[status(thm)],[115, 114])).
% 125.55/125.75 tff(117,plain,
% 125.55/125.75 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn))))) | ![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))),
% 125.55/125.75 inference(tautology,[status(thm)],[])).
% 125.55/125.75 tff(118,plain,
% 125.55/125.75 (![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))),
% 125.55/125.75 inference(unit_resolution,[status(thm)],[117, 69])).
% 125.55/125.75 tff(119,plain,
% 125.55/125.75 ((~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~(((~aElement0(szmzizndt0(sdtlpdtrp0(xN, xm)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))),
% 125.55/125.75 inference(quant_inst,[status(thm)],[])).
% 125.55/125.75 tff(120,plain,
% 125.55/125.75 (~(((~aElement0(szmzizndt0(sdtlpdtrp0(xN, xm)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.75 inference(unit_resolution,[status(thm)],[119, 118])).
% 125.55/125.75 tff(121,plain,
% 125.55/125.75 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))))),
% 125.55/125.75 inference(bind,[status(th)],[])).
% 125.55/125.75 tff(122,plain,
% 125.55/125.75 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 125.55/125.75 inference(quant_intro,[status(thm)],[121])).
% 125.55/125.75 tff(123,plain,
% 125.55/125.75 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))))),
% 125.55/125.75 inference(bind,[status(th)],[])).
% 125.55/125.75 tff(124,plain,
% 125.55/125.75 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 125.55/125.75 inference(quant_intro,[status(thm)],[123])).
% 125.55/125.75 tff(125,plain,
% 125.55/125.75 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 125.55/125.75 inference(rewrite,[status(thm)],[])).
% 125.55/125.75 tff(126,plain,
% 125.55/125.75 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))))),
% 125.55/125.75 inference(bind,[status(th)],[])).
% 125.55/125.75 tff(127,plain,
% 125.55/125.75 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 125.55/125.75 inference(quant_intro,[status(thm)],[126])).
% 125.55/125.75 tff(128,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSuccNum')).
% 125.55/125.75 tff(129,plain,
% 125.55/125.75 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 125.55/125.75 inference(modus_ponens,[status(thm)],[128, 127])).
% 125.55/125.75 tff(130,plain,
% 125.55/125.75 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 125.55/125.75 inference(modus_ponens,[status(thm)],[129, 125])).
% 125.55/125.75 tff(131,plain,(
% 125.55/125.76 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 125.55/125.76 inference(skolemize,[status(sab)],[130])).
% 125.55/125.76 tff(132,plain,
% 125.55/125.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[131, 124])).
% 125.55/125.76 tff(133,plain,
% 125.55/125.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[132, 122])).
% 125.55/125.76 tff(134,plain,
% 125.55/125.76 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(xn, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(xn, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00))))),
% 125.55/125.76 inference(rewrite,[status(thm)],[])).
% 125.55/125.76 tff(135,plain,
% 125.55/125.76 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(xn, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00))))),
% 125.55/125.76 inference(quant_inst,[status(thm)],[])).
% 125.55/125.76 tff(136,plain,
% 125.55/125.76 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(xn, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00)))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[135, 134])).
% 125.55/125.76 tff(137,plain,
% 125.55/125.76 (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00))),
% 125.55/125.76 inference(unit_resolution,[status(thm)],[136, 133, 4])).
% 125.55/125.76 tff(138,plain,
% 125.55/125.76 (((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00)) | aElementOf0(szszuzczcdt0(xn), szNzAzT0)),
% 125.55/125.76 inference(tautology,[status(thm)],[])).
% 125.55/125.76 tff(139,plain,
% 125.55/125.76 (aElementOf0(szszuzczcdt0(xn), szNzAzT0)),
% 125.55/125.76 inference(unit_resolution,[status(thm)],[138, 137])).
% 125.55/125.76 tff(140,plain,
% 125.55/125.76 (sdtlseqdt0(szszuzczcdt0(xn), xm) <=> sdtlseqdt0(szszuzczcdt0(xn), xm)),
% 125.55/125.76 inference(rewrite,[status(thm)],[])).
% 125.55/125.76 tff(141,plain,
% 125.55/125.76 ((~(sdtlseqdt0(szszuzczcdt0(xn), xm) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xn)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) => (![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xm)) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) & (~((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xm)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xn)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) <=> (~((~sdtlseqdt0(szszuzczcdt0(xn), xm)) | ((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))))))),
% 125.55/125.76 inference(rewrite,[status(thm)],[])).
% 125.55/125.76 tff(142,axiom,(~(sdtlseqdt0(szszuzczcdt0(xn), xm) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xn)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) => (![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xm)) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) & (~((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xm)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xn)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 125.55/125.76 tff(143,plain,
% 125.55/125.76 (~((~sdtlseqdt0(szszuzczcdt0(xn), xm)) | ((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[142, 141])).
% 125.55/125.76 tff(144,plain,
% 125.55/125.76 (sdtlseqdt0(szszuzczcdt0(xn), xm)),
% 125.55/125.76 inference(or_elim,[status(thm)],[143])).
% 125.55/125.76 tff(145,plain,
% 125.55/125.76 (sdtlseqdt0(szszuzczcdt0(xn), xm)),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[144, 140])).
% 125.55/125.76 tff(146,plain,
% 125.55/125.76 (aElementOf0(xm, szNzAzT0) <=> aElementOf0(xm, szNzAzT0)),
% 125.55/125.76 inference(rewrite,[status(thm)],[])).
% 125.55/125.76 tff(147,plain,
% 125.55/125.76 (aElementOf0(xm, szNzAzT0)),
% 125.55/125.76 inference(and_elim,[status(thm)],[2])).
% 125.55/125.76 tff(148,plain,
% 125.55/125.76 (aElementOf0(xm, szNzAzT0)),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[147, 146])).
% 125.55/125.76 tff(149,plain,
% 125.55/125.76 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))))))), (((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))))))))), rewrite(((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))), (((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))))),
% 125.55/125.76 inference(bind,[status(th)],[])).
% 125.55/125.76 tff(150,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))),
% 125.55/125.76 inference(quant_intro,[status(thm)],[149])).
% 125.55/125.76 tff(151,plain,
% 125.55/125.76 (^[W0: $i, W1: $i] : refl(((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))),
% 125.55/125.76 inference(bind,[status(th)],[])).
% 125.55/125.76 tff(152,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 125.55/125.76 inference(quant_intro,[status(thm)],[151])).
% 125.55/125.76 tff(153,plain,
% 125.55/125.76 (^[W0: $i, W1: $i] : rewrite(((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))),
% 125.55/125.76 inference(bind,[status(th)],[])).
% 125.55/125.76 tff(154,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 125.55/125.76 inference(quant_intro,[status(thm)],[153])).
% 125.55/125.76 tff(155,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 125.55/125.76 inference(transitivity,[status(thm)],[154, 152])).
% 125.55/125.76 tff(156,plain,
% 125.55/125.76 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) <=> (~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> (~(~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))))), rewrite((~(~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), rewrite((![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> (((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))), rewrite((((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))))),
% 125.55/125.76 inference(bind,[status(th)],[])).
% 125.55/125.76 tff(157,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 125.55/125.76 inference(quant_intro,[status(thm)],[156])).
% 125.55/125.76 tff(158,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 125.55/125.76 inference(rewrite,[status(thm)],[])).
% 125.55/125.76 tff(159,plain,
% 125.55/125.76 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))), ((sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> (sdtlseqdt0(W1, W0) => (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), rewrite((sdtlseqdt0(W1, W0) => (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))), ((sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))), rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 125.55/125.76 inference(bind,[status(th)],[])).
% 125.55/125.76 tff(160,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 125.55/125.76 inference(quant_intro,[status(thm)],[159])).
% 125.55/125.76 tff(161,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3754')).
% 125.55/125.76 tff(162,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[161, 160])).
% 125.55/125.76 tff(163,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[162, 158])).
% 125.55/125.76 tff(164,plain,(
% 125.55/125.76 ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 125.55/125.76 inference(skolemize,[status(sab)],[163])).
% 125.55/125.76 tff(165,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[164, 157])).
% 125.55/125.76 tff(166,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[165, 155])).
% 125.55/125.76 tff(167,plain,
% 125.55/125.76 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))),
% 125.55/125.76 inference(modus_ponens,[status(thm)],[166, 150])).
% 125.55/125.76 tff(168,plain,
% 125.55/125.76 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))),
% 125.55/125.76 inference(rewrite,[status(thm)],[])).
% 125.55/125.76 tff(169,plain,
% 125.55/125.76 (((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))) <=> ((~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))),
% 125.55/125.76 inference(rewrite,[status(thm)],[])).
% 125.55/125.76 tff(170,plain,
% 125.55/125.76 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))) <=> (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))),
% 125.55/125.76 inference(rewrite,[status(thm)],[])).
% 125.55/125.76 tff(171,plain,
% 125.55/125.76 (((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))),
% 125.55/125.76 inference(monotonicity,[status(thm)],[170])).
% 125.55/125.76 tff(172,plain,
% 125.55/125.76 ((~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))) <=> (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))),
% 125.55/125.76 inference(monotonicity,[status(thm)],[171])).
% 125.55/125.76 tff(173,plain,
% 125.55/125.76 (((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))) <=> ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))),
% 125.55/125.76 inference(monotonicity,[status(thm)],[172])).
% 125.55/125.76 tff(174,plain,
% 125.55/125.76 (((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))) <=> ((~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))),
% 125.55/125.76 inference(transitivity,[status(thm)],[173, 169])).
% 125.55/125.76 tff(175,plain,
% 125.55/125.76 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))))),
% 125.55/125.76 inference(monotonicity,[status(thm)],[174])).
% 125.55/125.76 tff(176,plain,
% 125.55/125.76 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))),
% 125.55/125.77 inference(transitivity,[status(thm)],[175, 168])).
% 125.55/125.77 tff(177,plain,
% 125.55/125.77 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))))),
% 125.55/125.77 inference(quant_inst,[status(thm)],[])).
% 125.55/125.77 tff(178,plain,
% 125.55/125.77 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~sdtlseqdt0(szszuzczcdt0(xn), xm)) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))),
% 125.55/125.77 inference(modus_ponens,[status(thm)],[177, 176])).
% 125.55/125.77 tff(179,plain,
% 125.55/125.77 ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))))),
% 125.55/125.77 inference(unit_resolution,[status(thm)],[178, 167, 148, 145])).
% 125.55/125.77 tff(180,plain,
% 125.55/125.77 (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))))),
% 125.55/125.77 inference(unit_resolution,[status(thm)],[179, 139])).
% 125.55/125.77 tff(181,plain,
% 125.55/125.77 (((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))))) | ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))),
% 125.55/125.77 inference(tautology,[status(thm)],[])).
% 125.55/125.77 tff(182,plain,
% 125.55/125.77 (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))),
% 125.55/125.77 inference(unit_resolution,[status(thm)],[181, 180])).
% 125.55/125.77 tff(183,plain,
% 125.55/125.77 (((~![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(xm, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), 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(xm, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)))))),
% 125.55/125.77 inference(rewrite,[status(thm)],[])).
% 125.55/125.77 tff(184,plain,
% 125.55/125.77 (((~aElementOf0(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0)))))) <=> ((~aElementOf0(xm, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)))))),
% 125.55/125.77 inference(rewrite,[status(thm)],[])).
% 125.55/125.77 tff(185,plain,
% 125.55/125.77 (((~![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(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | 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(xm, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0))))))),
% 125.55/125.77 inference(monotonicity,[status(thm)],[184])).
% 125.55/125.77 tff(186,plain,
% 125.55/125.77 (((~![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(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | 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(xm, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)))))),
% 125.55/125.77 inference(transitivity,[status(thm)],[185, 183])).
% 125.55/125.77 tff(187,plain,
% 125.55/125.77 ((~![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(xm, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))))))),
% 125.55/125.77 inference(quant_inst,[status(thm)],[])).
% 125.55/125.77 tff(188,plain,
% 125.55/125.77 ((~![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(xm, szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0))))),
% 125.55/125.77 inference(modus_ponens,[status(thm)],[187, 186])).
% 125.55/125.77 tff(189,plain,
% 125.55/125.77 (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)))),
% 125.55/125.77 inference(unit_resolution,[status(thm)],[188, 23, 148])).
% 125.55/125.77 tff(190,plain,
% 125.55/125.77 (((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0))) | isCountable0(sdtlpdtrp0(xN, xm))),
% 125.55/125.77 inference(tautology,[status(thm)],[])).
% 125.55/125.77 tff(191,plain,
% 125.55/125.77 (isCountable0(sdtlpdtrp0(xN, xm))),
% 125.55/125.77 inference(unit_resolution,[status(thm)],[190, 189])).
% 125.55/125.77 tff(192,plain,
% 125.55/125.77 (((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | aElementOf0(W1, szNzAzT0))) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~aSet0(sdtlpdtrp0(xN, xm))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)),
% 125.55/125.77 inference(tautology,[status(thm)],[])).
% 125.55/125.77 tff(193,plain,
% 125.55/125.77 (aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0)),
% 125.55/125.77 inference(unit_resolution,[status(thm)],[192, 189])).
% 125.55/125.77 tff(194,plain,
% 125.55/125.77 ((aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0))),
% 125.55/125.77 inference(tautology,[status(thm)],[])).
% 125.55/125.77 tff(195,plain,
% 125.55/125.77 (aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0)))))),
% 125.55/125.77 inference(unit_resolution,[status(thm)],[194, 193])).
% 125.55/125.77 tff(196,plain,
% 125.55/125.77 (((~![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(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))))) <=> ((~![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(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))))),
% 125.55/125.77 inference(rewrite,[status(thm)],[])).
% 125.55/125.77 tff(197,plain,
% 125.55/125.77 (((~aElementOf0(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))))) <=> ((~aElementOf0(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))))),
% 125.55/125.77 inference(rewrite,[status(thm)],[])).
% 125.55/125.77 tff(198,plain,
% 125.55/125.77 (((~![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(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))))))) <=> ((~![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(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))))))),
% 125.55/125.77 inference(monotonicity,[status(thm)],[197])).
% 125.55/125.77 tff(199,plain,
% 125.55/125.77 (((~![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(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))))))) <=> ((~![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(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))))),
% 125.55/125.78 inference(transitivity,[status(thm)],[198, 196])).
% 125.55/125.78 tff(200,plain,
% 125.55/125.78 ((~![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(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))))))),
% 125.55/125.78 inference(quant_inst,[status(thm)],[])).
% 125.55/125.78 tff(201,plain,
% 125.55/125.78 ((~![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(xm, szNzAzT0)) | (~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))))),
% 125.55/125.78 inference(modus_ponens,[status(thm)],[200, 199])).
% 125.55/125.78 tff(202,plain,
% 125.55/125.78 ((~isCountable0(sdtlpdtrp0(xN, xm))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), szNzAzT0) | (~((~aSet0(sdtlpdtrp0(xN, xm))) | (~((~aElementOf0(tptp_fun_W1_29(xm), sdtlpdtrp0(xN, xm))) | aElementOf0(tptp_fun_W1_29(xm), szNzAzT0))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[201, 61, 148])).
% 125.55/125.78 tff(203,plain,
% 125.55/125.78 (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[202, 195, 191])).
% 125.55/125.78 tff(204,plain,
% 125.55/125.78 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xm)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W1))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xm)), sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xm)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xm), szmzizndt0(sdtlpdtrp0(xN, xm)))))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))),
% 125.55/125.78 inference(tautology,[status(thm)],[])).
% 125.55/125.78 tff(205,plain,
% 125.55/125.78 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[204, 203])).
% 125.55/125.78 tff(206,plain,
% 125.55/125.78 (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn))))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn))))),
% 125.55/125.78 inference(rewrite,[status(thm)],[])).
% 125.55/125.78 tff(207,plain,
% 125.55/125.78 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn))))),
% 125.55/125.78 inference(quant_inst,[status(thm)],[])).
% 125.55/125.78 tff(208,plain,
% 125.55/125.78 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xm))) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn)))),
% 125.55/125.78 inference(modus_ponens,[status(thm)],[207, 206])).
% 125.55/125.78 tff(209,plain,
% 125.55/125.78 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn)))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[208, 205, 182])).
% 125.55/125.78 tff(210,plain,
% 125.55/125.78 (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W1))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xn)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xn))))) | ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.78 inference(tautology,[status(thm)],[])).
% 125.55/125.78 tff(211,plain,
% 125.55/125.78 (![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[210, 69])).
% 125.55/125.78 tff(212,plain,
% 125.55/125.78 (((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.78 inference(rewrite,[status(thm)],[])).
% 125.55/125.78 tff(213,plain,
% 125.55/125.78 ((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.78 inference(quant_inst,[status(thm)],[])).
% 125.55/125.78 tff(214,plain,
% 125.55/125.78 ((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, szszuzczcdt0(xn)))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.78 inference(modus_ponens,[status(thm)],[213, 212])).
% 125.55/125.78 tff(215,plain,
% 125.55/125.78 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[214, 211, 209])).
% 125.55/125.78 tff(216,plain,
% 125.55/125.78 ((((~aElement0(szmzizndt0(sdtlpdtrp0(xN, xm)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aElement0(szmzizndt0(sdtlpdtrp0(xN, xm)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.78 inference(tautology,[status(thm)],[])).
% 125.55/125.78 tff(217,plain,
% 125.55/125.78 ((((~aElement0(szmzizndt0(sdtlpdtrp0(xN, xm)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~((~aElement0(szmzizndt0(sdtlpdtrp0(xN, xm)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[216, 215])).
% 125.55/125.78 tff(218,plain,
% 125.55/125.78 (~((~aElement0(szmzizndt0(sdtlpdtrp0(xN, xm)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[217, 120])).
% 125.55/125.78 tff(219,plain,
% 125.55/125.78 (((~aElement0(szmzizndt0(sdtlpdtrp0(xN, xm)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.78 inference(tautology,[status(thm)],[])).
% 125.55/125.78 tff(220,plain,
% 125.55/125.78 (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[219, 218])).
% 125.55/125.78 tff(221,plain,
% 125.55/125.78 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)))) | (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))),
% 125.55/125.78 inference(tautology,[status(thm)],[])).
% 125.55/125.78 tff(222,plain,
% 125.55/125.78 ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)))),
% 125.55/125.78 inference(unit_resolution,[status(thm)],[221, 220])).
% 125.55/125.78 tff(223,plain,
% 125.55/125.78 (((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))))) <=> ((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))))),
% 125.55/125.78 inference(rewrite,[status(thm)],[])).
% 125.55/125.78 tff(224,plain,
% 125.55/125.78 (((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))))) <=> ((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))))),
% 125.55/125.78 inference(rewrite,[status(thm)],[])).
% 125.55/125.78 tff(225,plain,
% 125.55/125.78 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))) <=> ((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0))) | (~(szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn))) | (~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))))),
% 125.55/125.78 inference(rewrite,[status(thm)],[])).
% 125.55/125.78 tff(226,plain,
% 125.55/125.78 ((((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))),
% 125.55/125.78 inference(rewrite,[status(thm)],[])).
% 125.55/125.79 tff(227,plain,
% 125.55/125.79 ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))),
% 125.55/125.79 inference(rewrite,[status(thm)],[])).
% 125.55/125.79 tff(228,plain,
% 125.55/125.79 (((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))),
% 125.55/125.79 inference(rewrite,[status(thm)],[])).
% 125.55/125.79 tff(229,plain,
% 125.55/125.79 ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))),
% 125.55/125.79 inference(rewrite,[status(thm)],[])).
% 125.55/125.79 tff(230,plain,
% 125.55/125.79 ((aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) <=> (aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))),
% 125.55/125.79 inference(rewrite,[status(thm)],[])).
% 125.55/125.79 tff(231,plain,
% 125.55/125.79 (((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))),
% 125.55/125.79 inference(monotonicity,[status(thm)],[230, 229])).
% 125.55/125.79 tff(232,plain,
% 125.55/125.79 (((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))),
% 125.55/125.79 inference(transitivity,[status(thm)],[231, 228])).
% 125.55/125.79 tff(233,plain,
% 125.55/125.79 ((((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))) <=> (((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))),
% 125.55/125.79 inference(monotonicity,[status(thm)],[232, 227])).
% 125.55/125.79 tff(234,plain,
% 125.55/125.79 ((((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0)))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))) | ((~aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) & (~((~aElementOf0(W0!30, sdtlpdtrp0(xN, xm))) | aElementOf0(W0!30, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))),
% 125.55/125.79 inference(transitivity,[status(thm)],[233, 226])).
% 125.55/125.79 tff(235,plain,
% 125.55/125.79 (((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))) <=> ((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))))),
% 125.55/125.79 inference(rewrite,[status(thm)],[])).
% 125.55/125.79 tff(236,plain,
% 125.55/125.79 ((~((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))))) <=> (~((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))))),
% 125.55/125.79 inference(monotonicity,[status(thm)],[235])).
% 125.55/125.79 tff(237,plain,
% 125.55/125.79 ((~((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))))) <=> (~((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn)))))))),
% 125.55/125.79 inference(rewrite,[status(thm)],[])).
% 125.55/125.79 tff(238,plain,
% 125.55/125.79 (~((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))))),
% 125.55/125.79 inference(or_elim,[status(thm)],[143])).
% 125.55/125.79 tff(239,plain,
% 125.55/125.79 (~((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))))),
% 125.55/125.79 inference(modus_ponens,[status(thm)],[238, 236])).
% 125.55/125.79 tff(240,plain,
% 125.55/125.79 (~((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))))),
% 125.55/125.80 inference(modus_ponens,[status(thm)],[239, 237])).
% 125.55/125.80 tff(241,plain,
% 125.55/125.80 (~((aSubsetOf0(sdtlpdtrp0(xN, xm), sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) | ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xn)) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xn)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xn)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0))))) & (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xm)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xm))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xm)), sdtlpdtrp0(xN, xn)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xn))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xm)), W0)) & (szmzizndt0(sdtlpdtrp0(xN, xm)) = szmzizndt0(sdtlpdtrp0(xN, xn))))))),
% 125.55/125.80 inference(modus_ponens,[status(thm)],[240, 236])).
% 125.55/125.80 unexpected number of arguments: (let ((a!1 (aSubsetOf0 (sdtlpdtrp0 xN xm)
% 125.55/125.80 (sdtmndt0 (sdtlpdtrp0 xN xn)
% 125.55/125.80 (szmzizndt0 (sdtlpdtrp0 xN xn)))))
% 125.55/125.80 (a!2 (forall ((W0 $i))
% 125.55/125.80 (let ((a!1 (aElementOf0 W0
% 125.55/125.80 (sdtmndt0 (sdtlpdtrp0 xN xn)
% 125.55/125.80 (szmzizndt0 (sdtlpdtrp0 xN xn))))))
% 125.55/125.80 (or (not (aElementOf0 W0 (sdtlpdtrp0 xN xm))) a!1))))
% 125.55/125.80 (a!3 (aElementOf0 W0!30
% 125.55/125.80 (sdtmndt0 (sdtlpdtrp0 xN xn)
% 125.55/125.80 (szmzizndt0 (sdtlpdtrp0 xN xn)))))
% 125.55/125.80 (a!5 (aSet0 (sdtmndt0 (sdtlpdtrp0 xN xn) (szmzizndt0 (sdtlpdtrp0 xN xn)))))
% 125.55/125.80 (a!6 (proof-bind (lambda ((W0 $i))
% 125.55/125.80 (let ((a!1 (aElementOf0 W0
% 125.55/125.80 (sdtmndt0 (sdtlpdtrp0 xN xn)
% 125.55/125.80 (szmzizndt0 (sdtlpdtrp0 xN
% 125.55/125.80 xn)))))
% 125.55/125.80 (a!2 (not (= W0 (szmzizndt0 (sdtlpdtrp0 xN xn))))))
% 125.55/125.80 (let ((a!3 (= a!1
% 125.55/125.80 (and (aElement0 W0)
% 125.55/125.80 (aElementOf0 W0 (sdtlpdtrp0 xN xn))
% 125.55/125.80 a!2))))
% 125.55/125.80 (refl (~ a!3 a!3)))))))
% 125.55/125.80 (a!7 (forall ((W0 $i))
% 125.55/125.80 (let ((a!1 (aElementOf0 W0
% 125.55/125.80 (sdtmndt0 (sdtlpdtrp0 xN xn)
% 125.55/125.80 (szmzizndt0 (sdtlpdtrp0 xN xn)))))
% 125.55/125.80 (a!2 (not (= W0 (szmzizndt0 (sdtlpdtrp0 xN xn))))))
% 125.55/125.80 (= a!1
% 125.55/125.80 (and (aElement0 W0) (aElementOf0 W0 (sdtlpdtrp0 xN xn)) a!2)))))
% 125.55/125.80 (a!10 (~ (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xn)) (sdtlpdtrp0 xN xn))
% 125.55/125.80 (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xn)) (sdtlpdtrp0 xN xn))))
% 125.55/125.80 (a!11 (proof-bind (lambda ((W0 $i))
% 125.55/125.80 (let ((a!1 (or (not (aElementOf0 W0
% 125.55/125.80 (sdtlpdtrp0 xN xn)))
% 125.55/125.80 (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 xN
% 125.55/125.80 xn))
% 125.55/125.80 W0))))
% 125.55/125.80 (refl (~ a!1 a!1))))))
% 125.55/125.80 (a!12 (forall ((W0 $i))
% 125.55/125.80 (or (not (aElementOf0 W0 (sdtlpdtrp0 xN xn)))
% 125.55/125.80 (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 xN xn)) W0))))
% 125.55/125.80 (a!17 (~ (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xm)) (sdtlpdtrp0 xN xm))
% 125.55/125.80 (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xm)) (sdtlpdtrp0 xN xm))))
% 125.55/125.80 (a!18 (proof-bind (lambda ((W0 $i))
% 125.55/125.80 (let ((a!1 (or (not (aElementOf0 W0
% 125.55/125.80 (sdtlpdtrp0 xN xm)))
% 125.55/125.80 (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 xN
% 125.55/125.80 xm))
% 125.55/125.80 W0))))
% 125.55/125.80 (refl (~ a!1 a!1))))))
% 125.55/125.80 (a!19 (forall ((W0 $i))
% 125.55/125.80 (or (not (aElementOf0 W0 (sdtlpdtrp0 xN xm)))
% 125.55/125.80 (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 xN xm)) W0))))
% 125.55/125.80 (a!20 (~ (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xm)) (sdtlpdtrp0 xN xn))
% 125.55/125.80 (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xm)) (sdtlpdtrp0 xN xn))))
% 125.55/125.80 (a!21 (proof-bind (lambda ((W0 $i))
% 125.55/125.80 (let ((a!1 (or (not (aElementOf0 W0
% 125.55/125.80 (sdtlpdtrp0 xN xn)))
% 125.55/125.80 (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 xN
% 125.55/125.80 xm))
% 125.55/125.80 W0))))
% 125.55/125.80 (refl (~ a!1 a!1))))))
% 125.55/125.80 (a!22 (forall ((W0 $i))
% 125.55/125.80 (or (not (aElementOf0 W0 (sdtlpdtrp0 xN xn)))
% 125.55/125.80 (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 xN xm)) W0))))
% 125.55/125.80 (a!23 (~ (= (szmzizndt0 (sdtlpdtrp0 xN xm))
% 125.55/125.80 (szmzizndt0 (sdtlpdtrp0 xN xn)))
% 125.55/125.80 (= (szmzizndt0 (sdtlpdtrp0 xN xm))
% 125.55/125.80 (szmzizndt0 (sdtlpdtrp0 xN xn))))))
% 125.55/125.80 (let ((a!4 (or (not (aElementOf0 W0!30 (sdtlpdtrp0 xN xm))) a!3))
% 125.55/125.80 (a!8 (~ (not (not (and a!5 a!7))) (and a!5 a!7)))
% 125.55/125.80 (a!13 (and (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xn))
% 125.55/125.80 (sdtlpdtrp0 xN xn))
% 125.55/125.80 a!12))
% 125.55/125.80 (a!24 (and (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xm))
% 125.55/125.80 (sdtlpdtrp0 xN xm))
% 125.55/125.80 a!19
% 125.55/125.80 (aElementOf0 (szmzizndt0 (sdtlpdtrp0 xN xm))
% 125.55/125.80 (sdtlpdtrp0 xN xn))
% 125.55/125.80 a!22
% 125.55/125.80 (= (szmzizndt0 (sdtlpdtrp0 xN xm))
% 125.55/125.80 (szmzizndt0 (sdtlpdtrp0 xN xn))))))
% 125.55/125.80 (let ((a!9 (nnf-neg (monotonicity (refl (~ a!5 a!5))
% 125.55/125.80 (nnf-pos a!6 (~ a!7 a!7))
% 125.55/125.80 (~ (and a!5 a!7) (and a!5 a!7)))
% 125.55/125.80 a!8))
% 125.55/125.80 (a!14 (nnf-neg (monotonicity (refl a!10)
% 125.55/125.80 (nnf-pos a!11 (~ a!12 a!12))
% 125.55/125.80 (~ a!13 a!13))
% 125.55/125.80 (~ (not (not a!13)) a!13)))
% 125.55/125.80 (a!15 (not (or a!1 a!2 (not (and a!5 a!7)) (not a!13))))
% 125.55/125.80 (a!25 (nnf-neg (monotonicity (refl a!17)
% 125.55/125.80 (nnf-pos a!18 (~ a!19 a!19))
% 125.55/125.80 (refl a!20)
% 125.55/125.80 (nnf-pos a!21 (~ a!22 a!22))
% 125.55/125.80 (refl a!23)
% 125.55/125.80 (~ a!24 a!24))
% 125.55/125.80 (~ (not (not a!24)) a!24)))
% 125.55/125.80 (a!26 (and (or a!1 a!2 (not (and a!5 a!7)) (not a!13)) (not a!24))))
% 125.55/125.80 (let ((a!16 (nnf-neg (refl (~ (not a!1) (not a!1)))
% 125.55/125.80 (sk (~ (not a!2) (not a!4)))
% 125.55/125.80 a!9
% 125.55/125.80 a!14
% 125.55/125.80 (~ a!15 (and (not a!1) (not a!4) (and a!5 a!7) a!13))))
% 125.55/125.80 (a!27 (~ (not a!26)
% 125.55/125.80 (or (and (not a!1) (not a!4) (and a!5 a!7) a!13) a!24))))
% 125.55/125.80 (nnf-neg a!16 a!25 a!27)))))
% 125.55/125.80 Proof display could not be completed: unexpected number of arguments
% 125.93/126.11 % E exiting
%------------------------------------------------------------------------------