%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM588+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 05:21:30 AM UTC 2025
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM588+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:35:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(aSubsetOf0_type, type, (
% 0.19/0.46 aSubsetOf0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(tptp_fun_W1_34_type, type, (
% 0.19/0.46 tptp_fun_W1_34: $i)).
% 0.19/0.46 tff(tptp_fun_W2_35_type, type, (
% 0.19/0.46 tptp_fun_W2_35: $i)).
% 0.19/0.46 tff(aElementOf0_type, type, (
% 0.19/0.46 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(slbdtsldtrb0_type, type, (
% 0.19/0.46 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.19/0.46 tff(xk_type, type, (
% 0.19/0.46 xk: $i)).
% 0.19/0.46 tff(sbrdtbr0_type, type, (
% 0.19/0.46 sbrdtbr0: $i > $i)).
% 0.19/0.46 tff(aSet0_type, type, (
% 0.19/0.46 aSet0: $i > $o)).
% 0.19/0.46 tff(sdtlseqdt0_type, type, (
% 0.19/0.46 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(szmzizndt0_type, type, (
% 0.19/0.46 szmzizndt0: $i > $i)).
% 0.19/0.46 tff(sdtlpdtrp0_type, type, (
% 0.19/0.46 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_W0_33_type, type, (
% 0.19/0.46 tptp_fun_W0_33: $i)).
% 0.19/0.46 tff(xN_type, type, (
% 0.19/0.46 xN: $i)).
% 0.19/0.46 tff(aElement0_type, type, (
% 0.19/0.46 aElement0: $i > $o)).
% 0.19/0.46 tff(sdtmndt0_type, type, (
% 0.19/0.46 sdtmndt0: ( $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_W3_36_type, type, (
% 0.19/0.46 tptp_fun_W3_36: $i)).
% 0.19/0.46 tff(isCountable0_type, type, (
% 0.19/0.46 isCountable0: $i > $o)).
% 0.19/0.46 tff(szNzAzT0_type, type, (
% 0.19/0.46 szNzAzT0: $i)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 ((aElementOf0(W0!33, szNzAzT0) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34) & (~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))) <=> (aElementOf0(W0!33, szNzAzT0) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34) & (~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34)) & ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34) & (~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) & (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))) <=> ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(4,plain,
% 0.19/0.47 ((aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk))) <=> (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(5,plain,
% 0.19/0.47 ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) <=> (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(7,plain,
% 0.19/0.47 (((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) & (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))) <=> ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) & (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[6, 5, 4])).
% 0.19/0.47 tff(8,plain,
% 0.19/0.47 (((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) & (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))) <=> ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[7, 3])).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34)) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(10,plain,
% 0.19/0.47 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34)) & ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) & (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34)) & ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[9, 8])).
% 0.19/0.47 tff(11,plain,
% 0.19/0.47 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34)) & ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) & (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34) & (~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[10, 2])).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 ((aElementOf0(W0!33, szNzAzT0) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34)) & ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) & (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))))) <=> (aElementOf0(W0!33, szNzAzT0) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34) & (~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[11])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 ((aElementOf0(W0!33, szNzAzT0) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34)) & ((~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33))))))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3))) & (aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))))) <=> (aElementOf0(W0!33, szNzAzT0) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34) & (~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[12, 1])).
% 0.19/0.48 tff(14,plain,
% 0.19/0.48 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(W1))) | ![W2: $i] : (aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3)))) | (~(aSet0(W2) & ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, W1)) & aSubsetOf0(W2, W1) & (sbrdtbr0(W2) = xk) & aElementOf0(W2, slbdtsldtrb0(W1, xk)))))))) <=> (~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(W1))) | ![W2: $i] : (aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3)))) | (~(aSet0(W2) & ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, W1)) & aSubsetOf0(W2, W1) & (sbrdtbr0(W2) = xk) & aElementOf0(W2, slbdtsldtrb0(W1, xk))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(15,plain,
% 0.19/0.48 ((~![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(W1)) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(W1)) => ![W2: $i] : (((((aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, W1))) & aSubsetOf0(W2, W1)) & (sbrdtbr0(W2) = xk)) & aElementOf0(W2, slbdtsldtrb0(W1, xk))) => ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : (aElementOf0(W3, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0))) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => ((![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))))))))) <=> (~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(W1))) | ![W2: $i] : (aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3)))) | (~(aSet0(W2) & ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, W1)) & aSubsetOf0(W2, W1) & (sbrdtbr0(W2) = xk) & aElementOf0(W2, slbdtsldtrb0(W1, xk))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(16,axiom,(~![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(W1)) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(W1)) => ![W2: $i] : (((((aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, W1))) & aSubsetOf0(W2, W1)) & (sbrdtbr0(W2) = xk)) & aElementOf0(W2, slbdtsldtrb0(W1, xk))) => ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : (aElementOf0(W3, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0))) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => ((![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(W1))) | ![W2: $i] : (aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3)))) | (~(aSet0(W2) & ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, W1)) & aSubsetOf0(W2, W1) & (sbrdtbr0(W2) = xk) & aElementOf0(W2, slbdtsldtrb0(W1, xk)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 (~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(W1))) | ![W2: $i] : (aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3)))) | (~(aSet0(W2) & ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, W1)) & aSubsetOf0(W2, W1) & (sbrdtbr0(W2) = xk) & aElementOf0(W2, slbdtsldtrb0(W1, xk)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 (~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(W1))) | ![W2: $i] : (aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3)))) | (~(aSet0(W2) & ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, W1)) & aSubsetOf0(W2, W1) & (sbrdtbr0(W2) = xk) & aElementOf0(W2, slbdtsldtrb0(W1, xk)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.48 tff(20,plain,
% 0.19/0.48 (~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(W1))) | ![W2: $i] : (aElementOf0(W2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | aSubsetOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W3)))) | (~(aSet0(W2) & ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, W1)) & aSubsetOf0(W2, W1) & (sbrdtbr0(W2) = xk) & aElementOf0(W2, slbdtsldtrb0(W1, xk)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.48 tff(21,plain,
% 0.19/0.48 (aElementOf0(W0!33, szNzAzT0) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), sdtlpdtrp0(xN, W0!33)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W2)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0!33)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & aSet0(W1!34) & ![W2: $i] : ((~aElementOf0(W2, W1!34)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) & isCountable0(W1!34) & (~aElementOf0(W2!35, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))), xk))) & (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) & (~((~aElementOf0(W3!36, W2!35)) | aElementOf0(W3!36, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) <=> (aElement0(W3) & aElementOf0(W3, sdtlpdtrp0(xN, W0!33)) & (~(W3 = szmzizndt0(sdtlpdtrp0(xN, W0!33)))))) & ![W3: $i] : ((~aElementOf0(W3, sdtlpdtrp0(xN, W0!33))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!33)), W3)) & aSet0(W2!35) & ![W3: $i] : ((~aElementOf0(W3, W2!35)) | aElementOf0(W3, W1!34)) & aSubsetOf0(W2!35, W1!34) & (sbrdtbr0(W2!35) = xk) & aElementOf0(W2!35, slbdtsldtrb0(W1!34, xk))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.48 tff(22,plain,
% 0.19/0.48 (aSubsetOf0(W2!35, W1!34)),
% 0.19/0.48 inference(and_elim,[status(thm)],[21])).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (aSet0(W2!35)),
% 0.19/0.48 inference(and_elim,[status(thm)],[21])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 (~aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[21])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 (aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[21])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 (aSet0(W1!34)),
% 0.19/0.48 inference(and_elim,[status(thm)],[21])).
% 0.19/0.48 tff(27,plain,
% 0.19/0.48 (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[21])).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (^[W0: $i, W1: $i, W2: $i] : refl((aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0))) <=> (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 (![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.48 tff(30,plain,
% 0.19/0.48 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2)) <=> (~((~aSubsetOf0(W1, W2)) | (~aSubsetOf0(W0, W1))))), ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) <=> (~(~((~aSubsetOf0(W1, W2)) | (~aSubsetOf0(W0, W1))))))), rewrite((~(~((~aSubsetOf0(W1, W2)) | (~aSubsetOf0(W0, W1))))) <=> ((~aSubsetOf0(W1, W2)) | (~aSubsetOf0(W0, W1)))), ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) <=> ((~aSubsetOf0(W1, W2)) | (~aSubsetOf0(W0, W1))))), trans(monotonicity(rewrite((aSet0(W0) & aSet0(W1) & aSet0(W2)) <=> (~((~aSet0(W2)) | (~aSet0(W1)) | (~aSet0(W0))))), ((~(aSet0(W0) & aSet0(W1) & aSet0(W2))) <=> (~(~((~aSet0(W2)) | (~aSet0(W1)) | (~aSet0(W0))))))), rewrite((~(~((~aSet0(W2)) | (~aSet0(W1)) | (~aSet0(W0))))) <=> ((~aSet0(W2)) | (~aSet0(W1)) | (~aSet0(W0)))), ((~(aSet0(W0) & aSet0(W1) & aSet0(W2))) <=> ((~aSet0(W2)) | (~aSet0(W1)) | (~aSet0(W0))))), ((aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2)))) <=> (aSubsetOf0(W0, W2) | ((~aSubsetOf0(W1, W2)) | (~aSubsetOf0(W0, W1))) | ((~aSet0(W2)) | (~aSet0(W1)) | (~aSet0(W0)))))), rewrite((aSubsetOf0(W0, W2) | ((~aSubsetOf0(W1, W2)) | (~aSubsetOf0(W0, W1))) | ((~aSet0(W2)) | (~aSet0(W1)) | (~aSet0(W0)))) <=> (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))), ((aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2)))) <=> (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(31,plain,
% 0.19/0.48 (![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2)))) <=> ![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.48 tff(32,plain,
% 0.19/0.48 (![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2)))) <=> ![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(33,plain,
% 0.19/0.48 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aSet0(W0) & aSet0(W1)) & aSet0(W2)) <=> (aSet0(W0) & aSet0(W1) & aSet0(W2))), rewrite(((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2)) => aSubsetOf0(W0, W2)) <=> ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | aSubsetOf0(W0, W2))), ((((aSet0(W0) & aSet0(W1)) & aSet0(W2)) => ((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2)) => aSubsetOf0(W0, W2))) <=> ((aSet0(W0) & aSet0(W1) & aSet0(W2)) => ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | aSubsetOf0(W0, W2))))), rewrite(((aSet0(W0) & aSet0(W1) & aSet0(W2)) => ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | aSubsetOf0(W0, W2))) <=> (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2))))), ((((aSet0(W0) & aSet0(W1)) & aSet0(W2)) => ((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2)) => aSubsetOf0(W0, W2))) <=> (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 (![W0: $i, W1: $i, W2: $i] : (((aSet0(W0) & aSet0(W1)) & aSet0(W2)) => ((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2)) => aSubsetOf0(W0, W2))) <=> ![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.49 tff(35,axiom,(![W0: $i, W1: $i, W2: $i] : (((aSet0(W0) & aSet0(W1)) & aSet0(W2)) => ((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2)) => aSubsetOf0(W0, W2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSubTrans')).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 (![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 (![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.49 tff(38,plain,(
% 0.19/0.49 ![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W2))) | (~(aSet0(W0) & aSet0(W1) & aSet0(W2))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[37])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 (![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 (![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 (((~![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | (aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSet0(W2!35)) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W2!35, W1!34)))) <=> ((~![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSet0(W2!35)) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W2!35, W1!34)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 ((aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSubsetOf0(W2!35, W1!34)) | (~aSet0(W2!35))) <=> (aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSet0(W2!35)) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W2!35, W1!34)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 (((~![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | (aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSubsetOf0(W2!35, W1!34)) | (~aSet0(W2!35)))) <=> ((~![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | (aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSet0(W2!35)) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W2!35, W1!34))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (((~![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | (aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSubsetOf0(W2!35, W1!34)) | (~aSet0(W2!35)))) <=> ((~![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSet0(W2!35)) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W2!35, W1!34)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[43, 41])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 ((~![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | (aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSubsetOf0(W2!35, W1!34)) | (~aSet0(W2!35)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 ((~![W0: $i, W1: $i, W2: $i] : (aSubsetOf0(W0, W2) | (~aSet0(W2)) | (~aSubsetOf0(W1, W2)) | (~aSet0(W1)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | aSubsetOf0(W2!35, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33)))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSet0(W1!34)) | (~aSet0(W2!35)) | (~aSubsetOf0(W1!34, sdtmndt0(sdtlpdtrp0(xN, W0!33), szmzizndt0(sdtlpdtrp0(xN, W0!33))))) | (~aSubsetOf0(W2!35, W1!34))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[46, 40, 27, 26, 25, 24, 23, 22])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------