%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM601+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:21:33 AM UTC 2025
% Result : Theorem 16.43s 16.64s
% Output : Proof 16.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM601+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 01:35:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 16.43/16.64 % SZS status Theorem
% 16.43/16.64 % SZS output start Proof
% 16.43/16.64 tff(aElementOf0_type, type, (
% 16.43/16.64 aElementOf0: ( $i * $i ) > $o)).
% 16.43/16.64 tff(sdtlpdtrp0_type, type, (
% 16.43/16.64 sdtlpdtrp0: ( $i * $i ) > $i)).
% 16.43/16.64 tff(tptp_fun_W1_42_type, type, (
% 16.43/16.64 tptp_fun_W1_42: $i > $i)).
% 16.43/16.64 tff(tptp_fun_W0_43_type, type, (
% 16.43/16.64 tptp_fun_W0_43: $i)).
% 16.43/16.64 tff(xN_type, type, (
% 16.43/16.64 xN: $i)).
% 16.43/16.64 tff(xe_type, type, (
% 16.43/16.64 xe: $i)).
% 16.43/16.64 tff(szNzAzT0_type, type, (
% 16.43/16.64 szNzAzT0: $i)).
% 16.43/16.64 tff(szDzizrdt0_type, type, (
% 16.43/16.64 szDzizrdt0: $i > $i)).
% 16.43/16.64 tff(xd_type, type, (
% 16.43/16.64 xd: $i)).
% 16.43/16.64 tff(sdtlbdtrb0_type, type, (
% 16.43/16.64 sdtlbdtrb0: ( $i * $i ) > $i)).
% 16.43/16.64 tff(xO_type, type, (
% 16.43/16.64 xO: $i)).
% 16.43/16.64 tff(xS_type, type, (
% 16.43/16.64 xS: $i)).
% 16.43/16.64 tff(aSubsetOf0_type, type, (
% 16.43/16.64 aSubsetOf0: ( $i * $i ) > $o)).
% 16.43/16.64 tff(szmzizndt0_type, type, (
% 16.43/16.64 szmzizndt0: $i > $i)).
% 16.43/16.64 tff(sdtlseqdt0_type, type, (
% 16.43/16.64 sdtlseqdt0: ( $i * $i ) > $o)).
% 16.43/16.64 tff(szDzozmdt0_type, type, (
% 16.43/16.64 szDzozmdt0: $i > $i)).
% 16.43/16.64 tff(aFunction0_type, type, (
% 16.43/16.64 aFunction0: $i > $o)).
% 16.43/16.64 tff(sz00_type, type, (
% 16.43/16.64 sz00: $i)).
% 16.43/16.64 tff(isCountable0_type, type, (
% 16.43/16.64 isCountable0: $i > $o)).
% 16.43/16.64 tff(szszuzczcdt0_type, type, (
% 16.43/16.64 szszuzczcdt0: $i > $i)).
% 16.43/16.64 tff(sdtmndt0_type, type, (
% 16.43/16.64 sdtmndt0: ( $i * $i ) > $i)).
% 16.43/16.64 tff(aSet0_type, type, (
% 16.43/16.64 aSet0: $i > $o)).
% 16.43/16.64 tff(aElement0_type, type, (
% 16.43/16.64 aElement0: $i > $o)).
% 16.43/16.64 tff(1,plain,
% 16.43/16.64 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 16.43/16.64 inference(rewrite,[status(thm)],[])).
% 16.43/16.64 tff(2,plain,
% 16.43/16.64 ((~![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 16.43/16.64 inference(rewrite,[status(thm)],[])).
% 16.43/16.64 tff(3,axiom,(~(![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS)) | aSubsetOf0(xO, xS))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 16.43/16.64 tff(4,plain,
% 16.43/16.64 (~![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS))),
% 16.43/16.64 inference(or_elim,[status(thm)],[3])).
% 16.43/16.64 tff(5,plain,
% 16.43/16.64 (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 16.43/16.64 inference(modus_ponens,[status(thm)],[4, 2])).
% 16.43/16.64 tff(6,plain,
% 16.43/16.64 (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 16.43/16.64 inference(modus_ponens,[status(thm)],[5, 1])).
% 16.43/16.64 tff(7,plain,
% 16.43/16.64 (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 16.43/16.64 inference(modus_ponens,[status(thm)],[6, 1])).
% 16.43/16.64 tff(8,plain,
% 16.43/16.64 (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 16.43/16.64 inference(modus_ponens,[status(thm)],[7, 1])).
% 16.43/16.64 tff(9,plain,(
% 16.43/16.64 ~((~aElementOf0(W0!43, xO)) | aElementOf0(W0!43, xS))),
% 16.43/16.64 inference(skolemize,[status(sab)],[8])).
% 16.43/16.64 tff(10,plain,
% 16.43/16.64 (aElementOf0(W0!43, xO)),
% 16.43/16.64 inference(or_elim,[status(thm)],[9])).
% 16.43/16.64 tff(11,plain,
% 16.43/16.64 (((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO)) | (~aElementOf0(W0!43, xO))),
% 16.43/16.64 inference(tautology,[status(thm)],[])).
% 16.43/16.64 tff(12,plain,
% 16.43/16.64 ((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO)),
% 16.43/16.64 inference(unit_resolution,[status(thm)],[11, 10])).
% 16.43/16.64 tff(13,plain,
% 16.43/16.64 (^[W0: $i] : trans(monotonicity(monotonicity(monotonicity(rewrite((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) <=> (~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))), (((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO)) <=> ((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO)))), ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) <=> (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))), rewrite((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) <=> (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))), (((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))))), rewrite(((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))), (((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))))),
% 16.43/16.64 inference(bind,[status(th)],[])).
% 16.43/16.64 tff(14,plain,
% 16.43/16.64 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))),
% 16.43/16.64 inference(quant_intro,[status(thm)],[13])).
% 16.43/16.64 tff(15,plain,
% 16.43/16.64 (^[W0: $i] : refl(((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))))),
% 16.43/16.64 inference(bind,[status(th)],[])).
% 16.43/16.64 tff(16,plain,
% 16.43/16.64 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 16.43/16.64 inference(quant_intro,[status(thm)],[15])).
% 16.43/16.64 tff(17,plain,
% 16.43/16.64 (^[W0: $i] : rewrite(((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))))),
% 16.43/16.64 inference(bind,[status(th)],[])).
% 16.43/16.64 tff(18,plain,
% 16.43/16.64 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 16.43/16.64 inference(quant_intro,[status(thm)],[17])).
% 16.43/16.64 tff(19,plain,
% 16.43/16.64 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 16.43/16.64 inference(transitivity,[status(thm)],[18, 16])).
% 16.43/16.64 tff(20,plain,
% 16.43/16.64 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite((aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) <=> (~((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))), ((~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> (~(~((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))))), rewrite((~(~((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))) <=> ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))), ((~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))))), (![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))), ((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, xO))) <=> (![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, xO))))), rewrite((![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, xO))) <=> (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO)))), ((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, xO))) <=> (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))), rewrite((aElementOf0(tptp_fun_W1_42(W0), szNzAzT0) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)) <=> (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))), (((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, xO))) | (aElementOf0(tptp_fun_W1_42(W0), szNzAzT0) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))))), rewrite(((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))), (((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, xO))) | (aElementOf0(tptp_fun_W1_42(W0), szNzAzT0) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))))),
% 16.43/16.64 inference(bind,[status(th)],[])).
% 16.43/16.64 tff(21,plain,
% 16.43/16.64 (![W0: $i] : ((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, xO))) | (aElementOf0(tptp_fun_W1_42(W0), szNzAzT0) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))) <=> ![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 16.43/16.64 inference(quant_intro,[status(thm)],[20])).
% 16.43/16.64 tff(22,plain,
% 16.43/16.64 (![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 16.43/16.64 inference(rewrite,[status(thm)],[])).
% 16.43/16.64 tff(23,plain,
% 16.43/16.64 (^[W0: $i] : trans(monotonicity(rewrite((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) <=> (?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite(((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) <=> (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))), ((((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)) <=> ((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))), rewrite(((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)) <=> (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))), ((((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)) <=> (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))), (?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)) <=> ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))), (((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))), rewrite(((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))), (((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))))),
% 16.43/16.65 inference(bind,[status(th)],[])).
% 16.43/16.65 tff(24,plain,
% 16.43/16.65 (![W0: $i] : ((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 16.43/16.65 inference(quant_intro,[status(thm)],[23])).
% 16.43/16.65 tff(25,axiom,(![W0: $i] : ((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4982')).
% 16.43/16.65 tff(26,plain,
% 16.43/16.65 (![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[25, 24])).
% 16.43/16.65 tff(27,plain,
% 16.43/16.65 (![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[26, 22])).
% 16.43/16.65 tff(28,plain,(
% 16.43/16.65 ![W0: $i] : ((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, xO))) | (aElementOf0(tptp_fun_W1_42(W0), szNzAzT0) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))),
% 16.43/16.65 inference(skolemize,[status(sab)],[27])).
% 16.43/16.65 tff(29,plain,
% 16.43/16.65 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[28, 21])).
% 16.43/16.65 tff(30,plain,
% 16.43/16.65 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[29, 19])).
% 16.43/16.65 tff(31,plain,
% 16.43/16.65 (![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[30, 14])).
% 16.43/16.65 tff(32,plain,
% 16.43/16.65 (((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))) | ((~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO))))) <=> ((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))) | (~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO))))),
% 16.43/16.65 inference(rewrite,[status(thm)],[])).
% 16.43/16.65 tff(33,plain,
% 16.43/16.65 (((~((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO)))) <=> ((~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO))))),
% 16.43/16.65 inference(rewrite,[status(thm)],[])).
% 16.43/16.65 tff(34,plain,
% 16.43/16.65 (((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))) | ((~((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO))))) <=> ((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))) | ((~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO)))))),
% 16.43/16.65 inference(monotonicity,[status(thm)],[33])).
% 16.43/16.65 tff(35,plain,
% 16.43/16.65 (((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))) | ((~((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO))))) <=> ((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))) | (~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO))))),
% 16.43/16.65 inference(transitivity,[status(thm)],[34, 32])).
% 16.43/16.65 tff(36,plain,
% 16.43/16.65 ((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))) | ((~((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO))))),
% 16.43/16.65 inference(quant_inst,[status(thm)],[])).
% 16.43/16.65 tff(37,plain,
% 16.43/16.65 ((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szNzAzT0)) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, xO))))) | (~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, xO)))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[36, 35])).
% 16.43/16.65 tff(38,plain,
% 16.43/16.65 (~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)))),
% 16.43/16.65 inference(unit_resolution,[status(thm)],[37, 31, 12])).
% 16.43/16.65 tff(39,plain,
% 16.43/16.65 (((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0))) | (sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)),
% 16.43/16.65 inference(tautology,[status(thm)],[])).
% 16.43/16.65 tff(40,plain,
% 16.43/16.65 (sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43),
% 16.43/16.65 inference(unit_resolution,[status(thm)],[39, 38])).
% 16.43/16.65 tff(41,plain,
% 16.43/16.65 (W0!43 = sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43))),
% 16.43/16.65 inference(symmetry,[status(thm)],[40])).
% 16.43/16.65 tff(42,plain,
% 16.43/16.65 (aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))) <=> aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 16.43/16.65 inference(monotonicity,[status(thm)],[41])).
% 16.43/16.65 tff(43,plain,
% 16.43/16.65 (aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))) <=> aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 16.43/16.65 inference(symmetry,[status(thm)],[42])).
% 16.43/16.65 tff(44,plain,
% 16.43/16.65 (((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0))) | aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)),
% 16.43/16.65 inference(tautology,[status(thm)],[])).
% 16.43/16.65 tff(45,plain,
% 16.43/16.65 (aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)),
% 16.43/16.65 inference(unit_resolution,[status(thm)],[44, 38])).
% 16.43/16.65 tff(46,plain,
% 16.43/16.65 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))))),
% 16.43/16.65 inference(bind,[status(th)],[])).
% 16.43/16.65 tff(47,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))),
% 16.43/16.65 inference(quant_intro,[status(thm)],[46])).
% 16.43/16.65 tff(48,plain,
% 16.43/16.65 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))))),
% 16.43/16.65 inference(bind,[status(th)],[])).
% 16.43/16.65 tff(49,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))),
% 16.43/16.65 inference(quant_intro,[status(thm)],[48])).
% 16.43/16.65 tff(50,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))),
% 16.43/16.65 inference(transitivity,[status(thm)],[49, 47])).
% 16.43/16.65 tff(51,plain,
% 16.43/16.65 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))))),
% 16.43/16.65 inference(bind,[status(th)],[])).
% 16.43/16.65 tff(52,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))),
% 16.43/16.65 inference(quant_intro,[status(thm)],[51])).
% 16.43/16.65 tff(53,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 16.43/16.65 inference(rewrite,[status(thm)],[])).
% 16.43/16.65 tff(54,plain,
% 16.43/16.65 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) <=> (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))), (((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))), rewrite(((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))), (((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))), ((aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aElementOf0(W0, szNzAzT0) => (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite((aElementOf0(W0, szNzAzT0) => (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))), ((aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))))),
% 16.43/16.65 inference(bind,[status(th)],[])).
% 16.43/16.65 tff(55,plain,
% 16.43/16.65 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 16.43/16.65 inference(quant_intro,[status(thm)],[54])).
% 16.43/16.65 tff(56,axiom,((aFunction0(xe) & (szDzozmdt0(xe) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4660')).
% 16.43/16.65 tff(57,plain,
% 16.43/16.65 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 16.43/16.65 inference(and_elim,[status(thm)],[56])).
% 16.43/16.65 tff(58,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[57, 55])).
% 16.43/16.65 tff(59,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[58, 53])).
% 16.43/16.65 tff(60,plain,(
% 16.43/16.65 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 16.43/16.65 inference(skolemize,[status(sab)],[59])).
% 16.43/16.65 tff(61,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[60, 52])).
% 16.43/16.65 tff(62,plain,
% 16.43/16.65 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))),
% 16.43/16.65 inference(modus_ponens,[status(thm)],[61, 50])).
% 16.43/16.65 tff(63,plain,
% 16.43/16.65 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))))))),
% 16.43/16.65 inference(rewrite,[status(thm)],[])).
% 16.43/16.65 tff(64,plain,
% 16.43/16.65 (((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1)))))) <=> ((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))))))),
% 16.43/16.65 inference(rewrite,[status(thm)],[])).
% 16.43/16.65 tff(65,plain,
% 16.43/16.65 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))))))))),
% 16.43/16.65 inference(monotonicity,[status(thm)],[64])).
% 16.43/16.65 tff(66,plain,
% 16.43/16.65 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))))))),
% 16.43/16.65 inference(transitivity,[status(thm)],[65, 63])).
% 16.43/16.65 tff(67,plain,
% 16.43/16.65 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))))))),
% 16.43/16.66 inference(quant_inst,[status(thm)],[])).
% 16.43/16.66 tff(68,plain,
% 16.43/16.66 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))))))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[67, 66])).
% 16.43/16.66 tff(69,plain,
% 16.43/16.66 (~((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))))),
% 16.43/16.66 inference(unit_resolution,[status(thm)],[68, 62, 45])).
% 16.43/16.66 tff(70,plain,
% 16.43/16.66 (((~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))) | (~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))))) | aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 16.43/16.66 inference(tautology,[status(thm)],[])).
% 16.43/16.66 tff(71,plain,
% 16.43/16.66 (aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 16.43/16.66 inference(unit_resolution,[status(thm)],[70, 69])).
% 16.43/16.66 tff(72,plain,
% 16.43/16.66 (aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[71, 43])).
% 16.43/16.66 tff(73,plain,
% 16.43/16.66 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)))),
% 16.43/16.66 inference(bind,[status(th)],[])).
% 16.43/16.66 tff(74,plain,
% 16.43/16.66 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 16.43/16.66 inference(quant_intro,[status(thm)],[73])).
% 16.43/16.66 tff(75,plain,
% 16.43/16.66 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 16.43/16.66 inference(rewrite,[status(thm)],[])).
% 16.43/16.66 tff(76,plain,
% 16.43/16.66 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)))),
% 16.43/16.66 inference(bind,[status(th)],[])).
% 16.43/16.66 tff(77,plain,
% 16.43/16.66 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 16.43/16.66 inference(quant_intro,[status(thm)],[76])).
% 16.43/16.66 tff(78,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mZeroLess')).
% 16.43/16.66 tff(79,plain,
% 16.43/16.66 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[78, 77])).
% 16.43/16.66 tff(80,plain,
% 16.43/16.66 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[79, 75])).
% 16.43/16.66 tff(81,plain,(
% 16.43/16.66 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 16.43/16.66 inference(skolemize,[status(sab)],[80])).
% 16.43/16.66 tff(82,plain,
% 16.43/16.66 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[81, 74])).
% 16.43/16.66 tff(83,plain,
% 16.43/16.66 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43)))),
% 16.43/16.66 inference(rewrite,[status(thm)],[])).
% 16.43/16.66 tff(84,plain,
% 16.43/16.66 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43)))),
% 16.43/16.66 inference(quant_inst,[status(thm)],[])).
% 16.43/16.66 tff(85,plain,
% 16.43/16.66 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[84, 83])).
% 16.43/16.66 tff(86,plain,
% 16.43/16.66 (sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))),
% 16.43/16.66 inference(unit_resolution,[status(thm)],[85, 82, 45])).
% 16.43/16.66 tff(87,plain,
% 16.43/16.66 (^[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)))))))))),
% 16.43/16.66 inference(bind,[status(th)],[])).
% 16.43/16.66 tff(88,plain,
% 16.43/16.66 (![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)))))))),
% 16.43/16.66 inference(quant_intro,[status(thm)],[87])).
% 16.43/16.66 tff(89,plain,
% 16.43/16.66 (^[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)))))))),
% 16.43/16.66 inference(bind,[status(th)],[])).
% 16.43/16.66 tff(90,plain,
% 16.43/16.66 (![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))))))),
% 16.43/16.66 inference(quant_intro,[status(thm)],[89])).
% 16.43/16.66 tff(91,plain,
% 16.43/16.66 (^[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)))))))),
% 16.43/16.66 inference(bind,[status(th)],[])).
% 16.43/16.66 tff(92,plain,
% 16.43/16.66 (![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))))))),
% 16.43/16.66 inference(quant_intro,[status(thm)],[91])).
% 16.43/16.66 tff(93,plain,
% 16.43/16.66 (![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))))))),
% 16.43/16.66 inference(transitivity,[status(thm)],[92, 90])).
% 16.43/16.66 tff(94,plain,
% 16.43/16.66 (^[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))))))))),
% 16.43/16.66 inference(bind,[status(th)],[])).
% 16.43/16.66 tff(95,plain,
% 16.43/16.66 (![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))))))),
% 16.43/16.66 inference(quant_intro,[status(thm)],[94])).
% 16.43/16.66 tff(96,plain,
% 16.43/16.66 (![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))))),
% 16.43/16.66 inference(rewrite,[status(thm)],[])).
% 16.43/16.66 tff(97,plain,
% 16.43/16.66 (^[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))))))),
% 16.43/16.66 inference(bind,[status(th)],[])).
% 16.43/16.66 tff(98,plain,
% 16.43/16.66 (![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))))),
% 16.43/16.66 inference(quant_intro,[status(thm)],[97])).
% 16.43/16.66 tff(99,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3754')).
% 16.43/16.66 tff(100,plain,
% 16.43/16.66 (![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))))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[99, 98])).
% 16.43/16.66 tff(101,plain,
% 16.43/16.66 (![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))))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[100, 96])).
% 16.43/16.66 tff(102,plain,(
% 16.43/16.66 ![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))))),
% 16.43/16.66 inference(skolemize,[status(sab)],[101])).
% 16.43/16.66 tff(103,plain,
% 16.43/16.66 (![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))))))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[102, 95])).
% 16.43/16.66 tff(104,plain,
% 16.43/16.66 (![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))))))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[103, 93])).
% 16.43/16.66 tff(105,plain,
% 16.43/16.66 (![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)))))))),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[104, 88])).
% 16.43/16.66 tff(106,plain,
% 16.43/16.66 (aElementOf0(sz00, szNzAzT0) <=> aElementOf0(sz00, szNzAzT0)),
% 16.43/16.66 inference(rewrite,[status(thm)],[])).
% 16.43/16.66 tff(107,axiom,(aElementOf0(sz00, szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mZeroNum')).
% 16.43/16.66 tff(108,plain,
% 16.43/16.66 (aElementOf0(sz00, szNzAzT0)),
% 16.43/16.66 inference(modus_ponens,[status(thm)],[107, 106])).
% 16.43/16.66 tff(109,plain,
% 16.43/16.66 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))))),
% 16.43/16.66 inference(rewrite,[status(thm)],[])).
% 16.43/16.66 tff(110,plain,
% 16.43/16.66 (((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))))),
% 16.43/16.66 inference(rewrite,[status(thm)],[])).
% 16.43/16.66 tff(111,plain,
% 16.43/16.66 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) <=> (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))),
% 16.43/16.66 inference(rewrite,[status(thm)],[])).
% 16.43/16.66 tff(112,plain,
% 16.43/16.66 (((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))),
% 16.43/16.66 inference(monotonicity,[status(thm)],[111])).
% 16.43/16.66 tff(113,plain,
% 16.43/16.66 ((~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) <=> (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))),
% 16.43/16.66 inference(monotonicity,[status(thm)],[112])).
% 16.43/16.66 tff(114,plain,
% 16.43/16.66 (((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 16.43/16.66 inference(monotonicity,[status(thm)],[113])).
% 16.43/16.66 tff(115,plain,
% 16.43/16.66 (((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))))),
% 16.51/16.66 inference(transitivity,[status(thm)],[114, 110])).
% 16.51/16.66 tff(116,plain,
% 16.51/16.66 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43)))))),
% 16.51/16.66 inference(monotonicity,[status(thm)],[115])).
% 16.51/16.66 tff(117,plain,
% 16.51/16.66 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))))),
% 16.51/16.66 inference(transitivity,[status(thm)],[116, 109])).
% 16.51/16.66 tff(118,plain,
% 16.51/16.66 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 16.51/16.66 inference(quant_inst,[status(thm)],[])).
% 16.51/16.66 tff(119,plain,
% 16.51/16.66 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W0)) | (~aElementOf0(W0, szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_42(W0!43), szNzAzT0)) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43)))),
% 16.51/16.66 inference(modus_ponens,[status(thm)],[118, 117])).
% 16.51/16.66 tff(120,plain,
% 16.51/16.66 (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))),
% 16.51/16.66 inference(unit_resolution,[status(thm)],[119, 108, 105, 45, 86])).
% 16.51/16.66 tff(121,plain,
% 16.51/16.66 (((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))) | ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))),
% 16.51/16.66 inference(tautology,[status(thm)],[])).
% 16.51/16.66 tff(122,plain,
% 16.51/16.66 (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))),
% 16.51/16.66 inference(unit_resolution,[status(thm)],[121, 120])).
% 16.51/16.66 tff(123,plain,
% 16.51/16.66 ((sdtlpdtrp0(xN, sz00) = xS) <=> (sdtlpdtrp0(xN, sz00) = xS)),
% 16.51/16.66 inference(rewrite,[status(thm)],[])).
% 16.51/16.66 tff(124,axiom,(((aFunction0(xN) & (szDzozmdt0(xN) = szNzAzT0)) & (sdtlpdtrp0(xN, sz00) = xS)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3623')).
% 16.51/16.66 tff(125,plain,
% 16.51/16.66 ((aFunction0(xN) & (szDzozmdt0(xN) = szNzAzT0)) & (sdtlpdtrp0(xN, sz00) = xS)),
% 16.51/16.66 inference(and_elim,[status(thm)],[124])).
% 16.51/16.66 tff(126,plain,
% 16.51/16.66 (sdtlpdtrp0(xN, sz00) = xS),
% 16.51/16.66 inference(and_elim,[status(thm)],[125])).
% 16.51/16.66 tff(127,plain,
% 16.51/16.66 (sdtlpdtrp0(xN, sz00) = xS),
% 16.51/16.66 inference(modus_ponens,[status(thm)],[126, 123])).
% 16.51/16.66 tff(128,plain,
% 16.51/16.66 (aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)) <=> aElementOf0(W0!43, xS)),
% 16.51/16.66 inference(monotonicity,[status(thm)],[127])).
% 16.51/16.66 tff(129,plain,
% 16.51/16.66 (aElementOf0(W0!43, xS) <=> aElementOf0(W0!43, sdtlpdtrp0(xN, sz00))),
% 16.51/16.66 inference(symmetry,[status(thm)],[128])).
% 16.51/16.66 tff(130,plain,
% 16.51/16.66 ((~aElementOf0(W0!43, xS)) <=> (~aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)))),
% 16.51/16.66 inference(monotonicity,[status(thm)],[129])).
% 16.51/16.66 tff(131,plain,
% 16.51/16.66 (~aElementOf0(W0!43, xS)),
% 16.51/16.66 inference(or_elim,[status(thm)],[9])).
% 16.51/16.66 tff(132,plain,
% 16.51/16.66 (~aElementOf0(W0!43, sdtlpdtrp0(xN, sz00))),
% 16.51/16.66 inference(modus_ponens,[status(thm)],[131, 130])).
% 16.51/16.66 tff(133,plain,
% 16.51/16.66 (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)))),
% 16.51/16.66 inference(rewrite,[status(thm)],[])).
% 16.51/16.66 tff(134,plain,
% 16.51/16.66 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)))),
% 16.51/16.66 inference(quant_inst,[status(thm)],[])).
% 16.51/16.66 tff(135,plain,
% 16.51/16.66 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00))),
% 16.52/16.69 inference(modus_ponens,[status(thm)],[134, 133])).
% 16.52/16.69 tff(136,plain,
% 16.52/16.69 ($false),
% 16.52/16.69 inference(unit_resolution,[status(thm)],[135, 132, 122, 72])).
% 16.52/16.69 % SZS output end Proof
% 16.57/16.73 % E exiting
%------------------------------------------------------------------------------