%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM618+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:21:37 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM618+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 01:35:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(aElementOf0_type, type, (
% 0.20/0.48 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(szNzAzT0_type, type, (
% 0.20/0.48 szNzAzT0: $i)).
% 0.20/0.48 tff(tptp_fun_W0_45_type, type, (
% 0.20/0.48 tptp_fun_W0_45: $i)).
% 0.20/0.48 tff(szDzozmdt0_type, type, (
% 0.20/0.48 szDzozmdt0: $i > $i)).
% 0.20/0.48 tff(xd_type, type, (
% 0.20/0.48 xd: $i)).
% 0.20/0.48 tff(aFunction0_type, type, (
% 0.20/0.48 aFunction0: $i > $o)).
% 0.20/0.48 tff(sdtlpdtrp0_type, type, (
% 0.20/0.48 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.20/0.48 tff(xC_type, type, (
% 0.20/0.48 xC: $i)).
% 0.20/0.48 tff(slbdtsldtrb0_type, type, (
% 0.20/0.48 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.20/0.48 tff(xk_type, type, (
% 0.20/0.48 xk: $i)).
% 0.20/0.48 tff(szszuzczcdt0_type, type, (
% 0.20/0.48 szszuzczcdt0: $i > $i)).
% 0.20/0.48 tff(xN_type, type, (
% 0.20/0.48 xN: $i)).
% 0.20/0.48 tff(sbrdtbr0_type, type, (
% 0.20/0.48 sbrdtbr0: $i > $i)).
% 0.20/0.48 tff(aSubsetOf0_type, type, (
% 0.20/0.48 aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(aSet0_type, type, (
% 0.20/0.48 aSet0: $i > $o)).
% 0.20/0.48 tff(szDzizrdt0_type, type, (
% 0.20/0.48 szDzizrdt0: $i > $i)).
% 0.20/0.48 tff(sdtlbdtrb0_type, type, (
% 0.20/0.48 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.20/0.48 tff(xT_type, type, (
% 0.20/0.48 xT: $i)).
% 0.20/0.48 tff(xx_type, type, (
% 0.20/0.48 xx: $i)).
% 0.20/0.48 tff(xe_type, type, (
% 0.20/0.48 xe: $i)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 ((szDzozmdt0(xd) = szNzAzT0) <=> (szDzozmdt0(xd) = szNzAzT0)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(2,axiom,((aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4730')).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[2])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (szDzozmdt0(xd) = szNzAzT0),
% 0.20/0.48 inference(and_elim,[status(thm)],[3])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (szDzozmdt0(xd) = szNzAzT0),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (szNzAzT0 = szDzozmdt0(xd)),
% 0.20/0.48 inference(symmetry,[status(thm)],[5])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (aElementOf0(W0!45, szNzAzT0) <=> aElementOf0(W0!45, szDzozmdt0(xd))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[6])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (aElementOf0(W0!45, szDzozmdt0(xd)) <=> aElementOf0(W0!45, szNzAzT0)),
% 0.20/0.48 inference(symmetry,[status(thm)],[7])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (^[W0: $i] : refl((~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> ![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (^[W0: $i] : trans(trans(monotonicity(rewrite((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) <=> (~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))))), ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))))))), rewrite((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))), ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))))), rewrite((~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))), ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(14,axiom,((aElementOf0(szDzizrdt0(xd), xT) & aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4854')).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.20/0.48 inference(and_elim,[status(thm)],[14])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.20/0.48 tff(17,plain,(
% 0.20/0.48 ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[16])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 ((~![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~(((~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))) | (~aElementOf0(W0!45, szDzozmdt0(xd)))) <=> aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (~(((~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))) | (~aElementOf0(W0!45, szDzozmdt0(xd)))) <=> aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx)) <=> ?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(23,axiom,(aElementOf0(xx, szNzAzT0) & ?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__5365')).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx))),
% 0.20/0.48 inference(and_elim,[status(thm)],[23])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.20/0.48 tff(26,plain,(
% 0.20/0.48 aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0!45) = xx)),
% 0.20/0.48 inference(skolemize,[status(sab)],[25])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.20/0.48 inference(and_elim,[status(thm)],[26])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 ((((~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))) | (~aElementOf0(W0!45, szDzozmdt0(xd)))) <=> aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))) | (~aElementOf0(W0!45, szDzozmdt0(xd))))) | (~aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 ((((~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))) | (~aElementOf0(W0!45, szDzozmdt0(xd)))) <=> aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))) | (~aElementOf0(W0!45, szDzozmdt0(xd)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (~((~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))) | (~aElementOf0(W0!45, szDzozmdt0(xd))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[29, 21])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (((~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))) | (~aElementOf0(W0!45, szDzozmdt0(xd)))) | aElementOf0(W0!45, szDzozmdt0(xd))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (aElementOf0(W0!45, szDzozmdt0(xd))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (aElementOf0(W0!45, szNzAzT0)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[32, 8])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (sdtlpdtrp0(xe, W0!45) = xx),
% 0.20/0.48 inference(and_elim,[status(thm)],[26])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (xx = sdtlpdtrp0(xe, W0!45)),
% 0.20/0.48 inference(symmetry,[status(thm)],[34])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (^[W0: $i] : trans(monotonicity(rewrite((aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0))) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0)))))), ((~(aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))) <=> (~(~((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0)))))))), rewrite((~(~((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))), ((~(aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (![W0: $i] : (~(aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 ((~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))) <=> (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(41,axiom,(~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (^[W0: $i] : refl($oeq((~(aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))), (~(aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(47,plain,(
% 0.20/0.48 ![W0: $i] : (~(aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0))))),
% 0.20/0.49 inference(nnf-neg,[status(sab)],[45, 46])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[47, 39])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[48, 37])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))) | ((~aElementOf0(W0!45, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0!45))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))) | (~aElementOf0(W0!45, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0!45))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))) | ((~aElementOf0(W0!45, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0!45))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0))))) | (~aElementOf0(W0!45, szNzAzT0)) | (~(xx = sdtlpdtrp0(xe, W0!45)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (~aElementOf0(W0!45, szNzAzT0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[52, 49, 35])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[53, 33])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------