%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM554+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:21:23 AM UTC 2025
% Result : Theorem 1.38s 1.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM554+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:26:11 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.38/1.58 % SZS status Theorem
% 1.38/1.58 % SZS output start Proof
% 1.38/1.58 tff(aElementOf0_type, type, (
% 1.38/1.58 aElementOf0: ( $i * $i ) > $o)).
% 1.38/1.58 tff(xS_type, type, (
% 1.38/1.58 xS: $i)).
% 1.38/1.58 tff(tptp_fun_W0_14_type, type, (
% 1.38/1.58 tptp_fun_W0_14: $i)).
% 1.38/1.58 tff(xx_type, type, (
% 1.38/1.58 xx: $i)).
% 1.38/1.58 tff(sdtmndt0_type, type, (
% 1.38/1.58 sdtmndt0: ( $i * $i ) > $i)).
% 1.38/1.58 tff(xy_type, type, (
% 1.38/1.58 xy: $i)).
% 1.38/1.58 tff(xQ_type, type, (
% 1.38/1.58 xQ: $i)).
% 1.38/1.58 tff(aElement0_type, type, (
% 1.38/1.58 aElement0: $i > $o)).
% 1.38/1.58 tff(xP_type, type, (
% 1.38/1.58 xP: $i)).
% 1.38/1.58 tff(aSet0_type, type, (
% 1.38/1.58 aSet0: $i > $o)).
% 1.38/1.58 tff(sdtpldt0_type, type, (
% 1.38/1.58 sdtpldt0: ( $i * $i ) > $i)).
% 1.38/1.58 tff(aSubsetOf0_type, type, (
% 1.38/1.58 aSubsetOf0: ( $i * $i ) > $o)).
% 1.38/1.58 tff(xk_type, type, (
% 1.38/1.58 xk: $i)).
% 1.38/1.58 tff(sbrdtbr0_type, type, (
% 1.38/1.58 sbrdtbr0: $i > $i)).
% 1.38/1.58 tff(slbdtsldtrb0_type, type, (
% 1.38/1.58 slbdtsldtrb0: ( $i * $i ) > $i)).
% 1.38/1.58 tff(szszuzczcdt0_type, type, (
% 1.38/1.58 szszuzczcdt0: $i > $i)).
% 1.38/1.58 tff(isFinite0_type, type, (
% 1.38/1.58 isFinite0: $i > $o)).
% 1.38/1.58 tff(xT_type, type, (
% 1.38/1.58 xT: $i)).
% 1.38/1.58 tff(sz00_type, type, (
% 1.38/1.58 sz00: $i)).
% 1.38/1.58 tff(tptp_fun_W3_3_type, type, (
% 1.38/1.58 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 1.38/1.58 tff(tptp_fun_W2_1_type, type, (
% 1.38/1.58 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 1.38/1.58 tff(1,plain,
% 1.38/1.58 (^[W0: $i] : refl((~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(2,plain,
% 1.38/1.58 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[1])).
% 1.38/1.58 tff(3,plain,
% 1.38/1.58 (^[W0: $i] : trans(trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)) <=> (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))), ((aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))), rewrite((aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))))), ((aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))))), ((aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> (aElementOf0(W0, xP) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))))))), rewrite((aElementOf0(W0, xP) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))), ((aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP))))), rewrite((~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))), ((aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(4,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[3])).
% 1.38/1.58 tff(5,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(6,axiom,((((aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))) & aSet0(xP)) & ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))) & (xP = sdtpldt0(sdtmndt0(xQ, xy), xx))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2357')).
% 1.38/1.58 tff(7,plain,
% 1.38/1.58 (((aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))) & aSet0(xP)) & ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 1.38/1.58 inference(and_elim,[status(thm)],[6])).
% 1.38/1.58 tff(8,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 1.38/1.58 inference(and_elim,[status(thm)],[7])).
% 1.38/1.58 tff(9,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[8, 5])).
% 1.38/1.58 tff(10,plain,(
% 1.38/1.58 ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 1.38/1.58 inference(skolemize,[status(sab)],[9])).
% 1.38/1.58 tff(11,plain,
% 1.38/1.58 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[10, 4])).
% 1.38/1.58 tff(12,plain,
% 1.38/1.58 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[11, 2])).
% 1.38/1.58 tff(13,plain,
% 1.38/1.58 (((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP)))) <=> ((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(14,plain,
% 1.38/1.58 ((~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP))) <=> (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(15,plain,
% 1.38/1.58 ((((~aElement0(W0!14)) | (~(aElementOf0(W0!14, sdtmndt0(xQ, xy)) | (W0!14 = xx)))) <=> aElementOf0(W0!14, xP)) <=> (((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(16,plain,
% 1.38/1.58 ((~(((~aElement0(W0!14)) | (~(aElementOf0(W0!14, sdtmndt0(xQ, xy)) | (W0!14 = xx)))) <=> aElementOf0(W0!14, xP))) <=> (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP)))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[15])).
% 1.38/1.58 tff(17,plain,
% 1.38/1.58 ((~(((~aElement0(W0!14)) | (~(aElementOf0(W0!14, sdtmndt0(xQ, xy)) | (W0!14 = xx)))) <=> aElementOf0(W0!14, xP))) <=> (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[16, 14])).
% 1.38/1.58 tff(18,plain,
% 1.38/1.58 (((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!14)) | (~(aElementOf0(W0!14, sdtmndt0(xQ, xy)) | (W0!14 = xx)))) <=> aElementOf0(W0!14, xP)))) <=> ((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[17])).
% 1.38/1.58 tff(19,plain,
% 1.38/1.58 (((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!14)) | (~(aElementOf0(W0!14, sdtmndt0(xQ, xy)) | (W0!14 = xx)))) <=> aElementOf0(W0!14, xP)))) <=> ((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[18, 13])).
% 1.38/1.58 tff(20,plain,
% 1.38/1.58 ((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!14)) | (~(aElementOf0(W0!14, sdtmndt0(xQ, xy)) | (W0!14 = xx)))) <=> aElementOf0(W0!14, xP)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(21,plain,
% 1.38/1.58 ((~![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.38/1.58 tff(22,plain,
% 1.38/1.58 (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[21, 12])).
% 1.38/1.58 tff(23,plain,
% 1.38/1.58 ((sbrdtbr0(xQ) = xk) <=> (sbrdtbr0(xQ) = xk)),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(24,axiom,((((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)) & (sbrdtbr0(xQ) = xk)) & aElementOf0(xQ, slbdtsldtrb0(xS, xk))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2270')).
% 1.38/1.58 tff(25,plain,
% 1.38/1.58 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)) & (sbrdtbr0(xQ) = xk)),
% 1.38/1.58 inference(and_elim,[status(thm)],[24])).
% 1.38/1.58 tff(26,plain,
% 1.38/1.58 (sbrdtbr0(xQ) = xk),
% 1.38/1.58 inference(and_elim,[status(thm)],[25])).
% 1.38/1.58 tff(27,plain,
% 1.38/1.58 (sbrdtbr0(xQ) = xk),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.38/1.58 tff(28,plain,
% 1.38/1.58 (aSet0(xQ) <=> aSet0(xQ)),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(29,plain,
% 1.38/1.58 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)),
% 1.38/1.58 inference(and_elim,[status(thm)],[25])).
% 1.38/1.58 tff(30,plain,
% 1.38/1.58 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))),
% 1.38/1.58 inference(and_elim,[status(thm)],[29])).
% 1.38/1.58 tff(31,plain,
% 1.38/1.58 (aSet0(xQ)),
% 1.38/1.58 inference(and_elim,[status(thm)],[30])).
% 1.38/1.58 tff(32,plain,
% 1.38/1.58 (aSet0(xQ)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[31, 28])).
% 1.38/1.58 tff(33,plain,
% 1.38/1.58 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(34,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[33])).
% 1.38/1.58 tff(35,plain,
% 1.38/1.58 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(36,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[35])).
% 1.38/1.58 tff(37,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[36, 34])).
% 1.38/1.58 tff(38,plain,
% 1.38/1.58 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(39,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[38])).
% 1.38/1.58 tff(40,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(41,plain,
% 1.38/1.58 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite(((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))) <=> ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), (![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))) <=> ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), ((aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> (aSet0(W0) => ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))))), rewrite((aSet0(W0) => ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), ((aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(42,plain,
% 1.38/1.58 (![W0: $i] : (aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[41])).
% 1.38/1.58 tff(43,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mCardDiff')).
% 1.38/1.58 tff(44,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.38/1.58 tff(45,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.38/1.58 tff(46,plain,(
% 1.38/1.58 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 1.38/1.58 inference(skolemize,[status(sab)],[45])).
% 1.38/1.58 tff(47,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.38/1.58 tff(48,plain,
% 1.38/1.58 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[47, 37])).
% 1.38/1.58 tff(49,plain,
% 1.38/1.58 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | (~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(50,plain,
% 1.38/1.58 (((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)) | (~isFinite0(xQ)))) <=> ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(51,plain,
% 1.38/1.58 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)) | (~isFinite0(xQ))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[50])).
% 1.38/1.58 tff(52,plain,
% 1.38/1.58 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)) | (~isFinite0(xQ))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | (~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[51, 49])).
% 1.38/1.58 tff(53,plain,
% 1.38/1.58 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)) | (~isFinite0(xQ))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(54,plain,
% 1.38/1.58 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | (~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.38/1.58 tff(55,plain,
% 1.38/1.58 (![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[54, 48, 32])).
% 1.38/1.58 tff(56,plain,
% 1.38/1.58 (aElementOf0(xy, xQ) <=> aElementOf0(xy, xQ)),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(57,axiom,(aElement0(xy) & aElementOf0(xy, xQ)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2304')).
% 1.38/1.58 tff(58,plain,
% 1.38/1.58 (aElementOf0(xy, xQ)),
% 1.38/1.58 inference(and_elim,[status(thm)],[57])).
% 1.38/1.58 tff(59,plain,
% 1.38/1.58 (aElementOf0(xy, xQ)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[58, 56])).
% 1.38/1.58 tff(60,plain,
% 1.38/1.58 (isFinite0(xQ) <=> isFinite0(xQ)),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(61,axiom,((aSet0(xQ) & isFinite0(xQ)) & (sbrdtbr0(xQ) = xk)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2291')).
% 1.38/1.58 tff(62,plain,
% 1.38/1.58 (aSet0(xQ) & isFinite0(xQ)),
% 1.38/1.58 inference(and_elim,[status(thm)],[61])).
% 1.38/1.58 tff(63,plain,
% 1.38/1.58 (isFinite0(xQ)),
% 1.38/1.58 inference(and_elim,[status(thm)],[62])).
% 1.38/1.58 tff(64,plain,
% 1.38/1.58 (isFinite0(xQ)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[63, 60])).
% 1.38/1.58 tff(65,plain,
% 1.38/1.58 (((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | (~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(66,plain,
% 1.38/1.58 (((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ))) <=> ((~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(67,plain,
% 1.38/1.58 (((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[66])).
% 1.38/1.58 tff(68,plain,
% 1.38/1.58 (((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | (~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[67, 65])).
% 1.38/1.58 tff(69,plain,
% 1.38/1.58 ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(70,plain,
% 1.38/1.58 ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | (~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.38/1.58 tff(71,plain,
% 1.38/1.58 (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[70, 64, 59, 55])).
% 1.38/1.58 tff(72,plain,
% 1.38/1.58 (^[W0: $i] : refl((~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy)))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(73,plain,
% 1.38/1.58 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy)))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[72])).
% 1.38/1.58 tff(74,plain,
% 1.38/1.58 (^[W0: $i] : trans(trans(monotonicity(rewrite((aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)))), ((aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))) <=> (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)))))), rewrite((aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy))))), ((aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy)))))), rewrite((~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy)))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy))))), ((aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(75,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[74])).
% 1.38/1.58 tff(76,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(77,plain,
% 1.38/1.58 (^[W0: $i] : rewrite((aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy)))) <=> (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(78,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy)))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[77])).
% 1.38/1.58 tff(79,plain,
% 1.38/1.58 ((aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))) & aSet0(xP)),
% 1.38/1.58 inference(and_elim,[status(thm)],[7])).
% 1.38/1.58 tff(80,plain,
% 1.38/1.58 (aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))),
% 1.38/1.58 inference(and_elim,[status(thm)],[79])).
% 1.38/1.58 tff(81,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))),
% 1.38/1.58 inference(and_elim,[status(thm)],[80])).
% 1.38/1.58 tff(82,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[81, 78])).
% 1.38/1.58 tff(83,plain,
% 1.38/1.58 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[82, 76])).
% 1.38/1.58 tff(84,plain,(
% 1.38/1.58 ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 1.38/1.58 inference(skolemize,[status(sab)],[83])).
% 1.38/1.58 tff(85,plain,
% 1.38/1.58 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[84, 75])).
% 1.38/1.58 tff(86,plain,
% 1.38/1.58 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[85, 73])).
% 1.38/1.58 tff(87,plain,
% 1.38/1.58 ((~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)) <=> aElementOf0(W0, sdtmndt0(xQ, xy))))) | (~(((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)) <=> aElementOf0(xx, sdtmndt0(xQ, xy))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(88,plain,
% 1.38/1.58 (~(((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)) <=> aElementOf0(xx, sdtmndt0(xQ, xy)))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.38/1.58 tff(89,plain,
% 1.38/1.58 ((~aElementOf0(xx, xQ)) <=> (~aElementOf0(xx, xQ))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(90,axiom,(~aElementOf0(xx, xQ)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2323')).
% 1.38/1.58 tff(91,plain,
% 1.38/1.58 (~aElementOf0(xx, xQ)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.38/1.58 tff(92,plain,
% 1.38/1.58 (((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)) | aElementOf0(xx, xQ)),
% 1.38/1.58 inference(tautology,[status(thm)],[])).
% 1.38/1.58 tff(93,plain,
% 1.38/1.58 ((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.38/1.58 tff(94,plain,
% 1.38/1.58 ((((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)) <=> aElementOf0(xx, sdtmndt0(xQ, xy))) | (~((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy))) | (~aElementOf0(xx, sdtmndt0(xQ, xy)))),
% 1.38/1.58 inference(tautology,[status(thm)],[])).
% 1.38/1.58 tff(95,plain,
% 1.38/1.59 ((((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)) <=> aElementOf0(xx, sdtmndt0(xQ, xy))) | (~aElementOf0(xx, sdtmndt0(xQ, xy)))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.38/1.59 tff(96,plain,
% 1.38/1.59 (~aElementOf0(xx, sdtmndt0(xQ, xy))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[95, 88])).
% 1.38/1.59 tff(97,plain,
% 1.38/1.59 (aSet0(xS) <=> aSet0(xS)),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(98,axiom,((aSet0(xS) & aSet0(xT)) & (~(xk = sz00))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2202_02')).
% 1.38/1.59 tff(99,plain,
% 1.38/1.59 (aSet0(xS) & aSet0(xT)),
% 1.38/1.59 inference(and_elim,[status(thm)],[98])).
% 1.38/1.59 tff(100,plain,
% 1.38/1.59 (aSet0(xS)),
% 1.38/1.59 inference(and_elim,[status(thm)],[99])).
% 1.38/1.59 tff(101,plain,
% 1.38/1.59 (aSet0(xS)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[100, 97])).
% 1.38/1.59 tff(102,plain,
% 1.38/1.59 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(103,plain,
% 1.38/1.59 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[102])).
% 1.38/1.59 tff(104,plain,
% 1.38/1.59 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(105,plain,
% 1.38/1.59 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[104])).
% 1.38/1.59 tff(106,plain,
% 1.38/1.59 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(transitivity,[status(thm)],[105, 103])).
% 1.38/1.59 tff(107,plain,
% 1.38/1.59 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(108,plain,
% 1.38/1.59 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(109,plain,
% 1.38/1.59 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[108])).
% 1.38/1.59 tff(110,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 1.38/1.59 tff(111,plain,
% 1.38/1.59 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.38/1.59 tff(112,plain,
% 1.38/1.59 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.38/1.59 tff(113,plain,(
% 1.38/1.59 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(skolemize,[status(sab)],[112])).
% 1.38/1.59 tff(114,plain,
% 1.38/1.59 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[113, 106])).
% 1.38/1.59 tff(115,plain,
% 1.38/1.59 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(116,plain,
% 1.38/1.59 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(117,plain,
% 1.38/1.59 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.38/1.59 tff(118,plain,
% 1.38/1.59 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[117, 114, 101])).
% 1.38/1.59 tff(119,plain,
% 1.38/1.59 (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(120,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2256')).
% 1.38/1.59 tff(121,plain,
% 1.38/1.59 (aElementOf0(xx, xS)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.38/1.59 tff(122,plain,
% 1.38/1.59 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(123,plain,
% 1.38/1.59 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(124,plain,
% 1.38/1.59 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.38/1.59 tff(125,plain,
% 1.38/1.59 (aElement0(xx)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[124, 121, 118])).
% 1.38/1.59 tff(126,plain,
% 1.38/1.59 (aElement0(xy) <=> aElement0(xy)),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(127,plain,
% 1.38/1.59 (aElement0(xy)),
% 1.38/1.59 inference(and_elim,[status(thm)],[57])).
% 1.38/1.59 tff(128,plain,
% 1.38/1.59 (aElement0(xy)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.38/1.59 tff(129,plain,
% 1.38/1.59 (^[W0: $i] : refl(((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(130,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[129])).
% 1.38/1.59 tff(131,plain,
% 1.38/1.59 (^[W0: $i] : rewrite(((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(132,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[131])).
% 1.38/1.59 tff(133,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 1.38/1.59 inference(transitivity,[status(thm)],[132, 130])).
% 1.38/1.59 tff(134,plain,
% 1.38/1.59 (^[W0: $i] : rewrite(((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))) <=> ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(135,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[134])).
% 1.38/1.59 tff(136,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(137,plain,
% 1.38/1.59 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite(((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0))) <=> (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))), (![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0))) <=> ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))), ((aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0)))) <=> (aElement0(W0) => ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))))), rewrite((aElement0(W0) => ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))) <=> ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))), ((aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0)))) <=> ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(138,plain,
% 1.38/1.59 (![W0: $i] : (aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[137])).
% 1.38/1.59 tff(139,axiom,(![W0: $i] : (aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mFDiffSet')).
% 1.38/1.59 tff(140,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.38/1.59 tff(141,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[140, 136])).
% 1.38/1.59 tff(142,plain,(
% 1.38/1.59 ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 1.38/1.59 inference(skolemize,[status(sab)],[141])).
% 1.38/1.59 tff(143,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[142, 135])).
% 1.38/1.59 tff(144,plain,
% 1.38/1.59 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[143, 133])).
% 1.38/1.59 tff(145,plain,
% 1.38/1.59 (((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | (~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(146,plain,
% 1.38/1.59 (((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1)))) <=> ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(147,plain,
% 1.38/1.59 (((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[146])).
% 1.38/1.59 tff(148,plain,
% 1.38/1.59 (((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | (~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))),
% 1.38/1.59 inference(transitivity,[status(thm)],[147, 145])).
% 1.38/1.59 tff(149,plain,
% 1.38/1.59 ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1))))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(150,plain,
% 1.38/1.59 ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | (~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.38/1.59 tff(151,plain,
% 1.38/1.59 (![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[150, 144, 128])).
% 1.38/1.59 tff(152,plain,
% 1.38/1.59 (((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))) <=> ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | (~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(153,plain,
% 1.38/1.59 (((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy))) <=> ((~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(154,plain,
% 1.38/1.59 (((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))) <=> ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[153])).
% 1.38/1.59 tff(155,plain,
% 1.38/1.59 (((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))) <=> ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | (~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[154, 152])).
% 1.38/1.59 tff(156,plain,
% 1.38/1.59 ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(157,plain,
% 1.38/1.59 ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | (~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.38/1.59 tff(158,plain,
% 1.38/1.59 (isFinite0(sdtmndt0(xQ, xy))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[157, 32, 64, 151])).
% 1.38/1.59 tff(159,plain,
% 1.38/1.59 (aSet0(sdtmndt0(xQ, xy)) <=> aSet0(sdtmndt0(xQ, xy))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(160,plain,
% 1.38/1.59 (aSet0(sdtmndt0(xQ, xy))),
% 1.38/1.59 inference(and_elim,[status(thm)],[80])).
% 1.38/1.59 tff(161,plain,
% 1.38/1.59 (aSet0(sdtmndt0(xQ, xy))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.38/1.59 tff(162,plain,
% 1.38/1.59 (^[W0: $i] : refl(((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(163,plain,
% 1.38/1.59 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[162])).
% 1.38/1.59 tff(164,plain,
% 1.38/1.59 (^[W0: $i] : rewrite(((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(165,plain,
% 1.38/1.59 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[164])).
% 1.38/1.59 tff(166,plain,
% 1.38/1.59 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(transitivity,[status(thm)],[165, 163])).
% 1.38/1.59 tff(167,plain,
% 1.38/1.59 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & isFinite0(W0)) <=> (~((~aSet0(W0)) | (~isFinite0(W0))))), ((~(aSet0(W0) & isFinite0(W0))) <=> (~(~((~aSet0(W0)) | (~isFinite0(W0))))))), rewrite((~(~((~aSet0(W0)) | (~isFinite0(W0))))) <=> ((~aSet0(W0)) | (~isFinite0(W0)))), ((~(aSet0(W0) & isFinite0(W0))) <=> ((~aSet0(W0)) | (~isFinite0(W0))))), (((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> (((~aSet0(W0)) | (~isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))), rewrite((((~aSet0(W0)) | (~isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))), (((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(168,plain,
% 1.38/1.59 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[167])).
% 1.38/1.59 tff(169,plain,
% 1.38/1.59 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(170,plain,
% 1.38/1.59 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite(((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0)))) <=> (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))), ((aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))) <=> (aElement0(W1) => (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))))), rewrite((aElement0(W1) => (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))) <=> (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))), ((aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))) <=> (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))), (![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))) <=> ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))), (((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0)))))) <=> ((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))), rewrite(((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))), (((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0)))))) <=> ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(171,plain,
% 1.38/1.59 (![W0: $i] : ((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0)))))) <=> ![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[170])).
% 1.38/1.59 tff(172,axiom,(![W0: $i] : ((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mCardCons')).
% 1.38/1.59 tff(173,plain,
% 1.38/1.59 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.38/1.59 tff(174,plain,
% 1.38/1.59 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[173, 169])).
% 1.38/1.59 tff(175,plain,(
% 1.38/1.59 ![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(skolemize,[status(sab)],[174])).
% 1.38/1.59 tff(176,plain,
% 1.38/1.59 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[175, 168])).
% 1.38/1.59 tff(177,plain,
% 1.38/1.59 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[176, 166])).
% 1.38/1.59 tff(178,plain,
% 1.38/1.59 (((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | (~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(179,plain,
% 1.38/1.59 (((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) <=> ((~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(180,plain,
% 1.38/1.59 (^[W1: $i] : rewrite((aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))) <=> (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(181,plain,
% 1.38/1.59 (![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))) <=> ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[180])).
% 1.38/1.59 tff(182,plain,
% 1.38/1.59 (((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1)))) <=> ((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[181])).
% 1.38/1.59 tff(183,plain,
% 1.38/1.59 (((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1)))) <=> ((~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 1.38/1.59 inference(transitivity,[status(thm)],[182, 179])).
% 1.38/1.59 tff(184,plain,
% 1.38/1.59 (((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[183])).
% 1.38/1.59 tff(185,plain,
% 1.38/1.59 (((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | (~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 1.38/1.59 inference(transitivity,[status(thm)],[184, 178])).
% 1.38/1.59 tff(186,plain,
% 1.38/1.59 ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(187,plain,
% 1.38/1.59 ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | (~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.38/1.59 tff(188,plain,
% 1.38/1.59 ((~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[187, 177, 161])).
% 1.38/1.59 tff(189,plain,
% 1.38/1.59 (![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[188, 158])).
% 1.38/1.59 tff(190,plain,
% 1.38/1.59 (((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | ((~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) <=> ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(191,plain,
% 1.38/1.59 ((aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))) <=> ((~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(192,plain,
% 1.38/1.59 (((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) <=> ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | ((~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[191])).
% 1.38/1.59 tff(193,plain,
% 1.38/1.59 (((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) <=> ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.38/1.59 inference(transitivity,[status(thm)],[192, 190])).
% 1.38/1.59 tff(194,plain,
% 1.38/1.59 ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(195,plain,
% 1.38/1.59 ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.38/1.59 tff(196,plain,
% 1.38/1.59 (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[195, 189, 125, 96])).
% 1.38/1.59 tff(197,plain,
% 1.38/1.59 ((xP = sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (xP = sdtpldt0(sdtmndt0(xQ, xy), xx))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(198,plain,
% 1.38/1.59 (xP = sdtpldt0(sdtmndt0(xQ, xy), xx)),
% 1.38/1.59 inference(and_elim,[status(thm)],[6])).
% 1.38/1.59 tff(199,plain,
% 1.38/1.59 (xP = sdtpldt0(sdtmndt0(xQ, xy), xx)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.38/1.59 tff(200,plain,
% 1.38/1.59 (sbrdtbr0(xP) = sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[199])).
% 1.38/1.59 tff(201,plain,
% 1.38/1.59 (sbrdtbr0(xP) = xk),
% 1.38/1.59 inference(transitivity,[status(thm)],[200, 196, 71, 27])).
% 1.38/1.59 tff(202,plain,
% 1.38/1.59 (((~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS))) | (~(sbrdtbr0(xP) = xk))) <=> ((~(sbrdtbr0(xP) = xk)) | (~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS))))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(203,plain,
% 1.38/1.59 (((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) <=> (~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(204,plain,
% 1.38/1.59 ((((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(xP) = xk))) <=> ((~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS))) | (~(sbrdtbr0(xP) = xk)))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[203])).
% 1.38/1.59 tff(205,plain,
% 1.38/1.59 ((((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(xP) = xk))) <=> ((~(sbrdtbr0(xP) = xk)) | (~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS))))),
% 1.38/1.59 inference(transitivity,[status(thm)],[204, 202])).
% 1.38/1.59 tff(206,plain,
% 1.38/1.59 ((((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(xP) = xk))) <=> (((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(xP) = xk)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(207,plain,
% 1.38/1.59 ((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) <=> (aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(208,plain,
% 1.38/1.59 (((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)) <=> ((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[207])).
% 1.38/1.59 tff(209,plain,
% 1.38/1.59 ((~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[208])).
% 1.38/1.59 tff(210,plain,
% 1.38/1.59 ((~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(211,plain,
% 1.38/1.59 ((~((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(212,axiom,(~(((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk)) | aElementOf0(xP, slbdtsldtrb0(xS, xk)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.38/1.59 tff(213,plain,
% 1.38/1.59 (~((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk))),
% 1.38/1.60 inference(or_elim,[status(thm)],[212])).
% 1.38/1.60 tff(214,plain,
% 1.38/1.60 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[213, 211])).
% 1.38/1.60 tff(215,plain,
% 1.38/1.60 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[214, 209])).
% 1.38/1.60 tff(216,plain,
% 1.38/1.60 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[215, 210])).
% 1.38/1.60 tff(217,plain,
% 1.38/1.60 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[216, 209])).
% 1.38/1.60 unexpected number of arguments: (let ((a!1 (refl (~ (not (aSubsetOf0 xP xS)) (not (aSubsetOf0 xP xS)))))
% 1.38/1.60 (a!2 (forall ((W0 $i)) (or (not (aElementOf0 W0 xP)) (aElementOf0 W0 xS))))
% 1.38/1.60 (a!3 (not (or (not (aElementOf0 W0!14 xP)) (aElementOf0 W0!14 xS))))
% 1.38/1.60 (a!6 (~ (not (= (sbrdtbr0 xP) xk)) (not (= (sbrdtbr0 xP) xk)))))
% 1.38/1.60 (let ((a!4 (~ (not (or (aSubsetOf0 xP xS) a!2))
% 1.38/1.60 (and (not (aSubsetOf0 xP xS)) a!3)))
% 1.38/1.60 (a!7 (not (and (or (aSubsetOf0 xP xS) a!2) (= (sbrdtbr0 xP) xk))))
% 1.38/1.60 (a!8 (or (and (not (aSubsetOf0 xP xS)) a!3) (not (= (sbrdtbr0 xP) xk)))))
% 1.38/1.60 (let ((a!5 (nnf-neg a!1 (sk (~ (not a!2) a!3)) a!4)))
% 1.38/1.60 (nnf-neg a!5 (refl a!6) (~ a!7 a!8)))))
% 1.38/1.60 Proof display could not be completed: unexpected number of arguments
% 1.38/1.61 % E exiting
%------------------------------------------------------------------------------