%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM556+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 1.40s 1.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM556+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.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 01:25:40 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.40/1.61 % SZS status Theorem
% 1.40/1.61 % SZS output start Proof
% 1.40/1.61 tff(aElementOf0_type, type, (
% 1.40/1.61 aElementOf0: ( $i * $i ) > $o)).
% 1.40/1.61 tff(xS_type, type, (
% 1.40/1.61 xS: $i)).
% 1.40/1.61 tff(tptp_fun_W0_14_type, type, (
% 1.40/1.61 tptp_fun_W0_14: $i)).
% 1.40/1.61 tff(xx_type, type, (
% 1.40/1.61 xx: $i)).
% 1.40/1.61 tff(sdtmndt0_type, type, (
% 1.40/1.61 sdtmndt0: ( $i * $i ) > $i)).
% 1.40/1.61 tff(xy_type, type, (
% 1.40/1.61 xy: $i)).
% 1.40/1.61 tff(xQ_type, type, (
% 1.40/1.61 xQ: $i)).
% 1.40/1.61 tff(aElement0_type, type, (
% 1.40/1.61 aElement0: $i > $o)).
% 1.40/1.61 tff(xP_type, type, (
% 1.40/1.61 xP: $i)).
% 1.40/1.61 tff(aSet0_type, type, (
% 1.40/1.61 aSet0: $i > $o)).
% 1.40/1.61 tff(sdtpldt0_type, type, (
% 1.40/1.61 sdtpldt0: ( $i * $i ) > $i)).
% 1.40/1.61 tff(aSubsetOf0_type, type, (
% 1.40/1.61 aSubsetOf0: ( $i * $i ) > $o)).
% 1.40/1.61 tff(xk_type, type, (
% 1.40/1.61 xk: $i)).
% 1.40/1.61 tff(sbrdtbr0_type, type, (
% 1.40/1.61 sbrdtbr0: $i > $i)).
% 1.40/1.61 tff(slbdtsldtrb0_type, type, (
% 1.40/1.61 slbdtsldtrb0: ( $i * $i ) > $i)).
% 1.40/1.61 tff(szszuzczcdt0_type, type, (
% 1.40/1.61 szszuzczcdt0: $i > $i)).
% 1.40/1.61 tff(isFinite0_type, type, (
% 1.40/1.61 isFinite0: $i > $o)).
% 1.40/1.61 tff(xT_type, type, (
% 1.40/1.61 xT: $i)).
% 1.40/1.61 tff(sz00_type, type, (
% 1.40/1.61 sz00: $i)).
% 1.40/1.61 tff(tptp_fun_W3_3_type, type, (
% 1.40/1.61 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 1.40/1.61 tff(tptp_fun_W2_1_type, type, (
% 1.40/1.61 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 1.40/1.61 tff(1,plain,
% 1.40/1.61 (^[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))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(2,plain,
% 1.40/1.61 (![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)))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[1])).
% 1.40/1.61 tff(3,plain,
% 1.40/1.61 (^[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)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(4,plain,
% 1.40/1.61 (![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)))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[3])).
% 1.40/1.61 tff(5,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 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/sandbox/benchmark/theBenchmark.p','m__2357')).
% 1.40/1.61 tff(7,plain,
% 1.40/1.61 (((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))))),
% 1.40/1.61 inference(and_elim,[status(thm)],[6])).
% 1.40/1.61 tff(8,plain,
% 1.40/1.61 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 1.40/1.61 inference(and_elim,[status(thm)],[7])).
% 1.40/1.61 tff(9,plain,
% 1.40/1.61 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[8, 5])).
% 1.40/1.61 tff(10,plain,(
% 1.40/1.61 ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 1.40/1.61 inference(skolemize,[status(sab)],[9])).
% 1.40/1.61 tff(11,plain,
% 1.40/1.61 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[10, 4])).
% 1.40/1.61 tff(12,plain,
% 1.40/1.61 (![W0: $i] : (~(((~aElement0(W0)) | (~(aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx)))) <=> aElementOf0(W0, xP)))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11, 2])).
% 1.40/1.61 tff(13,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(14,plain,
% 1.40/1.61 ((~(((~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)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(15,plain,
% 1.40/1.61 ((((~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))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(16,plain,
% 1.40/1.61 ((~(((~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)))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[15])).
% 1.40/1.61 tff(17,plain,
% 1.40/1.61 ((~(((~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)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[16, 14])).
% 1.40/1.61 tff(18,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[17])).
% 1.40/1.61 tff(19,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(transitivity,[status(thm)],[18, 13])).
% 1.40/1.61 tff(20,plain,
% 1.40/1.61 ((~![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)))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(21,plain,
% 1.40/1.61 ((~![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)))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.40/1.61 tff(22,plain,
% 1.40/1.61 (~(((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))) <=> aElementOf0(W0!14, xP))),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[21, 12])).
% 1.40/1.61 tff(23,plain,
% 1.40/1.61 ((sbrdtbr0(xQ) = xk) <=> (sbrdtbr0(xQ) = xk)),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 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/sandbox/benchmark/theBenchmark.p','m__2270')).
% 1.40/1.61 tff(25,plain,
% 1.40/1.61 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)) & (sbrdtbr0(xQ) = xk)),
% 1.40/1.61 inference(and_elim,[status(thm)],[24])).
% 1.40/1.61 tff(26,plain,
% 1.40/1.61 (sbrdtbr0(xQ) = xk),
% 1.40/1.61 inference(and_elim,[status(thm)],[25])).
% 1.40/1.61 tff(27,plain,
% 1.40/1.61 (sbrdtbr0(xQ) = xk),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.40/1.61 tff(28,plain,
% 1.40/1.61 (aSet0(xQ) <=> aSet0(xQ)),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(29,plain,
% 1.40/1.61 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)),
% 1.40/1.61 inference(and_elim,[status(thm)],[25])).
% 1.40/1.61 tff(30,plain,
% 1.40/1.61 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))),
% 1.40/1.61 inference(and_elim,[status(thm)],[29])).
% 1.40/1.61 tff(31,plain,
% 1.40/1.61 (aSet0(xQ)),
% 1.40/1.61 inference(and_elim,[status(thm)],[30])).
% 1.40/1.61 tff(32,plain,
% 1.40/1.61 (aSet0(xQ)),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[31, 28])).
% 1.40/1.61 tff(33,plain,
% 1.40/1.61 (^[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)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(34,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[33])).
% 1.40/1.61 tff(35,plain,
% 1.40/1.61 (^[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)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(36,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[35])).
% 1.40/1.61 tff(37,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(transitivity,[status(thm)],[36, 34])).
% 1.40/1.61 tff(38,plain,
% 1.40/1.61 (^[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)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(39,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[38])).
% 1.40/1.61 tff(40,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(41,plain,
% 1.40/1.61 (^[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))))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(42,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[41])).
% 1.40/1.61 tff(43,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mCardDiff')).
% 1.40/1.61 tff(44,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.40/1.61 tff(45,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.40/1.61 tff(46,plain,(
% 1.40/1.61 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 1.40/1.61 inference(skolemize,[status(sab)],[45])).
% 1.40/1.61 tff(47,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.40/1.61 tff(48,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[47, 37])).
% 1.40/1.61 tff(49,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(50,plain,
% 1.40/1.61 (((~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))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(51,plain,
% 1.40/1.61 (((~![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)))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[50])).
% 1.40/1.61 tff(52,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(transitivity,[status(thm)],[51, 49])).
% 1.40/1.61 tff(53,plain,
% 1.40/1.61 ((~![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))))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(54,plain,
% 1.40/1.61 ((~![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)))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.40/1.61 tff(55,plain,
% 1.40/1.61 (![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[54, 48, 32])).
% 1.40/1.61 tff(56,plain,
% 1.40/1.61 (aElementOf0(xy, xQ) <=> aElementOf0(xy, xQ)),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(57,axiom,(aElement0(xy) & aElementOf0(xy, xQ)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2304')).
% 1.40/1.61 tff(58,plain,
% 1.40/1.61 (aElementOf0(xy, xQ)),
% 1.40/1.61 inference(and_elim,[status(thm)],[57])).
% 1.40/1.61 tff(59,plain,
% 1.40/1.61 (aElementOf0(xy, xQ)),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[58, 56])).
% 1.40/1.61 tff(60,plain,
% 1.40/1.61 (isFinite0(xQ) <=> isFinite0(xQ)),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(61,axiom,((aSet0(xQ) & isFinite0(xQ)) & (sbrdtbr0(xQ) = xk)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2291')).
% 1.40/1.61 tff(62,plain,
% 1.40/1.61 (aSet0(xQ) & isFinite0(xQ)),
% 1.40/1.61 inference(and_elim,[status(thm)],[61])).
% 1.40/1.61 tff(63,plain,
% 1.40/1.61 (isFinite0(xQ)),
% 1.40/1.61 inference(and_elim,[status(thm)],[62])).
% 1.40/1.61 tff(64,plain,
% 1.40/1.61 (isFinite0(xQ)),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[63, 60])).
% 1.40/1.61 tff(65,plain,
% 1.40/1.61 (((~![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)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(66,plain,
% 1.40/1.61 (((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ))) <=> ((~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(67,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[66])).
% 1.40/1.61 tff(68,plain,
% 1.40/1.61 (((~![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)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[67, 65])).
% 1.40/1.61 tff(69,plain,
% 1.40/1.61 ((~![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)))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(70,plain,
% 1.40/1.61 ((~![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))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.40/1.61 tff(71,plain,
% 1.40/1.61 (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[70, 64, 59, 55])).
% 1.40/1.61 tff(72,plain,
% 1.40/1.61 (aSet0(xS) <=> aSet0(xS)),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(73,axiom,((aSet0(xS) & aSet0(xT)) & (~(xk = sz00))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2202_02')).
% 1.40/1.61 tff(74,plain,
% 1.40/1.61 (aSet0(xS) & aSet0(xT)),
% 1.40/1.61 inference(and_elim,[status(thm)],[73])).
% 1.40/1.61 tff(75,plain,
% 1.40/1.61 (aSet0(xS)),
% 1.40/1.61 inference(and_elim,[status(thm)],[74])).
% 1.40/1.61 tff(76,plain,
% 1.40/1.61 (aSet0(xS)),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[75, 72])).
% 1.40/1.61 tff(77,plain,
% 1.40/1.61 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(78,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[77])).
% 1.40/1.61 tff(79,plain,
% 1.40/1.61 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(80,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[79])).
% 1.40/1.61 tff(81,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(transitivity,[status(thm)],[80, 78])).
% 1.40/1.61 tff(82,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(83,plain,
% 1.40/1.61 (^[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))))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(84,plain,
% 1.40/1.61 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[83])).
% 1.40/1.61 tff(85,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 1.40/1.61 tff(86,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.40/1.61 tff(87,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[86, 82])).
% 1.40/1.61 tff(88,plain,(
% 1.40/1.61 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(skolemize,[status(sab)],[87])).
% 1.40/1.61 tff(89,plain,
% 1.40/1.61 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[88, 81])).
% 1.40/1.61 tff(90,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(91,plain,
% 1.40/1.61 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(92,plain,
% 1.40/1.61 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.40/1.61 tff(93,plain,
% 1.40/1.61 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[92, 89, 76])).
% 1.40/1.61 tff(94,plain,
% 1.40/1.61 (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(95,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2256')).
% 1.40/1.61 tff(96,plain,
% 1.40/1.61 (aElementOf0(xx, xS)),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.40/1.61 tff(97,plain,
% 1.40/1.61 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(98,plain,
% 1.40/1.61 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(99,plain,
% 1.40/1.61 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.40/1.61 tff(100,plain,
% 1.40/1.61 (aElement0(xx)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[99, 96, 93])).
% 1.40/1.61 tff(101,plain,
% 1.40/1.61 (aElement0(xy) <=> aElement0(xy)),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(102,plain,
% 1.40/1.61 (aElement0(xy)),
% 1.40/1.61 inference(and_elim,[status(thm)],[57])).
% 1.40/1.61 tff(103,plain,
% 1.40/1.61 (aElement0(xy)),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.40/1.61 tff(104,plain,
% 1.40/1.61 (^[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)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(105,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[104])).
% 1.40/1.61 tff(106,plain,
% 1.40/1.61 (^[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)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(107,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[106])).
% 1.40/1.61 tff(108,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(transitivity,[status(thm)],[107, 105])).
% 1.40/1.61 tff(109,plain,
% 1.40/1.61 (^[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)))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(110,plain,
% 1.40/1.61 (![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))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[109])).
% 1.40/1.61 tff(111,plain,
% 1.40/1.61 (![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)))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(112,plain,
% 1.40/1.61 (^[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)))))))),
% 1.40/1.61 inference(bind,[status(th)],[])).
% 1.40/1.61 tff(113,plain,
% 1.40/1.61 (![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)))))),
% 1.40/1.61 inference(quant_intro,[status(thm)],[112])).
% 1.40/1.61 tff(114,axiom,(![W0: $i] : (aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mFDiffSet')).
% 1.40/1.61 tff(115,plain,
% 1.40/1.61 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.40/1.61 tff(116,plain,
% 1.40/1.61 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[115, 111])).
% 1.40/1.61 tff(117,plain,(
% 1.40/1.61 ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 1.40/1.61 inference(skolemize,[status(sab)],[116])).
% 1.40/1.61 tff(118,plain,
% 1.40/1.61 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[117, 110])).
% 1.40/1.61 tff(119,plain,
% 1.40/1.61 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[118, 108])).
% 1.40/1.61 tff(120,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(121,plain,
% 1.40/1.61 (((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1)))) <=> ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(122,plain,
% 1.40/1.61 (((~![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)))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[121])).
% 1.40/1.61 tff(123,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.61 inference(transitivity,[status(thm)],[122, 120])).
% 1.40/1.61 tff(124,plain,
% 1.40/1.61 ((~![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))))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(125,plain,
% 1.40/1.61 ((~![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)))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.40/1.61 tff(126,plain,
% 1.40/1.61 (![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[125, 119, 103])).
% 1.40/1.61 tff(127,plain,
% 1.40/1.61 (((~![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)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(128,plain,
% 1.40/1.61 (((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy))) <=> ((~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(129,plain,
% 1.40/1.61 (((~![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))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[128])).
% 1.40/1.62 tff(130,plain,
% 1.40/1.62 (((~![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)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[129, 127])).
% 1.40/1.62 tff(131,plain,
% 1.40/1.62 ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(132,plain,
% 1.40/1.62 ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | (~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.40/1.62 tff(133,plain,
% 1.40/1.62 (isFinite0(sdtmndt0(xQ, xy))),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[132, 32, 64, 126])).
% 1.40/1.62 tff(134,plain,
% 1.40/1.62 (aSet0(sdtmndt0(xQ, xy)) <=> aSet0(sdtmndt0(xQ, xy))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(135,plain,
% 1.40/1.62 ((aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))) & aSet0(xP)),
% 1.40/1.62 inference(and_elim,[status(thm)],[7])).
% 1.40/1.62 tff(136,plain,
% 1.40/1.62 (aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))),
% 1.40/1.62 inference(and_elim,[status(thm)],[135])).
% 1.40/1.62 tff(137,plain,
% 1.40/1.62 (aSet0(sdtmndt0(xQ, xy))),
% 1.40/1.62 inference(and_elim,[status(thm)],[136])).
% 1.40/1.62 tff(138,plain,
% 1.40/1.62 (aSet0(sdtmndt0(xQ, xy))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[137, 134])).
% 1.40/1.62 tff(139,plain,
% 1.40/1.62 (^[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)))))),
% 1.40/1.62 inference(bind,[status(th)],[])).
% 1.40/1.62 tff(140,plain,
% 1.40/1.62 (![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))))),
% 1.40/1.62 inference(quant_intro,[status(thm)],[139])).
% 1.40/1.62 tff(141,plain,
% 1.40/1.62 (^[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)))))),
% 1.40/1.62 inference(bind,[status(th)],[])).
% 1.40/1.62 tff(142,plain,
% 1.40/1.62 (![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))))),
% 1.40/1.62 inference(quant_intro,[status(thm)],[141])).
% 1.40/1.62 tff(143,plain,
% 1.40/1.62 (![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))))),
% 1.40/1.62 inference(transitivity,[status(thm)],[142, 140])).
% 1.40/1.62 tff(144,plain,
% 1.40/1.62 (^[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))))))),
% 1.40/1.62 inference(bind,[status(th)],[])).
% 1.40/1.62 tff(145,plain,
% 1.40/1.62 (![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))))),
% 1.40/1.62 inference(quant_intro,[status(thm)],[144])).
% 1.40/1.62 tff(146,plain,
% 1.40/1.62 (![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))))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(147,plain,
% 1.40/1.62 (^[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))))))),
% 1.40/1.62 inference(bind,[status(th)],[])).
% 1.40/1.62 tff(148,plain,
% 1.40/1.62 (![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))))),
% 1.40/1.62 inference(quant_intro,[status(thm)],[147])).
% 1.40/1.62 tff(149,axiom,(![W0: $i] : ((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mCardCons')).
% 1.40/1.62 tff(150,plain,
% 1.40/1.62 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.40/1.62 tff(151,plain,
% 1.40/1.62 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[150, 146])).
% 1.40/1.62 tff(152,plain,(
% 1.40/1.62 ![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.40/1.62 inference(skolemize,[status(sab)],[151])).
% 1.40/1.62 tff(153,plain,
% 1.40/1.62 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[152, 145])).
% 1.40/1.62 tff(154,plain,
% 1.40/1.62 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[153, 143])).
% 1.40/1.62 tff(155,plain,
% 1.40/1.62 (((~![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))))))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(156,plain,
% 1.40/1.62 (((~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))))))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(157,plain,
% 1.40/1.62 (^[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))))))),
% 1.40/1.62 inference(bind,[status(th)],[])).
% 1.40/1.62 tff(158,plain,
% 1.40/1.62 (![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)))))),
% 1.40/1.62 inference(quant_intro,[status(thm)],[157])).
% 1.40/1.62 tff(159,plain,
% 1.40/1.62 (((~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))))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[158])).
% 1.40/1.62 tff(160,plain,
% 1.40/1.62 (((~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))))))),
% 1.40/1.62 inference(transitivity,[status(thm)],[159, 156])).
% 1.40/1.62 tff(161,plain,
% 1.40/1.62 (((~![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)))))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[160])).
% 1.40/1.62 tff(162,plain,
% 1.40/1.62 (((~![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))))))),
% 1.40/1.62 inference(transitivity,[status(thm)],[161, 155])).
% 1.40/1.62 tff(163,plain,
% 1.40/1.62 ((~![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))))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(164,plain,
% 1.40/1.62 ((~![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)))))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.40/1.62 tff(165,plain,
% 1.40/1.62 ((~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[164, 154, 138])).
% 1.40/1.62 tff(166,plain,
% 1.40/1.62 (![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[165, 133])).
% 1.40/1.62 tff(167,plain,
% 1.40/1.62 ((~aElementOf0(xx, sdtmndt0(xQ, xy))) <=> (~aElementOf0(xx, sdtmndt0(xQ, xy)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(168,axiom,(((~aElementOf0(xx, sdtmndt0(xQ, xy))) & aSet0(sdtmndt0(xQ, xy))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2411')).
% 1.40/1.62 tff(169,plain,
% 1.40/1.62 ((~aElementOf0(xx, sdtmndt0(xQ, xy))) & aSet0(sdtmndt0(xQ, xy))),
% 1.40/1.62 inference(and_elim,[status(thm)],[168])).
% 1.40/1.62 tff(170,plain,
% 1.40/1.62 (~aElementOf0(xx, sdtmndt0(xQ, xy))),
% 1.40/1.62 inference(and_elim,[status(thm)],[169])).
% 1.40/1.62 tff(171,plain,
% 1.40/1.62 (~aElementOf0(xx, sdtmndt0(xQ, xy))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[170, 167])).
% 1.40/1.62 tff(172,plain,
% 1.40/1.62 (((~![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)))))) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(173,plain,
% 1.40/1.62 ((~![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)))))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(174,plain,
% 1.40/1.62 ((~![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))))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.40/1.62 tff(175,plain,
% 1.40/1.62 (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[174, 171, 166, 100])).
% 1.40/1.62 tff(176,plain,
% 1.40/1.62 ((xP = sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (xP = sdtpldt0(sdtmndt0(xQ, xy), xx))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(177,plain,
% 1.40/1.62 (xP = sdtpldt0(sdtmndt0(xQ, xy), xx)),
% 1.40/1.62 inference(and_elim,[status(thm)],[6])).
% 1.40/1.62 tff(178,plain,
% 1.40/1.62 (xP = sdtpldt0(sdtmndt0(xQ, xy), xx)),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.40/1.62 tff(179,plain,
% 1.40/1.62 (sbrdtbr0(xP) = sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[178])).
% 1.40/1.62 tff(180,plain,
% 1.40/1.62 (sbrdtbr0(xP) = xk),
% 1.40/1.62 inference(transitivity,[status(thm)],[179, 175, 71, 27])).
% 1.40/1.62 tff(181,plain,
% 1.40/1.62 (((~(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))))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(182,plain,
% 1.40/1.62 (((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) <=> (~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(183,plain,
% 1.40/1.62 ((((~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)))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[182])).
% 1.40/1.62 tff(184,plain,
% 1.40/1.62 ((((~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))))),
% 1.40/1.62 inference(transitivity,[status(thm)],[183, 181])).
% 1.40/1.62 tff(185,plain,
% 1.40/1.62 ((((~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)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(186,plain,
% 1.40/1.62 ((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) <=> (aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(187,plain,
% 1.40/1.62 (((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))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[186])).
% 1.40/1.62 tff(188,plain,
% 1.40/1.62 ((~((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)))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[187])).
% 1.40/1.62 tff(189,plain,
% 1.40/1.62 ((~((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)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(190,plain,
% 1.40/1.62 ((~((![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)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(191,axiom,(~((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 1.40/1.62 tff(192,plain,
% 1.40/1.62 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.40/1.62 tff(193,plain,
% 1.40/1.62 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[192, 188])).
% 1.40/1.62 tff(194,plain,
% 1.40/1.62 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[193, 189])).
% 1.40/1.62 tff(195,plain,
% 1.40/1.62 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[194, 188])).
% 1.40/1.62 unexpected number of arguments: (let ((a!1 (refl (~ (not (aSubsetOf0 xP xS)) (not (aSubsetOf0 xP xS)))))
% 1.40/1.62 (a!2 (forall ((W0 $i)) (or (not (aElementOf0 W0 xP)) (aElementOf0 W0 xS))))
% 1.40/1.62 (a!3 (not (or (not (aElementOf0 W0!14 xP)) (aElementOf0 W0!14 xS))))
% 1.40/1.62 (a!6 (~ (not (= (sbrdtbr0 xP) xk)) (not (= (sbrdtbr0 xP) xk)))))
% 1.40/1.62 (let ((a!4 (~ (not (or (aSubsetOf0 xP xS) a!2))
% 1.40/1.62 (and (not (aSubsetOf0 xP xS)) a!3)))
% 1.40/1.62 (a!7 (not (and (or (aSubsetOf0 xP xS) a!2) (= (sbrdtbr0 xP) xk))))
% 1.40/1.62 (a!8 (or (and (not (aSubsetOf0 xP xS)) a!3) (not (= (sbrdtbr0 xP) xk)))))
% 1.40/1.62 (let ((a!5 (nnf-neg a!1 (sk (~ (not a!2) a!3)) a!4)))
% 1.40/1.62 (nnf-neg a!5 (refl a!6) (~ a!7 a!8)))))
% 1.40/1.62 Proof display could not be completed: unexpected number of arguments
% 1.40/1.64 % E exiting
%------------------------------------------------------------------------------