Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : NUM534+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n007.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 05:21:18 AM UTC 2025

% Result   : Theorem 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : NUM534+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Jun 20 01:24:50 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 0.21/0.40  % SZS status Theorem
% 0.21/0.40  % SZS output start Proof
% 0.21/0.40  tff(aElementOf0_type, type, (
% 0.21/0.40     aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.40  tff(sdtmndt0_type, type, (
% 0.21/0.40     sdtmndt0: ( $i * $i ) > $i)).
% 0.21/0.40  tff(xx_type, type, (
% 0.21/0.40     xx: $i)).
% 0.21/0.40  tff(xS_type, type, (
% 0.21/0.40     xS: $i)).
% 0.21/0.40  tff(tptp_fun_W2_1_type, type, (
% 0.21/0.40     tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.21/0.40  tff(aElement0_type, type, (
% 0.21/0.40     aElement0: $i > $o)).
% 0.21/0.40  tff(aSubsetOf0_type, type, (
% 0.21/0.40     aSubsetOf0: ( $i * $i ) > $o)).
% 0.21/0.40  tff(aSet0_type, type, (
% 0.21/0.40     aSet0: $i > $o)).
% 0.21/0.40  tff(tptp_fun_W3_2_type, type, (
% 0.21/0.40     tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.21/0.40  tff(sdtpldt0_type, type, (
% 0.21/0.40     sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.40  tff(tptp_fun_W3_3_type, type, (
% 0.21/0.40     tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.21/0.40  tff(1,assumption,(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx), introduced(assumption)).
% 0.21/0.40  tff(2,plain,
% 0.21/0.40      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> aElementOf0(xx, xS)),
% 0.21/0.40      inference(monotonicity,[status(thm)],[1])).
% 0.21/0.40  tff(3,plain,
% 0.21/0.40      (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.40      inference(symmetry,[status(thm)],[2])).
% 0.21/0.40  tff(4,plain,
% 0.21/0.40      (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 0.21/0.40      inference(rewrite,[status(thm)],[])).
% 0.21/0.40  tff(5,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__617_02')).
% 0.21/0.40  tff(6,plain,
% 0.21/0.40      (aElementOf0(xx, xS)),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.40  tff(7,plain,
% 0.21/0.40      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[6, 3])).
% 0.21/0.40  tff(8,plain,
% 0.21/0.40      (((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | (~(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))),
% 0.21/0.40      inference(tautology,[status(thm)],[])).
% 0.21/0.40  tff(9,plain,
% 0.21/0.40      ((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[8, 1])).
% 0.21/0.40  tff(10,plain,
% 0.21/0.40      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) <=> aElement0(xx)),
% 0.21/0.40      inference(monotonicity,[status(thm)],[1])).
% 0.21/0.40  tff(11,plain,
% 0.21/0.40      (aElement0(xx) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.21/0.40      inference(symmetry,[status(thm)],[10])).
% 0.21/0.40  tff(12,plain,
% 0.21/0.40      (aSet0(xS) <=> aSet0(xS)),
% 0.21/0.40      inference(rewrite,[status(thm)],[])).
% 0.21/0.40  tff(13,axiom,(aSet0(xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__617')).
% 0.21/0.40  tff(14,plain,
% 0.21/0.40      (aSet0(xS)),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.40  tff(15,plain,
% 0.21/0.40      (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.21/0.40      inference(bind,[status(th)],[])).
% 0.21/0.40  tff(16,plain,
% 0.21/0.40      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(quant_intro,[status(thm)],[15])).
% 0.21/0.40  tff(17,plain,
% 0.21/0.40      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.21/0.40      inference(bind,[status(th)],[])).
% 0.21/0.40  tff(18,plain,
% 0.21/0.40      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(quant_intro,[status(thm)],[17])).
% 0.21/0.40  tff(19,plain,
% 0.21/0.40      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(transitivity,[status(thm)],[18, 16])).
% 0.21/0.40  tff(20,plain,
% 0.21/0.40      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(rewrite,[status(thm)],[])).
% 0.21/0.40  tff(21,plain,
% 0.21/0.40      (^[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))))))),
% 0.21/0.40      inference(bind,[status(th)],[])).
% 0.21/0.40  tff(22,plain,
% 0.21/0.40      (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(quant_intro,[status(thm)],[21])).
% 0.21/0.40  tff(23,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 0.21/0.40  tff(24,plain,
% 0.21/0.40      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.40  tff(25,plain,
% 0.21/0.40      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.40  tff(26,plain,(
% 0.21/0.40      ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(skolemize,[status(sab)],[25])).
% 0.21/0.40  tff(27,plain,
% 0.21/0.40      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.40  tff(28,plain,
% 0.21/0.40      (((~![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))))),
% 0.21/0.40      inference(rewrite,[status(thm)],[])).
% 0.21/0.40  tff(29,plain,
% 0.21/0.40      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.21/0.40      inference(quant_inst,[status(thm)],[])).
% 0.21/0.40  tff(30,plain,
% 0.21/0.40      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.40  tff(31,plain,
% 0.21/0.40      (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[30, 27, 14])).
% 0.21/0.40  tff(32,plain,
% 0.21/0.40      (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS)))),
% 0.21/0.40      inference(rewrite,[status(thm)],[])).
% 0.21/0.40  tff(33,plain,
% 0.21/0.40      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))),
% 0.21/0.40      inference(quant_inst,[status(thm)],[])).
% 0.21/0.40  tff(34,plain,
% 0.21/0.40      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.40  tff(35,plain,
% 0.21/0.40      (aElement0(xx)),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[34, 6, 31])).
% 0.21/0.40  tff(36,plain,
% 0.21/0.40      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[35, 11])).
% 0.21/0.40  tff(37,plain,
% 0.21/0.40      ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.21/0.40      inference(tautology,[status(thm)],[])).
% 0.21/0.40  tff(38,plain,
% 0.21/0.40      (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[37, 36, 9])).
% 0.21/0.40  tff(39,plain,
% 0.21/0.40      (aSet0(sdtmndt0(xS, xx)) <=> aSet0(sdtmndt0(xS, xx))),
% 0.21/0.40      inference(rewrite,[status(thm)],[])).
% 0.21/0.40  tff(40,plain,
% 0.21/0.40      ((~((aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> ((aElement0(W0) & aElementOf0(W0, xS)) & (~(W0 = xx))))) => ((aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xS, xx)) | (W0 = xx))))) => (sdtpldt0(sdtmndt0(xS, xx), xx) = xS)))) <=> (~((sdtpldt0(sdtmndt0(xS, xx), xx) = xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))))))),
% 0.21/0.40      inference(rewrite,[status(thm)],[])).
% 0.21/0.40  tff(41,axiom,(~((aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> ((aElement0(W0) & aElementOf0(W0, xS)) & (~(W0 = xx))))) => ((aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xS, xx)) | (W0 = xx))))) => (sdtpldt0(sdtmndt0(xS, xx), xx) = xS)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.21/0.40  tff(42,plain,
% 0.21/0.40      (~((sdtpldt0(sdtmndt0(xS, xx), xx) = xS) | (~(aSet0(sdtpldt0(sdtmndt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, sdtmndt0(xS, xx))))))) | (~(aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx)))))))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.40  tff(43,plain,
% 0.21/0.40      (aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))),
% 0.21/0.40      inference(or_elim,[status(thm)],[42])).
% 0.21/0.40  tff(44,plain,
% 0.21/0.40      (aSet0(sdtmndt0(xS, xx))),
% 0.21/0.40      inference(and_elim,[status(thm)],[43])).
% 0.21/0.40  tff(45,plain,
% 0.21/0.40      (aSet0(sdtmndt0(xS, xx))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[44, 39])).
% 0.21/0.40  tff(46,plain,
% 0.21/0.40      (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))) <=> (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))), (![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))) <=> ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))))),
% 0.21/0.40      inference(bind,[status(th)],[])).
% 0.21/0.40  tff(47,plain,
% 0.21/0.40      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.40      inference(quant_intro,[status(thm)],[46])).
% 0.21/0.40  tff(48,plain,
% 0.21/0.40      (^[W0: $i, W1: $i] : refl(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))))),
% 0.21/0.40      inference(bind,[status(th)],[])).
% 0.21/0.40  tff(49,plain,
% 0.21/0.40      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.21/0.40      inference(quant_intro,[status(thm)],[48])).
% 0.21/0.40  tff(50,plain,
% 0.21/0.40      (^[W0: $i, W1: $i] : rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))))),
% 0.21/0.40      inference(bind,[status(th)],[])).
% 0.21/0.40  tff(51,plain,
% 0.21/0.40      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.21/0.40      inference(quant_intro,[status(thm)],[50])).
% 0.21/0.40  tff(52,plain,
% 0.21/0.40      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.21/0.40      inference(transitivity,[status(thm)],[51, 49])).
% 0.21/0.40  tff(53,plain,
% 0.21/0.41      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aSet0(W0)) | (~aElement0(W1))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aSet0(W0)) | (~aElement0(W1))))))), rewrite((~(~((~aSet0(W0)) | (~aElement0(W1))))) <=> ((~aSet0(W0)) | (~aElement0(W1)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aSet0(W0)) | (~aElement0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) <=> ((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))), ((aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))), rewrite((aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> (~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> (~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))), rewrite((~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))) <=> (~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> (~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))), ((~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))) <=> (~(~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))), rewrite((~(~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) <=> (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))), ((~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))) <=> (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))), (((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))), rewrite(((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))), (((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))), ((((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> (((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2))))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))), rewrite((((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2))))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) <=> (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))), ((((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))))), (![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))) <=> (((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))))), rewrite((((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(54,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[53])).
% 0.21/0.41  tff(55,plain,
% 0.21/0.41      (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(56,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[55])).
% 0.21/0.41  tff(57,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.21/0.41      inference(rewrite,[status(thm)],[])).
% 0.21/0.41  tff(58,plain,
% 0.21/0.41      (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(59,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[58])).
% 0.21/0.41  tff(60,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefCons')).
% 0.21/0.41  tff(61,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.41  tff(62,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[61, 57])).
% 0.21/0.41  tff(63,plain,(
% 0.21/0.41      ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))),
% 0.21/0.41      inference(skolemize,[status(sab)],[62])).
% 0.21/0.41  tff(64,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[63, 56])).
% 0.21/0.41  tff(65,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[64, 54])).
% 0.21/0.41  tff(66,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[65, 52])).
% 0.21/0.41  tff(67,plain,
% 0.21/0.41      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.41      inference(modus_ponens,[status(thm)],[66, 47])).
% 0.21/0.41  tff(68,plain,
% 0.21/0.41      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.42      inference(rewrite,[status(thm)],[])).
% 0.21/0.42  tff(69,plain,
% 0.21/0.42      (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.42      inference(rewrite,[status(thm)],[])).
% 0.21/0.42  tff(70,plain,
% 0.21/0.42      (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(71,plain,
% 0.21/0.42      (![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[70])).
% 0.21/0.42  tff(72,plain,
% 0.21/0.42      (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.42      inference(monotonicity,[status(thm)],[71])).
% 0.21/0.42  tff(73,plain,
% 0.21/0.42      (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.42      inference(transitivity,[status(thm)],[72, 69])).
% 0.21/0.42  tff(74,plain,
% 0.21/0.42      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))))),
% 0.21/0.42      inference(monotonicity,[status(thm)],[73])).
% 0.21/0.42  tff(75,plain,
% 0.21/0.42      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.42      inference(transitivity,[status(thm)],[74, 68])).
% 0.21/0.42  tff(76,plain,
% 0.21/0.42      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.43      inference(quant_inst,[status(thm)],[])).
% 0.21/0.43  tff(77,plain,
% 0.21/0.43      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.43  tff(78,plain,
% 0.21/0.43      ((~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[77, 67, 45])).
% 0.21/0.43  tff(79,plain,
% 0.21/0.43      (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[78, 35])).
% 0.21/0.43  tff(80,plain,
% 0.21/0.43      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, xS))))))))))),
% 0.21/0.43      inference(quant_inst,[status(thm)],[])).
% 0.21/0.43  tff(81,plain,
% 0.21/0.43      (~((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, xS)))))))))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.43  tff(82,plain,
% 0.21/0.43      (((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, xS))))))))) | ((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))),
% 0.21/0.43      inference(tautology,[status(thm)],[])).
% 0.21/0.43  tff(83,plain,
% 0.21/0.43      ((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.43  tff(84,plain,
% 0.21/0.43      ((xS = sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (sdtpldt0(sdtmndt0(xS, xx), xx) = xS)),
% 0.21/0.43      inference(commutativity,[status(thm)],[])).
% 0.21/0.43  tff(85,plain,
% 0.21/0.43      ((sdtpldt0(sdtmndt0(xS, xx), xx) = xS) <=> (xS = sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.21/0.43      inference(symmetry,[status(thm)],[84])).
% 0.21/0.43  tff(86,plain,
% 0.21/0.43      ((~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)) <=> (~(xS = sdtpldt0(sdtmndt0(xS, xx), xx)))),
% 0.21/0.43      inference(monotonicity,[status(thm)],[85])).
% 0.21/0.43  tff(87,plain,
% 0.21/0.43      ((~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)) <=> (~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(88,plain,
% 0.21/0.43      (~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)),
% 0.21/0.43      inference(or_elim,[status(thm)],[42])).
% 0.21/0.43  tff(89,plain,
% 0.21/0.43      (~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.43  tff(90,plain,
% 0.21/0.43      (~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[89, 86])).
% 0.21/0.43  tff(91,plain,
% 0.21/0.43      ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.43      inference(tautology,[status(thm)],[])).
% 0.21/0.43  tff(92,plain,
% 0.21/0.43      ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[91, 14])).
% 0.21/0.43  tff(93,plain,
% 0.21/0.43      (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[92, 90, 83])).
% 0.21/0.43  tff(94,plain,
% 0.21/0.43      ((~(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.43      inference(tautology,[status(thm)],[])).
% 0.21/0.43  tff(95,plain,
% 0.21/0.43      (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.43  tff(96,plain,
% 0.21/0.43      ($false),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[95, 38, 7])).
% 0.21/0.43  tff(97,plain,(~(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43  tff(98,assumption,(![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))), introduced(assumption)).
% 0.21/0.43  tff(99,assumption,(~(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)), introduced(assumption)).
% 0.21/0.43  tff(100,assumption,(~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))), introduced(assumption)).
% 0.21/0.43  tff(101,plain,
% 0.21/0.43      (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[95, 100])).
% 0.21/0.43  tff(102,plain,
% 0.21/0.43      (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | ((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.43      inference(tautology,[status(thm)],[])).
% 0.21/0.43  tff(103,plain,
% 0.21/0.43      ((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[102, 100])).
% 0.21/0.43  tff(104,plain,
% 0.21/0.43      ((~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.43      inference(tautology,[status(thm)],[])).
% 0.21/0.43  tff(105,plain,
% 0.21/0.43      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[104, 103, 99])).
% 0.21/0.43  tff(106,plain,
% 0.21/0.43      (((~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))) | ((~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(107,plain,
% 0.21/0.43      ((~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))) | ((~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.43      inference(quant_inst,[status(thm)],[])).
% 0.21/0.43  tff(108,plain,
% 0.21/0.43      ((~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.43  tff(109,plain,
% 0.21/0.43      ((~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[108, 98])).
% 0.21/0.43  tff(110,plain,
% 0.21/0.43      ($false),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[109, 105, 101])).
% 0.21/0.43  tff(111,plain,(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44  tff(112,plain,
% 0.21/0.44      ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[111, 99, 98])).
% 0.21/0.44  tff(113,plain,
% 0.21/0.44      ((~(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(114,plain,
% 0.21/0.44      ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[113, 93])).
% 0.21/0.44  tff(115,plain,
% 0.21/0.44      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[114, 112])).
% 0.21/0.44  tff(116,plain,
% 0.21/0.44      (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(117,plain,
% 0.21/0.44      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))),
% 0.21/0.44      inference(quant_inst,[status(thm)],[])).
% 0.21/0.44  tff(118,plain,
% 0.21/0.44      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.44  tff(119,plain,
% 0.21/0.44      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[118, 31])).
% 0.21/0.44  tff(120,plain,
% 0.21/0.44      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[119, 115])).
% 0.21/0.44  tff(121,plain,
% 0.21/0.44      (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[37, 120, 112])).
% 0.21/0.44  tff(122,plain,
% 0.21/0.44      ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(123,plain,
% 0.21/0.44      (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[122, 120, 99, 115])).
% 0.21/0.44  tff(124,plain,
% 0.21/0.44      (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))) <=> (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))), (![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))) <=> ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(125,plain,
% 0.21/0.44      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[124])).
% 0.21/0.44  tff(126,plain,
% 0.21/0.44      (^[W0: $i, W1: $i] : refl(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(127,plain,
% 0.21/0.44      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[126])).
% 0.21/0.44  tff(128,plain,
% 0.21/0.44      (^[W0: $i, W1: $i] : rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(129,plain,
% 0.21/0.44      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[128])).
% 0.21/0.44  tff(130,plain,
% 0.21/0.44      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.21/0.44      inference(transitivity,[status(thm)],[129, 127])).
% 0.21/0.44  tff(131,plain,
% 0.21/0.44      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aSet0(W0)) | (~aElement0(W1))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aSet0(W0)) | (~aElement0(W1))))))), rewrite((~(~((~aSet0(W0)) | (~aElement0(W1))))) <=> ((~aSet0(W0)) | (~aElement0(W1)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aSet0(W0)) | (~aElement0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) <=> ((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))), ((aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))), rewrite((aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))), rewrite((~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))) <=> (~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))), ((~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> (~(~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))), rewrite((~(~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) <=> (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))), ((~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))), (((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))), rewrite(((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))), (((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))), ((((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> (((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2))))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))), rewrite((((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2))))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) <=> (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))), ((((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))))), (![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> (((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))))), rewrite((((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(132,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[131])).
% 0.21/0.45  tff(133,plain,
% 0.21/0.45      (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(134,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[133])).
% 0.21/0.45  tff(135,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(136,plain,
% 0.21/0.45      (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))) <=> ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(137,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[136])).
% 0.21/0.45  tff(138,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefDiff')).
% 0.21/0.45  tff(139,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.45  tff(140,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[139, 135])).
% 0.21/0.45  tff(141,plain,(
% 0.21/0.45      ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.21/0.45      inference(skolemize,[status(sab)],[140])).
% 0.21/0.45  tff(142,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[141, 134])).
% 0.21/0.45  tff(143,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[142, 132])).
% 0.21/0.45  tff(144,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[143, 130])).
% 0.21/0.45  tff(145,plain,
% 0.21/0.45      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[144, 125])).
% 0.21/0.45  tff(146,plain,
% 0.21/0.45      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(147,plain,
% 0.21/0.45      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(148,plain,
% 0.21/0.45      (^[W2: $i] : rewrite((~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(149,plain,
% 0.21/0.45      (![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[148])).
% 0.21/0.45  tff(150,plain,
% 0.21/0.45      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.45      inference(monotonicity,[status(thm)],[149])).
% 0.21/0.45  tff(151,plain,
% 0.21/0.45      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.45      inference(transitivity,[status(thm)],[150, 147])).
% 0.21/0.45  tff(152,plain,
% 0.21/0.45      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))))),
% 0.21/0.46      inference(monotonicity,[status(thm)],[151])).
% 0.21/0.46  tff(153,plain,
% 0.21/0.46      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.46      inference(transitivity,[status(thm)],[152, 146])).
% 0.21/0.46  tff(154,plain,
% 0.21/0.46      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.46      inference(quant_inst,[status(thm)],[])).
% 0.21/0.46  tff(155,plain,
% 0.21/0.46      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.46      inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.46  tff(156,plain,
% 0.21/0.46      ((~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[155, 145, 14])).
% 0.21/0.46  tff(157,plain,
% 0.21/0.46      (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[156, 35])).
% 0.21/0.46  tff(158,plain,
% 0.21/0.46      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))))),
% 0.21/0.46      inference(rewrite,[status(thm)],[])).
% 0.21/0.46  tff(159,plain,
% 0.21/0.46      ((~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))))))) <=> (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))),
% 0.21/0.46      inference(rewrite,[status(thm)],[])).
% 0.21/0.46  tff(160,plain,
% 0.21/0.46      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))))),
% 0.21/0.46      inference(monotonicity,[status(thm)],[159])).
% 0.21/0.46  tff(161,plain,
% 0.21/0.46      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))))),
% 0.21/0.46      inference(transitivity,[status(thm)],[160, 158])).
% 0.21/0.46  tff(162,plain,
% 0.21/0.46      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))))))),
% 0.21/0.46      inference(quant_inst,[status(thm)],[])).
% 0.21/0.46  tff(163,plain,
% 0.21/0.46      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))),
% 0.21/0.46      inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.46  tff(164,plain,
% 0.21/0.46      (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[163, 157])).
% 0.21/0.47  tff(165,plain,
% 0.21/0.47      (((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))) | ![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(166,plain,
% 0.21/0.47      (![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[165, 164])).
% 0.21/0.47  tff(167,plain,
% 0.21/0.47      ((~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))) | (~(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.21/0.47      inference(quant_inst,[status(thm)],[])).
% 0.21/0.47  tff(168,plain,
% 0.21/0.47      (~(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[167, 166])).
% 0.21/0.47  tff(169,plain,
% 0.21/0.47      ((((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(170,plain,
% 0.21/0.47      (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[169, 168])).
% 0.21/0.47  tff(171,plain,
% 0.21/0.47      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[170, 123])).
% 0.21/0.47  tff(172,plain,
% 0.21/0.47      (((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(173,plain,
% 0.21/0.47      ($false),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[172, 171, 121])).
% 0.21/0.47  tff(174,plain,((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47  tff(175,plain,
% 0.21/0.47      (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[174, 97])).
% 0.21/0.47  tff(176,plain,
% 0.21/0.47      (((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))) | ![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(177,plain,
% 0.21/0.47      ((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[176, 175])).
% 0.21/0.47  tff(178,plain,
% 0.21/0.47      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 0.21/0.47      inference(bind,[status(th)],[])).
% 0.21/0.47  tff(179,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.21/0.47      inference(quant_intro,[status(thm)],[178])).
% 0.21/0.47  tff(180,plain,
% 0.21/0.47      (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.21/0.47      inference(bind,[status(th)],[])).
% 0.21/0.47  tff(181,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47      inference(quant_intro,[status(thm)],[180])).
% 0.21/0.47  tff(182,plain,
% 0.21/0.47      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.21/0.47      inference(bind,[status(th)],[])).
% 0.21/0.47  tff(183,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47      inference(quant_intro,[status(thm)],[182])).
% 0.21/0.47  tff(184,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47      inference(transitivity,[status(thm)],[183, 181])).
% 0.21/0.47  tff(185,plain,
% 0.21/0.47      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.21/0.47      inference(bind,[status(th)],[])).
% 0.21/0.47  tff(186,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47      inference(quant_intro,[status(thm)],[185])).
% 0.21/0.47  tff(187,plain,
% 0.21/0.47      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.21/0.47      inference(bind,[status(th)],[])).
% 0.21/0.47  tff(188,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.21/0.47      inference(quant_intro,[status(thm)],[187])).
% 0.21/0.47  tff(189,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(190,plain,
% 0.21/0.47      (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 0.21/0.47      inference(bind,[status(th)],[])).
% 0.21/0.47  tff(191,plain,
% 0.21/0.47      (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.21/0.47      inference(quant_intro,[status(thm)],[190])).
% 0.21/0.47  tff(192,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefSub')).
% 0.21/0.47  tff(193,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[192, 191])).
% 0.21/0.47  tff(194,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[193, 189])).
% 0.21/0.47  tff(195,plain,(
% 0.21/0.47      ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.21/0.47      inference(skolemize,[status(sab)],[194])).
% 0.21/0.47  tff(196,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[195, 188])).
% 0.21/0.47  tff(197,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[196, 186])).
% 0.21/0.47  tff(198,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[197, 184])).
% 0.21/0.47  tff(199,plain,
% 0.21/0.47      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[198, 179])).
% 0.21/0.47  tff(200,plain,
% 0.21/0.47      (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(201,plain,
% 0.21/0.47      (((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) <=> ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(202,plain,
% 0.21/0.47      (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))))),
% 0.21/0.47      inference(monotonicity,[status(thm)],[201])).
% 0.21/0.47  tff(203,plain,
% 0.21/0.47      (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.21/0.47      inference(transitivity,[status(thm)],[202, 200])).
% 0.21/0.47  tff(204,plain,
% 0.21/0.47      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.21/0.47      inference(quant_inst,[status(thm)],[])).
% 0.21/0.47  tff(205,plain,
% 0.21/0.47      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.48  tff(206,plain,
% 0.21/0.48      (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[205, 199, 14])).
% 0.21/0.48  tff(207,plain,
% 0.21/0.48      ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))))))))),
% 0.21/0.48      inference(quant_inst,[status(thm)],[])).
% 0.21/0.48  tff(208,plain,
% 0.21/0.48      (~((~((~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))))))))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[207, 206])).
% 0.21/0.48  tff(209,plain,
% 0.21/0.48      (((~((~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))))))) | ((~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))))))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(210,plain,
% 0.21/0.48      ((~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[209, 208])).
% 0.21/0.48  tff(211,plain,
% 0.21/0.48      ((~((~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS))))))) | (~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(212,plain,
% 0.21/0.48      ((~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[211, 210])).
% 0.21/0.48  tff(213,plain,
% 0.21/0.48      (~aSubsetOf0(sdtmndt0(xS, xx), xS)),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[212, 177])).
% 0.21/0.48  tff(214,plain,
% 0.21/0.48      (((~((~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(xS, xx), xS)) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(xS, xx))) | aElementOf0(W2, xS)))))))) | ((~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(215,plain,
% 0.21/0.48      ((~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[214, 208])).
% 0.21/0.48  tff(216,plain,
% 0.21/0.48      ((~((~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))))) | (~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(217,plain,
% 0.21/0.48      ((~((~aSet0(sdtmndt0(xS, xx))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))))) | aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[216, 45])).
% 0.21/0.48  tff(218,plain,
% 0.21/0.48      (aSubsetOf0(sdtmndt0(xS, xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[217, 215])).
% 0.21/0.48  tff(219,plain,
% 0.21/0.48      (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[218, 213])).
% 0.21/0.48  tff(220,plain,
% 0.21/0.48      (((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(221,plain,
% 0.21/0.48      (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[220, 219])).
% 0.21/0.48  tff(222,plain,
% 0.21/0.48      (((~aElement0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)) | (tptp_fun_W2_1(sdtmndt0(xS, xx), xS) = xx)) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(223,plain,
% 0.21/0.48      ((~aElement0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)) | (tptp_fun_W2_1(sdtmndt0(xS, xx), xS) = xx)),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[222, 221])).
% 0.21/0.48  tff(224,plain,
% 0.21/0.48      (((~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)) | aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(225,plain,
% 0.21/0.48      (aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[224, 219])).
% 0.21/0.48  tff(226,plain,
% 0.21/0.48      ((((~aElement0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)) | (tptp_fun_W2_1(sdtmndt0(xS, xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)) | (tptp_fun_W2_1(sdtmndt0(xS, xx), xS) = xx))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx)))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(227,plain,
% 0.21/0.48      (((~aElement0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)) | (tptp_fun_W2_1(sdtmndt0(xS, xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[226, 225, 223])).
% 0.21/0.48  tff(228,plain,
% 0.21/0.48      ((~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))) | (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), xS)) | (tptp_fun_W2_1(sdtmndt0(xS, xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(xS, xx), xS), sdtmndt0(xS, xx))))),
% 0.21/0.48      inference(quant_inst,[status(thm)],[])).
% 0.21/0.48  tff(229,plain,
% 0.21/0.48      ($false),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[228, 166, 227])).
% 0.21/0.48  % SZS output end Proof
% 0.21/0.48  % E exiting
%------------------------------------------------------------------------------