TSTP Solution File: NUM534+2 by Z3---4.8.9.0

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM534+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n002.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 : Sun Sep 18 13:10:20 EDT 2022

% Result   : Theorem 0.20s 0.41s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM534+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Sep  2 11:45:01 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  % SZS output start Proof
% 0.20/0.41  tff(aElementOf0_type, type, (
% 0.20/0.41     aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.41  tff(sdtmndt0_type, type, (
% 0.20/0.41     sdtmndt0: ( $i * $i ) > $i)).
% 0.20/0.41  tff(xx_type, type, (
% 0.20/0.41     xx: $i)).
% 0.20/0.41  tff(xS_type, type, (
% 0.20/0.41     xS: $i)).
% 0.20/0.41  tff(tptp_fun_W3_2_type, type, (
% 0.20/0.41     tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.20/0.41  tff(aElement0_type, type, (
% 0.20/0.41     aElement0: $i > $o)).
% 0.20/0.41  tff(sdtpldt0_type, type, (
% 0.20/0.41     sdtpldt0: ( $i * $i ) > $i)).
% 0.20/0.41  tff(aSet0_type, type, (
% 0.20/0.41     aSet0: $i > $o)).
% 0.20/0.41  tff(tptp_fun_W3_3_type, type, (
% 0.20/0.41     tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.20/0.41  tff(1,assumption,(~((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)).
% 0.20/0.41  tff(2,plain,
% 0.20/0.41      (((~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)))),
% 0.20/0.41      inference(tautology,[status(thm)],[])).
% 0.20/0.41  tff(3,plain,
% 0.20/0.41      ((~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))))),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.41  tff(4,plain,
% 0.20/0.41      (aSet0(xS) <=> aSet0(xS)),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(5,axiom,(aSet0(xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__617')).
% 0.20/0.41  tff(6,plain,
% 0.20/0.41      (aSet0(xS)),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41  tff(7,plain,
% 0.20/0.41      (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(8,plain,
% 0.20/0.41      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[7])).
% 0.20/0.41  tff(9,plain,
% 0.20/0.41      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(10,plain,
% 0.20/0.41      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[9])).
% 0.20/0.41  tff(11,plain,
% 0.20/0.41      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(transitivity,[status(thm)],[10, 8])).
% 0.20/0.41  tff(12,plain,
% 0.20/0.41      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(13,plain,
% 0.20/0.41      (^[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))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(14,plain,
% 0.20/0.41      (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41  tff(15,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 0.20/0.41  tff(16,plain,
% 0.20/0.41      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.41  tff(17,plain,
% 0.20/0.41      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.41  tff(18,plain,(
% 0.20/0.41      ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(skolemize,[status(sab)],[17])).
% 0.20/0.41  tff(19,plain,
% 0.20/0.41      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.41  tff(20,plain,
% 0.20/0.41      (((~![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))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(21,plain,
% 0.20/0.41      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.20/0.41      inference(quant_inst,[status(thm)],[])).
% 0.20/0.41  tff(22,plain,
% 0.20/0.41      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.41  tff(23,plain,
% 0.20/0.41      (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[22, 19, 6])).
% 0.20/0.41  tff(24,plain,
% 0.20/0.41      (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(25,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__617_02')).
% 0.20/0.41  tff(26,plain,
% 0.20/0.41      (aElementOf0(xx, xS)),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.41  tff(27,plain,
% 0.20/0.41      (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS)))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(28,plain,
% 0.20/0.41      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))),
% 0.20/0.41      inference(quant_inst,[status(thm)],[])).
% 0.20/0.41  tff(29,plain,
% 0.20/0.41      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41  tff(30,plain,
% 0.20/0.41      (aElement0(xx)),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[29, 26, 23])).
% 0.20/0.41  tff(31,plain,
% 0.20/0.41      (aSet0(sdtmndt0(xS, xx)) <=> aSet0(sdtmndt0(xS, xx))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(32,plain,
% 0.20/0.41      ((~((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))))))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(33,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/sandbox/benchmark/theBenchmark.p','m__')).
% 0.20/0.41  tff(34,plain,
% 0.20/0.41      (~((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)))))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.41  tff(35,plain,
% 0.20/0.41      (aSet0(sdtmndt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xS, xx)) <=> (aElement0(W0) & aElementOf0(W0, xS) & (~(W0 = xx))))),
% 0.20/0.41      inference(or_elim,[status(thm)],[34])).
% 0.20/0.41  tff(36,plain,
% 0.20/0.41      (aSet0(sdtmndt0(xS, xx))),
% 0.20/0.41      inference(and_elim,[status(thm)],[35])).
% 0.20/0.41  tff(37,plain,
% 0.20/0.41      (aSet0(sdtmndt0(xS, xx))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[36, 31])).
% 0.20/0.41  tff(38,plain,
% 0.20/0.41      (^[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)) | (~((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)) | (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] : (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)) | (~((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)) | (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] : (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))))))))))) | (~((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)) | (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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (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))))))))))) | (~((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)) | (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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(39,plain,
% 0.20/0.41      (![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)) | (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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[38])).
% 0.20/0.41  tff(40,plain,
% 0.20/0.41      (^[W0: $i, W1: $i] : refl(((~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)))))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(41,plain,
% 0.20/0.41      (![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))))))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[40])).
% 0.20/0.41  tff(42,plain,
% 0.20/0.41      (^[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)))))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(43,plain,
% 0.20/0.41      (![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))))))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[42])).
% 0.20/0.41  tff(44,plain,
% 0.20/0.41      (![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))))))))))),
% 0.20/0.41      inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.41  tff(45,plain,
% 0.20/0.41      (^[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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))), trans(monotonicity(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)))))) <=> (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)))) <=> (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)) | ((~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)) | (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(((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)) | (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)) | ((~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)) | (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] : (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] : (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))))))))), 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)) | (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] : (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] : (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] : (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] : (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] : (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))))))) <=> (((~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)))))))))))), 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))))))))))), (((~(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))))))))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(46,plain,
% 0.20/0.42      (![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))))))))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42  tff(47,plain,
% 0.20/0.42      (^[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))))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(48,plain,
% 0.20/0.42      (![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)))))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[47])).
% 0.20/0.42  tff(49,plain,
% 0.20/0.42      (![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)))))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(50,plain,
% 0.20/0.42      (^[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)))))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(51,plain,
% 0.20/0.42      (![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)))))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[50])).
% 0.20/0.42  tff(52,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/sandbox/benchmark/theBenchmark.p','mDefCons')).
% 0.20/0.42  tff(53,plain,
% 0.20/0.42      (![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)))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.42  tff(54,plain,
% 0.20/0.42      (![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)))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.42  tff(55,plain,(
% 0.20/0.42      ![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)))))))))),
% 0.20/0.42      inference(skolemize,[status(sab)],[54])).
% 0.20/0.42  tff(56,plain,
% 0.20/0.42      (![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)))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.42  tff(57,plain,
% 0.20/0.42      (![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))))))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.42  tff(58,plain,
% 0.20/0.42      (![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))))))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[57, 44])).
% 0.20/0.42  tff(59,plain,
% 0.20/0.42      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[58, 39])).
% 0.20/0.42  tff(60,plain,
% 0.20/0.42      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(61,plain,
% 0.20/0.42      (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(62,plain,
% 0.20/0.42      (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(63,plain,
% 0.20/0.43      (![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[62])).
% 0.20/0.43  tff(64,plain,
% 0.20/0.43      (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.20/0.43      inference(monotonicity,[status(thm)],[63])).
% 0.20/0.43  tff(65,plain,
% 0.20/0.43      (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.20/0.43      inference(transitivity,[status(thm)],[64, 61])).
% 0.20/0.43  tff(66,plain,
% 0.20/0.43      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))))),
% 0.20/0.43      inference(monotonicity,[status(thm)],[65])).
% 0.20/0.43  tff(67,plain,
% 0.20/0.43      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.20/0.43      inference(transitivity,[status(thm)],[66, 60])).
% 0.20/0.43  tff(68,plain,
% 0.20/0.43      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.20/0.43      inference(quant_inst,[status(thm)],[])).
% 0.20/0.43  tff(69,plain,
% 0.20/0.43      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.43  tff(70,plain,
% 0.20/0.43      ((~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[69, 59, 37])).
% 0.20/0.43  tff(71,plain,
% 0.20/0.43      (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[70, 30])).
% 0.20/0.43  tff(72,plain,
% 0.20/0.43      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), 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)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))) | (~((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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)))))))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(73,plain,
% 0.20/0.44      (~((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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)))))))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.44  tff(74,plain,
% 0.20/0.44      (((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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)))))))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))) | ((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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)))))))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(75,plain,
% 0.20/0.44      ((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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))))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.44  tff(76,plain,
% 0.20/0.44      ((xS = sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (sdtpldt0(sdtmndt0(xS, xx), xx) = xS)),
% 0.20/0.44      inference(commutativity,[status(thm)],[])).
% 0.20/0.44  tff(77,plain,
% 0.20/0.44      ((sdtpldt0(sdtmndt0(xS, xx), xx) = xS) <=> (xS = sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.20/0.44      inference(symmetry,[status(thm)],[76])).
% 0.20/0.44  tff(78,plain,
% 0.20/0.44      ((~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)) <=> (~(xS = sdtpldt0(sdtmndt0(xS, xx), xx)))),
% 0.20/0.44      inference(monotonicity,[status(thm)],[77])).
% 0.20/0.44  tff(79,plain,
% 0.20/0.44      ((~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)) <=> (~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(80,plain,
% 0.20/0.44      (~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)),
% 0.20/0.44      inference(or_elim,[status(thm)],[34])).
% 0.20/0.44  tff(81,plain,
% 0.20/0.44      (~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.44  tff(82,plain,
% 0.20/0.44      (~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[81, 78])).
% 0.20/0.44  tff(83,plain,
% 0.20/0.44      ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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)))))))) | (~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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))))))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(84,plain,
% 0.20/0.44      ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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)))))))) | (xS = sdtpldt0(sdtmndt0(xS, xx), 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))))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[83, 6])).
% 0.20/0.44  tff(85,plain,
% 0.20/0.44      (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)))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[84, 82, 75])).
% 0.20/0.44  tff(86,plain,
% 0.20/0.44      ((~(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) | (~((~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))))))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(87,plain,
% 0.20/0.44      (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))))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.44  tff(88,plain,
% 0.20/0.44      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[87, 3])).
% 0.20/0.44  tff(89,plain,
% 0.20/0.44      (((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(90,plain,
% 0.20/0.44      (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[89, 1])).
% 0.20/0.44  tff(91,plain,
% 0.20/0.44      (^[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)) | (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)) | (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] : (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 = 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)) | (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] : (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))))))))) | (~((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)) | (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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (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))))))))) | (~((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)) | (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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(92,plain,
% 0.20/0.44      (![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)) | (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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[91])).
% 0.20/0.44  tff(93,plain,
% 0.20/0.44      (^[W0: $i, W1: $i] : refl(((~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)))))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(94,plain,
% 0.20/0.44      (![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))))))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[93])).
% 0.20/0.44  tff(95,plain,
% 0.20/0.44      (^[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)))))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(96,plain,
% 0.20/0.44      (![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))))))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[95])).
% 0.20/0.44  tff(97,plain,
% 0.20/0.44      (![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))))))))),
% 0.20/0.44      inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.44  tff(98,plain,
% 0.20/0.44      (^[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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))), trans(monotonicity(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)))) <=> (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)))) <=> (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)) | ((~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)) | (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(((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)) | (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)) | ((~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)) | (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] : (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] : (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))))))), 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)) | (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] : (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] : (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] : (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] : (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] : (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))))))) <=> (((~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)))))))))), 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))))))))), (((~(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))))))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(99,plain,
% 0.20/0.45      (![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))))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[98])).
% 0.20/0.45  tff(100,plain,
% 0.20/0.45      (^[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))))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(101,plain,
% 0.20/0.45      (![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)))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[100])).
% 0.20/0.45  tff(102,plain,
% 0.20/0.45      (![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)))))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(103,plain,
% 0.20/0.45      (^[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)))))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(104,plain,
% 0.20/0.45      (![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)))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[103])).
% 0.20/0.45  tff(105,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/sandbox/benchmark/theBenchmark.p','mDefDiff')).
% 0.20/0.45  tff(106,plain,
% 0.20/0.45      (![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)))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.45  tff(107,plain,
% 0.20/0.45      (![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)))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.45  tff(108,plain,(
% 0.20/0.45      ![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)))))))))),
% 0.20/0.45      inference(skolemize,[status(sab)],[107])).
% 0.20/0.45  tff(109,plain,
% 0.20/0.45      (![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)))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.45  tff(110,plain,
% 0.20/0.45      (![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))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[109, 99])).
% 0.20/0.45  tff(111,plain,
% 0.20/0.45      (![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))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[110, 97])).
% 0.20/0.45  tff(112,plain,
% 0.20/0.45      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[111, 92])).
% 0.20/0.45  tff(113,plain,
% 0.20/0.45      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(114,plain,
% 0.20/0.45      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(115,plain,
% 0.20/0.45      (^[W2: $i] : rewrite((~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(116,plain,
% 0.20/0.45      (![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[115])).
% 0.20/0.45  tff(117,plain,
% 0.20/0.45      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.20/0.45      inference(monotonicity,[status(thm)],[116])).
% 0.20/0.45  tff(118,plain,
% 0.20/0.45      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.20/0.45      inference(transitivity,[status(thm)],[117, 114])).
% 0.20/0.45  tff(119,plain,
% 0.20/0.45      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))))),
% 0.20/0.45      inference(monotonicity,[status(thm)],[118])).
% 0.20/0.45  tff(120,plain,
% 0.20/0.45      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.20/0.45      inference(transitivity,[status(thm)],[119, 113])).
% 0.20/0.45  tff(121,plain,
% 0.20/0.45      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(122,plain,
% 0.20/0.46      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((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] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.46  tff(123,plain,
% 0.20/0.46      ((~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[122, 112, 6])).
% 0.20/0.46  tff(124,plain,
% 0.20/0.46      (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[123, 30])).
% 0.20/0.46  tff(125,plain,
% 0.20/0.46      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(126,plain,
% 0.20/0.46      ((~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), 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))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))) <=> (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(127,plain,
% 0.20/0.46      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), 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))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[126])).
% 0.20/0.46  tff(128,plain,
% 0.20/0.46      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), 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))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))),
% 0.20/0.46      inference(transitivity,[status(thm)],[127, 125])).
% 0.20/0.46  tff(129,plain,
% 0.20/0.46      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), 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))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(130,plain,
% 0.20/0.46      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), 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))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.46  tff(131,plain,
% 0.20/0.46      (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[130, 124])).
% 0.20/0.46  tff(132,plain,
% 0.20/0.46      (((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))) | ![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(133,plain,
% 0.20/0.46      (![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[132, 131])).
% 0.20/0.46  tff(134,plain,
% 0.20/0.46      ((~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = 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))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(135,plain,
% 0.20/0.46      (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)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[134, 133])).
% 0.20/0.46  tff(136,plain,
% 0.20/0.46      ((~(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)) | ((~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))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(137,plain,
% 0.20/0.46      (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))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.46  tff(138,plain,
% 0.20/0.46      ((~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)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[137, 90])).
% 0.20/0.46  tff(139,plain,
% 0.20/0.46      (((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))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(140,plain,
% 0.20/0.46      (~(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[139, 1])).
% 0.20/0.46  tff(141,plain,
% 0.20/0.46      ((~((~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)),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(142,plain,
% 0.20/0.46      (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[141, 88, 140, 138])).
% 0.20/0.46  tff(143,plain,
% 0.20/0.46      (((~![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)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(144,plain,
% 0.20/0.46      ((~![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)))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(145,plain,
% 0.20/0.46      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.46  tff(146,plain,
% 0.20/0.46      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[145, 23])).
% 0.20/0.46  tff(147,plain,
% 0.20/0.46      ($false),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[146, 142, 88])).
% 0.20/0.46  tff(148,plain,((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46  tff(149,assumption,(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))), introduced(assumption)).
% 0.20/0.46  tff(150,plain,
% 0.20/0.46      ((~(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))) | (~((~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)))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(151,plain,
% 0.20/0.46      ((~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)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[150, 135])).
% 0.20/0.46  tff(152,plain,
% 0.20/0.46      (~((~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))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[151, 149])).
% 0.20/0.46  tff(153,plain,
% 0.20/0.46      (((~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)), xS)),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(154,plain,
% 0.20/0.46      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[153, 152])).
% 0.20/0.46  tff(155,plain,
% 0.20/0.46      (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(sdtmndt0(xS, xx))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx)))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(sdtmndt0(xS, xx))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx)))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(156,plain,
% 0.20/0.46      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(sdtmndt0(xS, xx))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx)))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(157,plain,
% 0.20/0.46      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(sdtmndt0(xS, xx))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.47  tff(158,plain,
% 0.20/0.47      (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[157, 19, 37])).
% 0.20/0.47  tff(159,plain,
% 0.20/0.47      (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx))))) | (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx))))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(160,plain,
% 0.20/0.47      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx))))) | (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(161,plain,
% 0.20/0.47      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(xS, xx))))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.47  tff(162,plain,
% 0.20/0.47      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[161, 158])).
% 0.20/0.47  tff(163,plain,
% 0.20/0.47      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[162, 149])).
% 0.20/0.47  tff(164,plain,
% 0.20/0.47      ((~((~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))))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(165,plain,
% 0.20/0.47      (~((~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)))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[164, 163, 148])).
% 0.20/0.47  tff(166,plain,
% 0.20/0.47      ((~(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)) | ((~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)))))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(167,plain,
% 0.20/0.47      ((~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)))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[166, 85])).
% 0.20/0.47  tff(168,plain,
% 0.20/0.47      ($false),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[167, 165, 154])).
% 0.20/0.47  tff(169,plain,(~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47  tff(170,plain,
% 0.20/0.47      ((~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(171,plain,
% 0.20/0.47      (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[170, 169, 148])).
% 0.20/0.47  tff(172,plain,
% 0.20/0.47      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) <=> aElement0(xx)),
% 0.20/0.47      inference(monotonicity,[status(thm)],[171])).
% 0.20/0.47  tff(173,plain,
% 0.20/0.47      (aElement0(xx) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.20/0.47      inference(symmetry,[status(thm)],[172])).
% 0.20/0.47  tff(174,plain,
% 0.20/0.47      (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[30, 173])).
% 0.20/0.47  tff(175,plain,
% 0.20/0.47      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> aElementOf0(xx, xS)),
% 0.20/0.47      inference(monotonicity,[status(thm)],[171])).
% 0.20/0.47  tff(176,plain,
% 0.20/0.47      (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.20/0.47      inference(symmetry,[status(thm)],[175])).
% 0.20/0.47  tff(177,plain,
% 0.20/0.47      (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[26, 176])).
% 0.20/0.47  tff(178,plain,
% 0.20/0.47      ((~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))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[167, 177])).
% 0.20/0.47  tff(179,plain,
% 0.20/0.47      ($false),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[164, 178, 174, 148])).
% 0.20/0.47  % SZS output end Proof
%------------------------------------------------------------------------------