TSTP Solution File: NUM581+3 by Z3---4.8.9.0

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM581+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n012.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 13:10:39 EDT 2022

% Result   : Theorem 0.98s 0.89s
% Output   : Proof 1.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : NUM581+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n012.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Sep  2 12:00:19 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33  Usage: tptp [options] [-file:]file
% 0.12/0.33    -h, -?       prints this message.
% 0.12/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.33    -m, -model   generate model.
% 0.12/0.33    -p, -proof   generate proof.
% 0.12/0.33    -c, -core    generate unsat core of named formulas.
% 0.12/0.33    -st, -statistics display statistics.
% 0.12/0.33    -t:timeout   set timeout (in second).
% 0.12/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33    -<param>:<value> configuration parameter and value.
% 0.12/0.33    -o:<output-file> file to place output in.
% 0.98/0.89  % SZS status Theorem
% 0.98/0.89  % SZS output start Proof
% 0.98/0.89  tff(aElementOf0_type, type, (
% 0.98/0.89     aElementOf0: ( $i * $i ) > $o)).
% 0.98/0.89  tff(sdtlpdtrp0_type, type, (
% 0.98/0.89     sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.98/0.89  tff(sz00_type, type, (
% 0.98/0.89     sz00: $i)).
% 0.98/0.89  tff(xN_type, type, (
% 0.98/0.89     xN: $i)).
% 0.98/0.89  tff(tptp_fun_W0_31_type, type, (
% 0.98/0.89     tptp_fun_W0_31: $i)).
% 0.98/0.89  tff(szmzizndt0_type, type, (
% 0.98/0.89     szmzizndt0: $i > $i)).
% 0.98/0.89  tff(xi_type, type, (
% 0.98/0.89     xi: $i)).
% 0.98/0.89  tff(xQ_type, type, (
% 0.98/0.89     xQ: $i)).
% 0.98/0.89  tff(aElement0_type, type, (
% 0.98/0.89     aElement0: $i > $o)).
% 0.98/0.89  tff(sdtpldt0_type, type, (
% 0.98/0.89     sdtpldt0: ( $i * $i ) > $i)).
% 0.98/0.89  tff(aSet0_type, type, (
% 0.98/0.89     aSet0: $i > $o)).
% 0.98/0.89  tff(sdtlseqdt0_type, type, (
% 0.98/0.89     sdtlseqdt0: ( $i * $i ) > $o)).
% 0.98/0.89  tff(xK_type, type, (
% 0.98/0.89     xK: $i)).
% 0.98/0.89  tff(sbrdtbr0_type, type, (
% 0.98/0.89     sbrdtbr0: $i > $i)).
% 0.98/0.89  tff(xS_type, type, (
% 0.98/0.89     xS: $i)).
% 0.98/0.89  tff(aSubsetOf0_type, type, (
% 0.98/0.89     aSubsetOf0: ( $i * $i ) > $o)).
% 0.98/0.89  tff(sdtmndt0_type, type, (
% 0.98/0.89     sdtmndt0: ( $i * $i ) > $i)).
% 0.98/0.89  tff(szszuzczcdt0_type, type, (
% 0.98/0.89     szszuzczcdt0: $i > $i)).
% 0.98/0.89  tff(isCountable0_type, type, (
% 0.98/0.89     isCountable0: $i > $o)).
% 0.98/0.89  tff(szDzozmdt0_type, type, (
% 0.98/0.89     szDzozmdt0: $i > $i)).
% 0.98/0.89  tff(szNzAzT0_type, type, (
% 0.98/0.89     szNzAzT0: $i)).
% 0.98/0.89  tff(tptp_fun_W1_29_type, type, (
% 0.98/0.89     tptp_fun_W1_29: $i > $i)).
% 0.98/0.89  tff(aFunction0_type, type, (
% 0.98/0.89     aFunction0: $i > $o)).
% 0.98/0.89  tff(tptp_fun_W2_1_type, type, (
% 0.98/0.89     tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.98/0.89  tff(xk_type, type, (
% 0.98/0.89     xk: $i)).
% 0.98/0.89  tff(slbdtsldtrb0_type, type, (
% 0.98/0.89     slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.98/0.89  tff(1,plain,
% 0.98/0.89      (^[W0: $i] : refl((aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) <=> (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 0.98/0.89      inference(bind,[status(th)],[])).
% 0.98/0.89  tff(2,plain,
% 0.98/0.89      (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) <=> ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.98/0.89      inference(quant_intro,[status(thm)],[1])).
% 0.98/0.89  tff(3,plain,
% 0.98/0.89      (^[W0: $i] : rewrite((aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 0.98/0.89      inference(bind,[status(th)],[])).
% 0.98/0.89  tff(4,plain,
% 0.98/0.89      (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.98/0.89      inference(quant_intro,[status(thm)],[3])).
% 0.98/0.89  tff(5,plain,
% 0.98/0.89      (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.98/0.89      inference(rewrite,[status(thm)],[])).
% 0.98/0.89  tff(6,axiom,((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & (sbrdtbr0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) = xK)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4007')).
% 0.98/0.89  tff(7,plain,
% 0.98/0.89      (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.98/0.89      inference(and_elim,[status(thm)],[6])).
% 0.98/0.89  tff(8,plain,
% 0.98/0.89      (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.98/0.89      inference(and_elim,[status(thm)],[7])).
% 0.98/0.89  tff(9,plain,
% 0.98/0.89      (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[8, 5])).
% 0.98/0.89  tff(10,plain,(
% 0.98/0.89      ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.98/0.89      inference(skolemize,[status(sab)],[9])).
% 0.98/0.89  tff(11,plain,
% 0.98/0.89      (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[10, 4])).
% 0.98/0.89  tff(12,plain,
% 0.98/0.89      (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[11, 2])).
% 0.98/0.89  tff(13,plain,
% 0.98/0.89      ((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.98/0.89      inference(quant_inst,[status(thm)],[])).
% 0.98/0.89  tff(14,plain,
% 0.98/0.89      (aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 0.98/0.89      inference(unit_resolution,[status(thm)],[13, 12])).
% 0.98/0.89  tff(15,plain,
% 0.98/0.89      ((~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))))),
% 0.98/0.89      inference(rewrite,[status(thm)],[])).
% 0.98/0.89  tff(16,plain,
% 0.98/0.89      ((~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))))),
% 0.98/0.89      inference(rewrite,[status(thm)],[])).
% 0.98/0.89  tff(17,plain,
% 0.98/0.89      ((~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS)))),
% 0.98/0.89      inference(rewrite,[status(thm)],[])).
% 0.98/0.89  tff(18,plain,
% 0.98/0.89      ((~((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) => ((aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) => (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) => aElementOf0(W0, xS)) | aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS))))) <=> (~(aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS)) | (~(aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))))))),
% 0.98/0.89      inference(rewrite,[status(thm)],[])).
% 0.98/0.89  tff(19,axiom,(~((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) => ((aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) => (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) => aElementOf0(W0, xS)) | aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.98/0.89  tff(20,plain,
% 0.98/0.89      (~(aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS)) | (~(aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0)))))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[19, 18])).
% 0.98/0.89  tff(21,plain,
% 0.98/0.89      (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.98/0.89      inference(or_elim,[status(thm)],[20])).
% 0.98/0.89  tff(22,plain,
% 0.98/0.89      (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[21, 17])).
% 0.98/0.89  tff(23,plain,
% 0.98/0.89      (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[22, 17])).
% 0.98/0.89  tff(24,plain,
% 0.98/0.89      (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[23, 17])).
% 0.98/0.89  tff(25,plain,
% 0.98/0.89      (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[24, 16])).
% 0.98/0.89  tff(26,plain,
% 0.98/0.89      (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[25, 15])).
% 0.98/0.89  tff(27,plain,
% 0.98/0.89      (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[26, 15])).
% 0.98/0.89  tff(28,plain,
% 0.98/0.89      (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[27, 15])).
% 0.98/0.89  tff(29,plain,(
% 0.98/0.89      ~((~aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 0.98/0.89      inference(skolemize,[status(sab)],[28])).
% 0.98/0.89  tff(30,plain,
% 0.98/0.89      (aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.98/0.89      inference(or_elim,[status(thm)],[29])).
% 0.98/0.89  tff(31,plain,
% 0.98/0.89      ((~(aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 0.98/0.89      inference(tautology,[status(thm)],[])).
% 0.98/0.89  tff(32,plain,
% 0.98/0.89      ((~(aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 0.98/0.89      inference(unit_resolution,[status(thm)],[31, 30])).
% 0.98/0.89  tff(33,plain,
% 0.98/0.89      (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.98/0.89      inference(unit_resolution,[status(thm)],[32, 14])).
% 0.98/0.89  tff(34,plain,
% 0.98/0.89      (((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.98/0.89      inference(tautology,[status(thm)],[])).
% 0.98/0.89  tff(35,plain,
% 0.98/0.89      (aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 0.98/0.89      inference(unit_resolution,[status(thm)],[34, 33])).
% 0.98/0.89  tff(36,plain,
% 0.98/0.89      (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szDzozmdt0(xN))),
% 0.98/0.89      inference(rewrite,[status(thm)],[])).
% 0.98/0.89  tff(37,plain,
% 0.98/0.89      (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 0.98/0.89      inference(rewrite,[status(thm)],[])).
% 0.98/0.89  tff(38,axiom,(aElementOf0(xi, szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3989')).
% 0.98/0.89  tff(39,plain,
% 0.98/0.89      (aElementOf0(xi, szNzAzT0)),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[38, 37])).
% 0.98/0.89  tff(40,plain,
% 0.98/0.89      (aElementOf0(xi, szDzozmdt0(xN))),
% 0.98/0.89      inference(modus_ponens,[status(thm)],[39, 36])).
% 0.98/0.89  tff(41,plain,
% 0.98/0.89      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))))))))),
% 0.98/0.89      inference(bind,[status(th)],[])).
% 0.98/0.89  tff(42,plain,
% 0.98/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))))))),
% 0.98/0.89      inference(quant_intro,[status(thm)],[41])).
% 0.98/0.89  tff(43,plain,
% 0.98/0.89      (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 0.98/0.89      inference(bind,[status(th)],[])).
% 0.98/0.89  tff(44,plain,
% 0.98/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.98/0.89      inference(quant_intro,[status(thm)],[43])).
% 0.98/0.89  tff(45,plain,
% 0.98/0.89      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 0.98/0.89      inference(bind,[status(th)],[])).
% 0.98/0.89  tff(46,plain,
% 0.98/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.98/0.89      inference(quant_intro,[status(thm)],[45])).
% 0.98/0.89  tff(47,plain,
% 0.98/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.98/0.89      inference(transitivity,[status(thm)],[46, 44])).
% 0.98/0.89  tff(48,plain,
% 0.98/0.89      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 0.98/0.89      inference(bind,[status(th)],[])).
% 0.98/0.89  tff(49,plain,
% 0.98/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.98/0.89      inference(quant_intro,[status(thm)],[48])).
% 0.98/0.89  tff(50,plain,
% 0.98/0.89      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 0.98/0.89      inference(bind,[status(th)],[])).
% 0.98/0.89  tff(51,plain,
% 0.98/0.89      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.98/0.89      inference(quant_intro,[status(thm)],[50])).
% 0.98/0.89  tff(52,plain,
% 0.98/0.89      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.98/0.89      inference(rewrite,[status(thm)],[])).
% 0.98/0.89  tff(53,plain,
% 0.98/0.89      (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))), (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) <=> ((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)))), rewrite(((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0))), (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)))), ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) <=> ((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))))), rewrite(((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))), ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) <=> (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))), ((aElementOf0(W0, szNzAzT0) => (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> (aElementOf0(W0, szNzAzT0) => (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))))), rewrite((aElementOf0(W0, szNzAzT0) => (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))), ((aElementOf0(W0, szNzAzT0) => (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.98/0.90      inference(bind,[status(th)],[])).
% 0.98/0.90  tff(54,plain,
% 0.98/0.90      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.98/0.90      inference(quant_intro,[status(thm)],[53])).
% 0.98/0.90  tff(55,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3671')).
% 0.98/0.90  tff(56,plain,
% 0.98/0.90      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.98/0.90      inference(modus_ponens,[status(thm)],[55, 54])).
% 0.98/0.90  tff(57,plain,
% 0.98/0.90      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)) & aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.98/0.90      inference(modus_ponens,[status(thm)],[56, 52])).
% 0.98/0.90  tff(58,plain,
% 0.98/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.98/0.90      inference(modus_ponens,[status(thm)],[57, 51])).
% 0.98/0.90  tff(59,plain,(
% 0.98/0.90      ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))) & aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) & isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.98/0.90      inference(skolemize,[status(sab)],[58])).
% 0.98/0.90  tff(60,plain,
% 0.98/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.98/0.90      inference(modus_ponens,[status(thm)],[59, 49])).
% 0.98/0.90  tff(61,plain,
% 0.98/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.98/0.90      inference(modus_ponens,[status(thm)],[60, 47])).
% 0.98/0.90  tff(62,plain,
% 0.98/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))))))),
% 0.98/0.90      inference(modus_ponens,[status(thm)],[61, 42])).
% 0.98/0.90  tff(63,plain,
% 0.98/0.90      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szDzozmdt0(xN)))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szDzozmdt0(xN)))))))),
% 0.98/0.90      inference(rewrite,[status(thm)],[])).
% 0.98/0.90  tff(64,plain,
% 0.98/0.90      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szDzozmdt0(xN)))))))),
% 0.98/0.90      inference(quant_inst,[status(thm)],[])).
% 0.98/0.90  tff(65,plain,
% 0.98/0.90      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN)))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szDzozmdt0(xN))))))),
% 0.98/0.90      inference(modus_ponens,[status(thm)],[64, 63])).
% 0.98/0.90  tff(66,plain,
% 0.98/0.90      (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szDzozmdt0(xN)))))),
% 0.98/0.90      inference(unit_resolution,[status(thm)],[65, 62, 40])).
% 0.98/0.90  tff(67,plain,
% 0.98/0.90      (((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szDzozmdt0(xN))))) | isCountable0(sdtlpdtrp0(xN, xi))),
% 0.98/0.90      inference(tautology,[status(thm)],[])).
% 0.98/0.90  tff(68,plain,
% 0.98/0.90      (isCountable0(sdtlpdtrp0(xN, xi))),
% 0.98/0.90      inference(unit_resolution,[status(thm)],[67, 66])).
% 0.98/0.90  tff(69,plain,
% 0.98/0.90      (((~aSet0(sdtlpdtrp0(xN, xi))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | aElementOf0(W1, szDzozmdt0(xN))))) | aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))),
% 0.98/0.90      inference(tautology,[status(thm)],[])).
% 0.98/0.90  tff(70,plain,
% 0.98/0.90      (aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))),
% 0.98/0.90      inference(unit_resolution,[status(thm)],[69, 66])).
% 0.98/0.90  tff(71,plain,
% 0.98/0.90      ((aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN))))))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)))),
% 0.98/0.90      inference(tautology,[status(thm)],[])).
% 0.98/0.90  tff(72,plain,
% 0.98/0.90      (aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN))))))),
% 0.98/0.90      inference(unit_resolution,[status(thm)],[71, 70])).
% 0.98/0.90  tff(73,plain,
% 0.98/0.90      (^[W0: $i] : trans(monotonicity(rewrite((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) <=> (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite((~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) <=> (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))), (((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))))), rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), (((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 0.98/0.90      inference(bind,[status(th)],[])).
% 0.98/0.90  tff(74,plain,
% 0.98/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.98/0.90      inference(quant_intro,[status(thm)],[73])).
% 0.98/0.90  tff(75,plain,
% 0.98/0.90      (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))))),
% 0.98/0.90      inference(bind,[status(th)],[])).
% 0.98/0.90  tff(76,plain,
% 0.98/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))))),
% 0.98/0.91      inference(quant_intro,[status(thm)],[75])).
% 0.98/0.91  tff(77,plain,
% 0.98/0.91      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))))),
% 0.98/0.91      inference(bind,[status(th)],[])).
% 0.98/0.91  tff(78,plain,
% 0.98/0.91      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))))),
% 0.98/0.91      inference(quant_intro,[status(thm)],[77])).
% 0.98/0.91  tff(79,plain,
% 0.98/0.91      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))))),
% 0.98/0.91      inference(transitivity,[status(thm)],[78, 76])).
% 0.98/0.91  tff(80,plain,
% 0.98/0.91      (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))), ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))), rewrite(((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) <=> (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN))))))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))), rewrite(((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))))))),
% 0.98/0.91      inference(bind,[status(th)],[])).
% 0.98/0.91  tff(81,plain,
% 0.98/0.91      (![W0: $i] : ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))))),
% 0.98/0.91      inference(quant_intro,[status(thm)],[80])).
% 0.98/0.91  tff(82,plain,
% 0.98/0.91      (^[W0: $i] : trans(monotonicity(rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))), rewrite((((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))) <=> (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))))),
% 0.98/0.92      inference(bind,[status(th)],[])).
% 0.98/0.92  tff(83,plain,
% 0.98/0.92      (![W0: $i] : ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))),
% 0.98/0.92      inference(quant_intro,[status(thm)],[82])).
% 0.98/0.92  tff(84,plain,
% 0.98/0.92      (^[W0: $i] : trans(monotonicity(rewrite((~aElementOf0(W0, szNzAzT0)) <=> (~aElementOf0(W0, szDzozmdt0(xN)))), rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))), rewrite((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))) <=> (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))))) & isCountable0(sdtlpdtrp0(xN, W0))))), (((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))))) & isCountable0(sdtlpdtrp0(xN, W0))))))), rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))))) & isCountable0(sdtlpdtrp0(xN, W0))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))))) & isCountable0(sdtlpdtrp0(xN, W0)))))), (((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))))) & isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 0.98/0.92      inference(bind,[status(th)],[])).
% 0.98/0.92  tff(85,plain,
% 0.98/0.92      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 0.98/0.92      inference(quant_intro,[status(thm)],[84])).
% 0.98/0.92  tff(86,plain,
% 0.98/0.92      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 0.98/0.92      inference(rewrite,[status(thm)],[])).
% 0.98/0.92  tff(87,plain,
% 0.98/0.92      (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) <=> ((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))), (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), (![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))), (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), ((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))), ((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), (((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))) <=> (((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))), rewrite((((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))) <=> ((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))), (((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))) <=> ((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))), ((aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) <=> (aElementOf0(W0, szNzAzT0) => ((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))), rewrite((aElementOf0(W0, szNzAzT0) => ((~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))), ((aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))))),
% 1.09/0.94      inference(bind,[status(th)],[])).
% 1.09/0.94  tff(88,plain,
% 1.09/0.94      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 1.09/0.94      inference(quant_intro,[status(thm)],[87])).
% 1.09/0.94  tff(89,axiom,(((aFunction0(xN) & (szDzozmdt0(xN) = szNzAzT0)) & (sdtlpdtrp0(xN, sz00) = xS)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3623')).
% 1.09/0.94  tff(90,plain,
% 1.09/0.94      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => aElementOf0(W1, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) => aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0))))))),
% 1.09/0.94      inference(and_elim,[status(thm)],[89])).
% 1.09/0.94  tff(91,plain,
% 1.09/0.94      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[90, 88])).
% 1.09/0.94  tff(92,plain,
% 1.09/0.94      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szNzAzT0) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szNzAzT0)))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[91, 86])).
% 1.09/0.94  tff(93,plain,
% 1.09/0.94      (![W0: $i] : ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (aSet0(sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | aElementOf0(W1, szDzozmdt0(xN))))) & isCountable0(sdtlpdtrp0(xN, W0)))))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[92, 85])).
% 1.09/0.94  tff(94,plain,(
% 1.09/0.94      ![W0: $i] : ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0)))))),
% 1.09/0.94      inference(skolemize,[status(sab)],[93])).
% 1.09/0.94  tff(95,plain,
% 1.09/0.94      (![W0: $i] : ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aElementOf0(W0, szDzozmdt0(xN))) | ((~aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN))) & ((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))) | (~isCountable0(sdtlpdtrp0(xN, W0))))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[94, 83])).
% 1.09/0.94  tff(96,plain,
% 1.09/0.94      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[95, 81])).
% 1.09/0.94  tff(97,plain,
% 1.09/0.94      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[96, 79])).
% 1.09/0.94  tff(98,plain,
% 1.09/0.94      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[97, 74])).
% 1.09/0.94  tff(99,plain,
% 1.09/0.94      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 1.09/0.94      inference(rewrite,[status(thm)],[])).
% 1.09/0.94  tff(100,plain,
% 1.09/0.94      (((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) <=> ((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 1.09/0.94      inference(rewrite,[status(thm)],[])).
% 1.09/0.94  tff(101,plain,
% 1.09/0.94      ((~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) <=> (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 1.09/0.95      inference(rewrite,[status(thm)],[])).
% 1.09/0.95  tff(102,plain,
% 1.09/0.95      ((~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) <=> (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN))))))))),
% 1.09/0.95      inference(rewrite,[status(thm)],[])).
% 1.09/0.95  tff(103,plain,
% 1.09/0.95      (((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) <=> ((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 1.09/0.95      inference(monotonicity,[status(thm)],[102, 101])).
% 1.09/0.95  tff(104,plain,
% 1.09/0.95      (((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) <=> ((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 1.09/0.95      inference(transitivity,[status(thm)],[103, 100])).
% 1.09/0.95  tff(105,plain,
% 1.09/0.95      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))),
% 1.09/0.95      inference(monotonicity,[status(thm)],[104])).
% 1.09/0.95  tff(106,plain,
% 1.09/0.95      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 1.09/0.95      inference(transitivity,[status(thm)],[105, 99])).
% 1.09/0.95  tff(107,plain,
% 1.09/0.95      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 1.09/0.95      inference(quant_inst,[status(thm)],[])).
% 1.09/0.95  tff(108,plain,
% 1.09/0.95      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, W0))) | (~(aSubsetOf0(sdtlpdtrp0(xN, W0), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, W0))) | (~((~aElementOf0(tptp_fun_W1_29(W0), sdtlpdtrp0(xN, W0))) | aElementOf0(tptp_fun_W1_29(W0), szDzozmdt0(xN)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 1.09/0.95      inference(modus_ponens,[status(thm)],[107, 106])).
% 1.09/0.95  tff(109,plain,
% 1.09/0.95      ((~isCountable0(sdtlpdtrp0(xN, xi))) | (~(aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN)) | (~((~aSet0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W1_29(xi), sdtlpdtrp0(xN, xi))) | aElementOf0(tptp_fun_W1_29(xi), szDzozmdt0(xN)))))))) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 1.09/0.96      inference(unit_resolution,[status(thm)],[108, 98, 40])).
% 1.09/0.96  tff(110,plain,
% 1.09/0.96      (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 1.09/0.96      inference(unit_resolution,[status(thm)],[109, 72, 68])).
% 1.09/0.96  tff(111,plain,
% 1.09/0.96      (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.09/0.96      inference(tautology,[status(thm)],[])).
% 1.09/0.96  tff(112,plain,
% 1.09/0.96      (![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.09/0.96      inference(unit_resolution,[status(thm)],[111, 110])).
% 1.09/0.96  tff(113,plain,
% 1.09/0.96      ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.09/0.96      inference(quant_inst,[status(thm)],[])).
% 1.09/0.96  tff(114,plain,
% 1.09/0.96      (aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 1.09/0.96      inference(unit_resolution,[status(thm)],[113, 112])).
% 1.09/0.96  tff(115,plain,
% 1.09/0.96      (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0)))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(116,plain,
% 1.09/0.96      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[115])).
% 1.09/0.96  tff(117,plain,
% 1.09/0.96      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0)))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(118,plain,
% 1.09/0.96      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[117])).
% 1.09/0.96  tff(119,plain,
% 1.09/0.96      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(rewrite,[status(thm)],[])).
% 1.09/0.96  tff(120,plain,
% 1.09/0.96      (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(121,plain,
% 1.09/0.96      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[120])).
% 1.09/0.96  tff(122,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mZeroLess')).
% 1.09/0.96  tff(123,plain,
% 1.09/0.96      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[122, 121])).
% 1.09/0.96  tff(124,plain,
% 1.09/0.96      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[123, 119])).
% 1.09/0.96  tff(125,plain,
% 1.09/0.96      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[124, 118])).
% 1.09/0.96  tff(126,plain,(
% 1.09/0.96      ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(skolemize,[status(sab)],[125])).
% 1.09/0.96  tff(127,plain,
% 1.09/0.96      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[126, 116])).
% 1.09/0.96  tff(128,plain,
% 1.09/0.96      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | sdtlseqdt0(sz00, xi))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))) | (~aElementOf0(xi, szDzozmdt0(xN))) | sdtlseqdt0(sz00, xi))),
% 1.09/0.96      inference(rewrite,[status(thm)],[])).
% 1.09/0.96  tff(129,plain,
% 1.09/0.96      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | sdtlseqdt0(sz00, xi))),
% 1.09/0.96      inference(quant_inst,[status(thm)],[])).
% 1.09/0.96  tff(130,plain,
% 1.09/0.96      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))) | (~aElementOf0(xi, szDzozmdt0(xN))) | sdtlseqdt0(sz00, xi)),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[129, 128])).
% 1.09/0.96  tff(131,plain,
% 1.09/0.96      (sdtlseqdt0(sz00, xi)),
% 1.09/0.96      inference(unit_resolution,[status(thm)],[130, 127, 40])).
% 1.09/0.96  tff(132,plain,
% 1.09/0.96      (^[W0: $i, W1: $i] : rewrite(((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))))))))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(133,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[132])).
% 1.09/0.96  tff(134,plain,
% 1.09/0.96      (^[W0: $i, W1: $i] : refl(((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(135,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[134])).
% 1.09/0.96  tff(136,plain,
% 1.09/0.96      (^[W0: $i, W1: $i] : rewrite(((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(137,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[136])).
% 1.09/0.96  tff(138,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 1.09/0.96      inference(transitivity,[status(thm)],[137, 135])).
% 1.09/0.96  tff(139,plain,
% 1.09/0.96      (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), trans(monotonicity(rewrite((aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))) <=> (~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN)))))), ((~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))) <=> (~(~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN)))))))), rewrite((~(~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN)))))) <=> ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))))), ((~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))) <=> ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN)))))), (((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))))) <=> ((~sdtlseqdt0(W1, W0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) | ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))))))), rewrite(((~sdtlseqdt0(W1, W0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) | ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))), (((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(140,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[139])).
% 1.09/0.96  tff(141,plain,
% 1.09/0.96      (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))))), rewrite((![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), rewrite(((~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(142,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[141])).
% 1.09/0.96  tff(143,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 1.09/0.96      inference(rewrite,[status(thm)],[])).
% 1.09/0.96  tff(144,plain,
% 1.09/0.96      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))), ((sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> (sdtlseqdt0(W1, W0) => (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), rewrite((sdtlseqdt0(W1, W0) => (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))), ((sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))), rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 1.09/0.96      inference(bind,[status(th)],[])).
% 1.09/0.96  tff(145,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 1.09/0.96      inference(quant_intro,[status(thm)],[144])).
% 1.09/0.96  tff(146,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3754')).
% 1.09/0.96  tff(147,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[146, 145])).
% 1.09/0.96  tff(148,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[147, 143])).
% 1.09/0.96  tff(149,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[148, 142])).
% 1.09/0.96  tff(150,plain,(
% 1.09/0.96      ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))),
% 1.09/0.96      inference(skolemize,[status(sab)],[149])).
% 1.09/0.96  tff(151,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[150, 140])).
% 1.09/0.96  tff(152,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[151, 138])).
% 1.09/0.96  tff(153,plain,
% 1.09/0.96      (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[152, 133])).
% 1.09/0.96  tff(154,plain,
% 1.09/0.96      (aElementOf0(sz00, szNzAzT0) <=> aElementOf0(sz00, szDzozmdt0(xN))),
% 1.09/0.96      inference(rewrite,[status(thm)],[])).
% 1.09/0.96  tff(155,plain,
% 1.09/0.96      (aElementOf0(sz00, szNzAzT0) <=> aElementOf0(sz00, szNzAzT0)),
% 1.09/0.96      inference(rewrite,[status(thm)],[])).
% 1.09/0.96  tff(156,axiom,(aElementOf0(sz00, szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mZeroNum')).
% 1.09/0.96  tff(157,plain,
% 1.09/0.96      (aElementOf0(sz00, szNzAzT0)),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[156, 155])).
% 1.09/0.96  tff(158,plain,
% 1.09/0.96      (aElementOf0(sz00, szDzozmdt0(xN))),
% 1.09/0.96      inference(modus_ponens,[status(thm)],[157, 154])).
% 1.09/0.96  tff(159,plain,
% 1.09/0.96      (((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~sdtlseqdt0(sz00, xi)) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 1.09/0.97      inference(rewrite,[status(thm)],[])).
% 1.09/0.97  tff(160,plain,
% 1.09/0.97      ((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~sdtlseqdt0(sz00, xi)) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 1.09/0.97      inference(quant_inst,[status(thm)],[])).
% 1.09/0.97  tff(161,plain,
% 1.09/0.97      ((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~sdtlseqdt0(sz00, xi)) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[160, 159])).
% 1.09/0.97  tff(162,plain,
% 1.09/0.97      (~((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))),
% 1.09/0.97      inference(unit_resolution,[status(thm)],[161, 158, 153, 40, 131])).
% 1.09/0.97  tff(163,plain,
% 1.09/0.97      (((~aSubsetOf0(sdtlpdtrp0(xN, xi), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))) | ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))),
% 1.09/0.97      inference(tautology,[status(thm)],[])).
% 1.09/0.97  tff(164,plain,
% 1.09/0.97      (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))),
% 1.09/0.97      inference(unit_resolution,[status(thm)],[163, 162])).
% 1.09/0.97  tff(165,plain,
% 1.09/0.97      (~aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 1.09/0.97      inference(or_elim,[status(thm)],[29])).
% 1.09/0.97  tff(166,plain,
% 1.09/0.97      (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 1.09/0.97      inference(rewrite,[status(thm)],[])).
% 1.09/0.97  tff(167,plain,
% 1.09/0.97      ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 1.09/0.97      inference(quant_inst,[status(thm)],[])).
% 1.09/0.97  tff(168,plain,
% 1.09/0.97      ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[167, 166])).
% 1.09/0.97  tff(169,plain,
% 1.09/0.97      (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 1.09/0.97      inference(unit_resolution,[status(thm)],[168, 165, 164])).
% 1.09/0.97  tff(170,plain,
% 1.09/0.97      (((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 1.09/0.97      inference(tautology,[status(thm)],[])).
% 1.09/0.97  tff(171,plain,
% 1.09/0.97      ((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 1.09/0.97      inference(unit_resolution,[status(thm)],[170, 169])).
% 1.09/0.97  tff(172,plain,
% 1.09/0.97      ((~(aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 1.09/0.97      inference(tautology,[status(thm)],[])).
% 1.09/0.97  tff(173,plain,
% 1.09/0.97      (~aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.97      inference(unit_resolution,[status(thm)],[172, 171, 114])).
% 1.09/0.97  tff(174,plain,
% 1.09/0.97      (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.97      inference(rewrite,[status(thm)],[])).
% 1.09/0.97  tff(175,axiom,((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & (sbrdtbr0(xQ) = xk)) & aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3989_02')).
% 1.09/0.97  tff(176,plain,
% 1.09/0.97      (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & (sbrdtbr0(xQ) = xk)),
% 1.09/0.97      inference(and_elim,[status(thm)],[175])).
% 1.09/0.97  tff(177,plain,
% 1.09/0.97      ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.97      inference(and_elim,[status(thm)],[176])).
% 1.09/0.97  tff(178,plain,
% 1.09/0.97      (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 1.09/0.97      inference(and_elim,[status(thm)],[177])).
% 1.09/0.97  tff(179,plain,
% 1.09/0.97      ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)),
% 1.09/0.97      inference(and_elim,[status(thm)],[178])).
% 1.09/0.97  tff(180,plain,
% 1.09/0.97      (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.09/0.97      inference(and_elim,[status(thm)],[179])).
% 1.09/0.97  tff(181,plain,
% 1.09/0.97      ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.97      inference(and_elim,[status(thm)],[180])).
% 1.09/0.97  tff(182,plain,
% 1.09/0.97      (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.97      inference(and_elim,[status(thm)],[181])).
% 1.09/0.97  tff(183,plain,
% 1.09/0.97      (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[182, 174])).
% 1.09/0.97  tff(184,plain,
% 1.09/0.97      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 1.09/0.97      inference(bind,[status(th)],[])).
% 1.09/0.97  tff(185,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 1.09/0.97      inference(quant_intro,[status(thm)],[184])).
% 1.09/0.97  tff(186,plain,
% 1.09/0.97      (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.09/0.97      inference(bind,[status(th)],[])).
% 1.09/0.97  tff(187,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.09/0.97      inference(quant_intro,[status(thm)],[186])).
% 1.09/0.97  tff(188,plain,
% 1.09/0.97      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.09/0.97      inference(bind,[status(th)],[])).
% 1.09/0.97  tff(189,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.09/0.97      inference(quant_intro,[status(thm)],[188])).
% 1.09/0.97  tff(190,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.09/0.97      inference(transitivity,[status(thm)],[189, 187])).
% 1.09/0.97  tff(191,plain,
% 1.09/0.97      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.09/0.97      inference(bind,[status(th)],[])).
% 1.09/0.97  tff(192,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.09/0.97      inference(quant_intro,[status(thm)],[191])).
% 1.09/0.97  tff(193,plain,
% 1.09/0.97      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 1.09/0.97      inference(bind,[status(th)],[])).
% 1.09/0.97  tff(194,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 1.09/0.97      inference(quant_intro,[status(thm)],[193])).
% 1.09/0.97  tff(195,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.09/0.97      inference(rewrite,[status(thm)],[])).
% 1.09/0.97  tff(196,plain,
% 1.09/0.97      (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 1.09/0.97      inference(bind,[status(th)],[])).
% 1.09/0.97  tff(197,plain,
% 1.09/0.97      (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.09/0.97      inference(quant_intro,[status(thm)],[196])).
% 1.09/0.97  tff(198,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSub')).
% 1.09/0.97  tff(199,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[198, 197])).
% 1.09/0.97  tff(200,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[199, 195])).
% 1.09/0.97  tff(201,plain,(
% 1.09/0.97      ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 1.09/0.97      inference(skolemize,[status(sab)],[200])).
% 1.09/0.97  tff(202,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[201, 194])).
% 1.09/0.97  tff(203,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[202, 192])).
% 1.09/0.97  tff(204,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[203, 190])).
% 1.09/0.97  tff(205,plain,
% 1.09/0.97      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 1.09/0.97      inference(modus_ponens,[status(thm)],[204, 185])).
% 1.09/0.97  tff(206,plain,
% 1.09/0.97      (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 1.09/0.97      inference(rewrite,[status(thm)],[])).
% 1.09/0.97  tff(207,plain,
% 1.09/0.97      (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) <=> ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 1.09/0.97      inference(rewrite,[status(thm)],[])).
% 1.09/0.97  tff(208,plain,
% 1.09/0.98      (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))),
% 1.09/0.98      inference(monotonicity,[status(thm)],[207])).
% 1.09/0.98  tff(209,plain,
% 1.09/0.98      (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 1.09/0.98      inference(transitivity,[status(thm)],[208, 206])).
% 1.09/0.98  tff(210,plain,
% 1.09/0.98      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 1.09/0.98      inference(quant_inst,[status(thm)],[])).
% 1.09/0.98  tff(211,plain,
% 1.09/0.98      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 1.09/0.98      inference(modus_ponens,[status(thm)],[210, 209])).
% 1.09/0.98  tff(212,plain,
% 1.09/0.98      (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 1.09/0.98      inference(unit_resolution,[status(thm)],[211, 205, 183])).
% 1.09/0.98  tff(213,plain,
% 1.09/0.98      (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 1.09/0.98      inference(rewrite,[status(thm)],[])).
% 1.09/0.98  tff(214,plain,
% 1.09/0.98      ((~((~((~aSet0(xQ)) | aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) <=> (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 1.09/0.98      inference(rewrite,[status(thm)],[])).
% 1.09/0.98  tff(215,plain,
% 1.09/0.98      (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~((~aSet0(xQ)) | aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 1.15/0.98      inference(monotonicity,[status(thm)],[214])).
% 1.15/0.98  tff(216,plain,
% 1.15/0.98      (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~((~aSet0(xQ)) | aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 1.15/0.98      inference(transitivity,[status(thm)],[215, 213])).
% 1.15/0.98  tff(217,plain,
% 1.15/0.98      ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~((~aSet0(xQ)) | aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 1.15/0.98      inference(quant_inst,[status(thm)],[])).
% 1.15/0.98  tff(218,plain,
% 1.15/0.98      ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))) | (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 1.15/0.98      inference(modus_ponens,[status(thm)],[217, 216])).
% 1.15/0.98  tff(219,plain,
% 1.15/0.98      (~((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))),
% 1.15/0.98      inference(unit_resolution,[status(thm)],[218, 212])).
% 1.15/0.98  tff(220,plain,
% 1.15/0.98      (((~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aSet0(xQ)) | (~((~aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), xQ)) | aElementOf0(tptp_fun_W2_1(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | ((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 1.15/0.98      inference(tautology,[status(thm)],[])).
% 1.15/0.98  tff(221,plain,
% 1.15/0.98      ((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 1.15/0.98      inference(unit_resolution,[status(thm)],[220, 219])).
% 1.15/0.98  tff(222,plain,
% 1.15/0.98      (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.15/0.98      inference(rewrite,[status(thm)],[])).
% 1.15/0.98  tff(223,plain,
% 1.15/0.98      (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.15/0.98      inference(and_elim,[status(thm)],[177])).
% 1.15/0.98  tff(224,plain,
% 1.15/0.98      (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.15/0.98      inference(modus_ponens,[status(thm)],[223, 222])).
% 1.15/0.99  tff(225,plain,
% 1.15/0.99      ((~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 1.15/0.99      inference(tautology,[status(thm)],[])).
% 1.15/0.99  tff(226,plain,
% 1.15/0.99      ((~((~aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 1.15/0.99      inference(unit_resolution,[status(thm)],[225, 224])).
% 1.15/0.99  tff(227,plain,
% 1.15/0.99      (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 1.15/0.99      inference(unit_resolution,[status(thm)],[226, 221])).
% 1.15/0.99  tff(228,plain,
% 1.15/0.99      (((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | ![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 1.15/0.99      inference(tautology,[status(thm)],[])).
% 1.15/0.99  tff(229,plain,
% 1.15/0.99      (![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 1.15/0.99      inference(unit_resolution,[status(thm)],[228, 227])).
% 1.15/0.99  tff(230,plain,
% 1.15/0.99      (((~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | ((~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 1.15/0.99      inference(rewrite,[status(thm)],[])).
% 1.15/0.99  tff(231,plain,
% 1.15/0.99      ((~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | ((~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 1.15/0.99      inference(quant_inst,[status(thm)],[])).
% 1.15/0.99  tff(232,plain,
% 1.15/0.99      ((~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.15/0.99      inference(modus_ponens,[status(thm)],[231, 230])).
% 1.15/0.99  tff(233,plain,
% 1.15/0.99      ((~aElementOf0(W0!31, xQ)) | aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.15/0.99      inference(unit_resolution,[status(thm)],[232, 229])).
% 1.15/0.99  tff(234,plain,
% 1.15/0.99      (~aElementOf0(W0!31, xQ)),
% 1.15/0.99      inference(unit_resolution,[status(thm)],[233, 173])).
% 1.15/0.99  tff(235,plain,
% 1.15/0.99      ((~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 1.15/0.99      inference(tautology,[status(thm)],[])).
% 1.15/0.99  tff(236,plain,
% 1.15/0.99      (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))),
% 1.15/0.99      inference(unit_resolution,[status(thm)],[235, 234, 35])).
% 1.15/0.99  tff(237,plain,
% 1.15/0.99      (aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00))),
% 1.15/0.99      inference(monotonicity,[status(thm)],[236])).
% 1.15/0.99  tff(238,plain,
% 1.15/0.99      (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)) <=> aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 1.15/0.99      inference(symmetry,[status(thm)],[237])).
% 1.15/0.99  tff(239,plain,
% 1.15/0.99      (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) <=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 1.15/0.99      inference(rewrite,[status(thm)],[])).
% 1.15/0.99  tff(240,plain,
% 1.15/0.99      (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))),
% 1.15/0.99      inference(and_elim,[status(thm)],[181])).
% 1.15/0.99  tff(241,plain,
% 1.15/0.99      (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 1.15/0.99      inference(and_elim,[status(thm)],[240])).
% 1.15/0.99  tff(242,plain,
% 1.15/0.99      (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))),
% 1.15/0.99      inference(modus_ponens,[status(thm)],[241, 239])).
% 1.15/0.99  tff(243,plain,
% 1.15/0.99      (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)))),
% 1.15/0.99      inference(rewrite,[status(thm)],[])).
% 1.15/0.99  tff(244,plain,
% 1.15/0.99      ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00)))),
% 1.15/0.99      inference(quant_inst,[status(thm)],[])).
% 1.15/0.99  tff(245,plain,
% 1.15/0.99      ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00))),
% 1.15/0.99      inference(modus_ponens,[status(thm)],[244, 243])).
% 1.15/0.99  tff(246,plain,
% 1.15/0.99      (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, sz00))),
% 1.15/0.99      inference(unit_resolution,[status(thm)],[245, 242, 164])).
% 1.15/0.99  tff(247,plain,
% 1.15/0.99      (aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 1.15/0.99      inference(modus_ponens,[status(thm)],[246, 238])).
% 1.15/0.99  tff(248,plain,
% 1.15/0.99      ($false),
% 1.15/0.99      inference(unit_resolution,[status(thm)],[165, 247])).
% 1.15/0.99  % SZS output end Proof
%------------------------------------------------------------------------------