TSTP Solution File: NUM583+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM583+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 13:10:40 EDT 2022
% Result : Theorem 1.01s 0.88s
% Output : Proof 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM583+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 12:06:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 1.01/0.88 % SZS status Theorem
% 1.01/0.88 % SZS output start Proof
% 1.01/0.88 tff(szmzizndt0_type, type, (
% 1.01/0.88 szmzizndt0: $i > $i)).
% 1.01/0.88 tff(sdtlpdtrp0_type, type, (
% 1.01/0.88 sdtlpdtrp0: ( $i * $i ) > $i)).
% 1.01/0.88 tff(xi_type, type, (
% 1.01/0.88 xi: $i)).
% 1.01/0.88 tff(xN_type, type, (
% 1.01/0.88 xN: $i)).
% 1.01/0.88 tff(tptp_fun_W0_31_type, type, (
% 1.01/0.88 tptp_fun_W0_31: $i)).
% 1.01/0.88 tff(aElementOf0_type, type, (
% 1.01/0.88 aElementOf0: ( $i * $i ) > $o)).
% 1.01/0.88 tff(xQ_type, type, (
% 1.01/0.88 xQ: $i)).
% 1.01/0.88 tff(aElement0_type, type, (
% 1.01/0.88 aElement0: $i > $o)).
% 1.01/0.88 tff(sdtpldt0_type, type, (
% 1.01/0.88 sdtpldt0: ( $i * $i ) > $i)).
% 1.01/0.88 tff(aSet0_type, type, (
% 1.01/0.88 aSet0: $i > $o)).
% 1.01/0.88 tff(sdtlseqdt0_type, type, (
% 1.01/0.88 sdtlseqdt0: ( $i * $i ) > $o)).
% 1.01/0.88 tff(xK_type, type, (
% 1.01/0.88 xK: $i)).
% 1.01/0.88 tff(sbrdtbr0_type, type, (
% 1.01/0.88 sbrdtbr0: $i > $i)).
% 1.01/0.88 tff(sz00_type, type, (
% 1.01/0.88 sz00: $i)).
% 1.01/0.88 tff(xS_type, type, (
% 1.01/0.88 xS: $i)).
% 1.01/0.88 tff(aSubsetOf0_type, type, (
% 1.01/0.88 aSubsetOf0: ( $i * $i ) > $o)).
% 1.01/0.88 tff(sdtmndt0_type, type, (
% 1.01/0.88 sdtmndt0: ( $i * $i ) > $i)).
% 1.01/0.88 tff(tptp_fun_W2_1_type, type, (
% 1.01/0.88 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 1.01/0.88 tff(xk_type, type, (
% 1.01/0.88 xk: $i)).
% 1.01/0.88 tff(slbdtsldtrb0_type, type, (
% 1.01/0.88 slbdtsldtrb0: ( $i * $i ) > $i)).
% 1.01/0.88 tff(szszuzczcdt0_type, type, (
% 1.01/0.88 szszuzczcdt0: $i > $i)).
% 1.01/0.88 tff(isCountable0_type, type, (
% 1.01/0.88 isCountable0: $i > $o)).
% 1.01/0.88 tff(szDzozmdt0_type, type, (
% 1.01/0.88 szDzozmdt0: $i > $i)).
% 1.01/0.88 tff(szNzAzT0_type, type, (
% 1.01/0.88 szNzAzT0: $i)).
% 1.01/0.88 tff(tptp_fun_W1_29_type, type, (
% 1.01/0.88 tptp_fun_W1_29: $i > $i)).
% 1.01/0.88 tff(aFunction0_type, type, (
% 1.01/0.88 aFunction0: $i > $o)).
% 1.01/0.88 tff(tptp_fun_W2_6_type, type, (
% 1.01/0.88 tptp_fun_W2_6: ( $i * $i ) > $i)).
% 1.01/0.88 tff(slbdtrb0_type, type, (
% 1.01/0.88 slbdtrb0: $i > $i)).
% 1.01/0.88 tff(slcrc0_type, type, (
% 1.01/0.88 slcrc0: $i)).
% 1.01/0.88 tff(1,plain,
% 1.01/0.88 (^[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)))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(2,plain,
% 1.01/0.88 (![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))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[1])).
% 1.01/0.88 tff(3,plain,
% 1.01/0.88 (^[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)))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(4,plain,
% 1.01/0.88 (![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))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[3])).
% 1.01/0.88 tff(5,plain,
% 1.01/0.88 (![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))))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 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')).
% 1.01/0.88 tff(7,plain,
% 1.01/0.88 (((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))))))),
% 1.01/0.88 inference(and_elim,[status(thm)],[6])).
% 1.01/0.88 tff(8,plain,
% 1.01/0.88 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.01/0.88 inference(and_elim,[status(thm)],[7])).
% 1.01/0.88 tff(9,plain,
% 1.01/0.88 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[8, 5])).
% 1.01/0.88 tff(10,plain,(
% 1.01/0.88 ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.01/0.88 inference(skolemize,[status(sab)],[9])).
% 1.01/0.88 tff(11,plain,
% 1.01/0.88 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[10, 4])).
% 1.01/0.88 tff(12,plain,
% 1.01/0.88 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0)) | (~(aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[11, 2])).
% 1.01/0.88 tff(13,plain,
% 1.01/0.88 ((~![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))))))))),
% 1.01/0.88 inference(quant_inst,[status(thm)],[])).
% 1.01/0.88 tff(14,plain,
% 1.01/0.88 (aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[13, 12])).
% 1.01/0.88 tff(15,plain,
% 1.01/0.88 ((~![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))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(16,plain,
% 1.01/0.88 ((~![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))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(17,plain,
% 1.01/0.88 ((~![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)))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(18,plain,
% 1.01/0.88 ((~((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))))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 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__')).
% 1.01/0.88 tff(20,plain,
% 1.01/0.88 (~(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)))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.01/0.88 tff(21,plain,
% 1.01/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 1.01/0.88 inference(or_elim,[status(thm)],[20])).
% 1.01/0.88 tff(22,plain,
% 1.01/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[21, 17])).
% 1.01/0.88 tff(23,plain,
% 1.01/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[22, 17])).
% 1.01/0.88 tff(24,plain,
% 1.01/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, xS))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[23, 17])).
% 1.01/0.88 tff(25,plain,
% 1.01/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[24, 16])).
% 1.01/0.88 tff(26,plain,
% 1.01/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[25, 15])).
% 1.01/0.88 tff(27,plain,
% 1.01/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[26, 15])).
% 1.01/0.88 tff(28,plain,
% 1.01/0.88 (~![W0: $i] : ((~aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[27, 15])).
% 1.01/0.88 tff(29,plain,(
% 1.01/0.88 ~((~aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 1.01/0.88 inference(skolemize,[status(sab)],[28])).
% 1.01/0.88 tff(30,plain,
% 1.01/0.88 (aElementOf0(W0!31, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.01/0.88 inference(or_elim,[status(thm)],[29])).
% 1.01/0.88 tff(31,plain,
% 1.01/0.88 ((~(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)))))))),
% 1.01/0.88 inference(tautology,[status(thm)],[])).
% 1.01/0.88 tff(32,plain,
% 1.01/0.88 ((~(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)))))))),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[31, 30])).
% 1.01/0.88 tff(33,plain,
% 1.01/0.88 (~((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[32, 14])).
% 1.01/0.88 tff(34,plain,
% 1.01/0.88 (((~aElement0(W0!31)) | (~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.01/0.88 inference(tautology,[status(thm)],[])).
% 1.01/0.88 tff(35,plain,
% 1.01/0.88 (aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[34, 33])).
% 1.01/0.88 tff(36,plain,
% 1.01/0.88 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(37,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')).
% 1.01/0.88 tff(38,plain,
% 1.01/0.88 (((((((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)),
% 1.01/0.88 inference(and_elim,[status(thm)],[37])).
% 1.01/0.88 tff(39,plain,
% 1.01/0.88 ((((((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))))),
% 1.01/0.88 inference(and_elim,[status(thm)],[38])).
% 1.01/0.88 tff(40,plain,
% 1.01/0.88 (((((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)))))),
% 1.01/0.88 inference(and_elim,[status(thm)],[39])).
% 1.01/0.88 tff(41,plain,
% 1.01/0.88 ((((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)),
% 1.01/0.88 inference(and_elim,[status(thm)],[40])).
% 1.01/0.88 tff(42,plain,
% 1.01/0.88 (((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))))))),
% 1.01/0.88 inference(and_elim,[status(thm)],[41])).
% 1.01/0.88 tff(43,plain,
% 1.01/0.88 ((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))))),
% 1.01/0.88 inference(and_elim,[status(thm)],[42])).
% 1.01/0.88 tff(44,plain,
% 1.01/0.88 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.01/0.88 inference(and_elim,[status(thm)],[43])).
% 1.01/0.88 tff(45,plain,
% 1.01/0.88 (aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[44, 36])).
% 1.01/0.88 tff(46,plain,
% 1.01/0.88 (^[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)))))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(47,plain,
% 1.01/0.88 (![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))))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[46])).
% 1.01/0.88 tff(48,plain,
% 1.01/0.88 (^[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)))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(49,plain,
% 1.01/0.88 (![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))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[48])).
% 1.01/0.88 tff(50,plain,
% 1.01/0.88 (^[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)))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(51,plain,
% 1.01/0.88 (![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))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[50])).
% 1.01/0.88 tff(52,plain,
% 1.01/0.88 (![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))))))))),
% 1.01/0.88 inference(transitivity,[status(thm)],[51, 49])).
% 1.01/0.88 tff(53,plain,
% 1.01/0.88 (^[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)))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(54,plain,
% 1.01/0.88 (![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))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[53])).
% 1.01/0.88 tff(55,plain,
% 1.01/0.88 (^[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)))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(56,plain,
% 1.01/0.88 (![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))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[55])).
% 1.01/0.88 tff(57,plain,
% 1.01/0.88 (![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)))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(58,plain,
% 1.01/0.88 (^[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)))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(59,plain,
% 1.01/0.88 (![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)))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[58])).
% 1.01/0.88 tff(60,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')).
% 1.01/0.88 tff(61,plain,
% 1.01/0.88 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.01/0.88 tff(62,plain,
% 1.01/0.88 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[61, 57])).
% 1.01/0.88 tff(63,plain,(
% 1.01/0.88 ![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)))))))),
% 1.01/0.88 inference(skolemize,[status(sab)],[62])).
% 1.01/0.88 tff(64,plain,
% 1.01/0.88 (![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))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[63, 56])).
% 1.01/0.88 tff(65,plain,
% 1.01/0.88 (![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))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[64, 54])).
% 1.01/0.88 tff(66,plain,
% 1.01/0.88 (![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))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[65, 52])).
% 1.01/0.88 tff(67,plain,
% 1.01/0.88 (![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))))))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[66, 47])).
% 1.01/0.89 tff(68,plain,
% 1.01/0.89 (((~![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)))))))))))))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(69,plain,
% 1.01/0.89 (((~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)))))))))))))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(70,plain,
% 1.01/0.89 (((~![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))))))))))))))),
% 1.01/0.89 inference(monotonicity,[status(thm)],[69])).
% 1.01/0.89 tff(71,plain,
% 1.01/0.89 (((~![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)))))))))))))),
% 1.01/0.89 inference(transitivity,[status(thm)],[70, 68])).
% 1.01/0.89 tff(72,plain,
% 1.01/0.89 ((~![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)))))))))))))),
% 1.01/0.89 inference(quant_inst,[status(thm)],[])).
% 1.01/0.89 tff(73,plain,
% 1.01/0.89 ((~![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))))))))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.01/0.89 tff(74,plain,
% 1.01/0.89 (![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))))))))))))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[73, 67, 45])).
% 1.01/0.89 tff(75,plain,
% 1.01/0.89 (((~![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)))))))))))))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(76,plain,
% 1.01/0.89 ((~((~((~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))))))))))))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(77,plain,
% 1.01/0.89 (((~![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)))))))))))))),
% 1.01/0.89 inference(monotonicity,[status(thm)],[76])).
% 1.01/0.89 tff(78,plain,
% 1.01/0.89 (((~![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)))))))))))))),
% 1.01/0.89 inference(transitivity,[status(thm)],[77, 75])).
% 1.01/0.89 tff(79,plain,
% 1.01/0.89 ((~![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))))))))))))),
% 1.01/0.89 inference(quant_inst,[status(thm)],[])).
% 1.01/0.89 tff(80,plain,
% 1.01/0.89 ((~![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))))))))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.01/0.89 tff(81,plain,
% 1.01/0.89 (~((~(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)))))))))))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[80, 74])).
% 1.01/0.89 tff(82,plain,
% 1.01/0.89 (((~(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)))))))))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(83,plain,
% 1.01/0.89 ((~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))))))))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[82, 81])).
% 1.01/0.89 tff(84,plain,
% 1.01/0.89 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(85,plain,
% 1.01/0.89 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.01/0.89 inference(and_elim,[status(thm)],[39])).
% 1.01/0.89 tff(86,plain,
% 1.01/0.89 (aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.01/0.89 tff(87,plain,
% 1.01/0.89 ((~((~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))))))))),
% 1.01/0.90 inference(tautology,[status(thm)],[])).
% 1.01/0.90 tff(88,plain,
% 1.01/0.90 ((~((~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))))))))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.01/0.90 tff(89,plain,
% 1.01/0.90 (~((~aSet0(xQ)) | (~![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[88, 83])).
% 1.01/0.90 tff(90,plain,
% 1.01/0.90 (((~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)))))),
% 1.01/0.90 inference(tautology,[status(thm)],[])).
% 1.01/0.90 tff(91,plain,
% 1.01/0.90 (![W2: $i] : ((~aElementOf0(W2, xQ)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[90, 89])).
% 1.01/0.90 tff(92,plain,
% 1.01/0.90 (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szDzozmdt0(xN))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(93,plain,
% 1.01/0.90 (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(94,axiom,(aElementOf0(xi, szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3989')).
% 1.01/0.90 tff(95,plain,
% 1.01/0.90 (aElementOf0(xi, szNzAzT0)),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.01/0.90 tff(96,plain,
% 1.01/0.90 (aElementOf0(xi, szDzozmdt0(xN))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[95, 92])).
% 1.01/0.90 tff(97,plain,
% 1.01/0.90 (^[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))))))))),
% 1.01/0.90 inference(bind,[status(th)],[])).
% 1.01/0.90 tff(98,plain,
% 1.01/0.90 (![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)))))) <=> ![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)))))))),
% 1.01/0.90 inference(quant_intro,[status(thm)],[97])).
% 1.01/0.90 tff(99,plain,
% 1.01/0.90 (^[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)))))))),
% 1.01/0.90 inference(bind,[status(th)],[])).
% 1.01/0.90 tff(100,plain,
% 1.01/0.90 (![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)))))) <=> ![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))))))),
% 1.01/0.90 inference(quant_intro,[status(thm)],[99])).
% 1.01/0.90 tff(101,plain,
% 1.01/0.90 (^[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)))))))),
% 1.01/0.90 inference(bind,[status(th)],[])).
% 1.01/0.90 tff(102,plain,
% 1.01/0.90 (![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)))))) <=> ![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))))))),
% 1.01/0.90 inference(quant_intro,[status(thm)],[101])).
% 1.01/0.90 tff(103,plain,
% 1.01/0.90 (![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)))))) <=> ![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))))))),
% 1.01/0.90 inference(transitivity,[status(thm)],[102, 100])).
% 1.01/0.90 tff(104,plain,
% 1.01/0.90 (^[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)))))))),
% 1.01/0.90 inference(bind,[status(th)],[])).
% 1.01/0.90 tff(105,plain,
% 1.01/0.90 (![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)))) <=> ![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))))))),
% 1.01/0.90 inference(quant_intro,[status(thm)],[104])).
% 1.01/0.90 tff(106,plain,
% 1.01/0.90 (^[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)))))),
% 1.01/0.90 inference(bind,[status(th)],[])).
% 1.01/0.90 tff(107,plain,
% 1.01/0.90 (![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, 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))))),
% 1.01/0.90 inference(quant_intro,[status(thm)],[106])).
% 1.01/0.90 tff(108,plain,
% 1.01/0.90 (![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))))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(109,plain,
% 1.01/0.90 (^[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))))))),
% 1.01/0.90 inference(bind,[status(th)],[])).
% 1.01/0.90 tff(110,plain,
% 1.01/0.90 (![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))))),
% 1.01/0.90 inference(quant_intro,[status(thm)],[109])).
% 1.01/0.90 tff(111,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')).
% 1.01/0.90 tff(112,plain,
% 1.01/0.90 (![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))))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.01/0.90 tff(113,plain,
% 1.01/0.90 (![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))))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.01/0.90 tff(114,plain,
% 1.01/0.90 (![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))))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[113, 107])).
% 1.01/0.90 tff(115,plain,(
% 1.01/0.90 ![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))))),
% 1.01/0.90 inference(skolemize,[status(sab)],[114])).
% 1.01/0.90 tff(116,plain,
% 1.01/0.90 (![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))))))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[115, 105])).
% 1.01/0.90 tff(117,plain,
% 1.01/0.90 (![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))))))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[116, 103])).
% 1.01/0.90 tff(118,plain,
% 1.01/0.90 (![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)))))))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[117, 98])).
% 1.01/0.90 tff(119,plain,
% 1.01/0.90 (((~![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)))))))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(120,plain,
% 1.01/0.90 ((~![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)))))))),
% 1.01/0.90 inference(quant_inst,[status(thm)],[])).
% 1.01/0.90 tff(121,plain,
% 1.01/0.90 ((~![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))))))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.01/0.90 tff(122,plain,
% 1.01/0.90 (~((~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)))))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[121, 118, 96])).
% 1.01/0.90 tff(123,plain,
% 1.01/0.90 (((~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))),
% 1.01/0.90 inference(tautology,[status(thm)],[])).
% 1.01/0.90 tff(124,plain,
% 1.01/0.90 (isCountable0(sdtlpdtrp0(xN, xi))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[123, 122])).
% 1.01/0.90 tff(125,plain,
% 1.01/0.90 (((~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))),
% 1.01/0.90 inference(tautology,[status(thm)],[])).
% 1.01/0.90 tff(126,plain,
% 1.01/0.90 (aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[125, 122])).
% 1.01/0.90 tff(127,plain,
% 1.01/0.90 ((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)))),
% 1.01/0.90 inference(tautology,[status(thm)],[])).
% 1.01/0.90 tff(128,plain,
% 1.01/0.90 (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))))))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.01/0.90 tff(129,plain,
% 1.01/0.90 (^[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)))))))))))),
% 1.01/0.90 inference(bind,[status(th)],[])).
% 1.01/0.90 tff(130,plain,
% 1.01/0.90 (![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)))))))))),
% 1.01/0.90 inference(quant_intro,[status(thm)],[129])).
% 1.01/0.90 tff(131,plain,
% 1.01/0.90 (^[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))))))))))),
% 1.01/0.91 inference(bind,[status(th)],[])).
% 1.01/0.91 tff(132,plain,
% 1.01/0.91 (![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)))))))))),
% 1.01/0.91 inference(quant_intro,[status(thm)],[131])).
% 1.01/0.91 tff(133,plain,
% 1.01/0.91 (^[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))))))))))),
% 1.01/0.91 inference(bind,[status(th)],[])).
% 1.01/0.91 tff(134,plain,
% 1.01/0.91 (![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)))))))))),
% 1.01/0.91 inference(quant_intro,[status(thm)],[133])).
% 1.01/0.91 tff(135,plain,
% 1.01/0.91 (![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)))))))))),
% 1.01/0.91 inference(transitivity,[status(thm)],[134, 132])).
% 1.01/0.91 tff(136,plain,
% 1.01/0.91 (^[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)))))))))))),
% 1.01/0.91 inference(bind,[status(th)],[])).
% 1.01/0.91 tff(137,plain,
% 1.01/0.91 (![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)))))))))),
% 1.01/0.91 inference(quant_intro,[status(thm)],[136])).
% 1.01/0.91 tff(138,plain,
% 1.01/0.91 (^[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))))))),
% 1.01/0.91 inference(bind,[status(th)],[])).
% 1.01/0.91 tff(139,plain,
% 1.01/0.91 (![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(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))))),
% 1.01/0.91 inference(quant_intro,[status(thm)],[138])).
% 1.01/0.91 tff(140,plain,
% 1.01/0.91 (^[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)))))))),
% 1.01/0.92 inference(bind,[status(th)],[])).
% 1.01/0.92 tff(141,plain,
% 1.01/0.92 (![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)))))),
% 1.01/0.92 inference(quant_intro,[status(thm)],[140])).
% 1.01/0.92 tff(142,plain,
% 1.01/0.92 (![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)))))),
% 1.01/0.92 inference(rewrite,[status(thm)],[])).
% 1.01/0.92 tff(143,plain,
% 1.01/0.92 (^[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)))))))),
% 1.06/0.93 inference(bind,[status(th)],[])).
% 1.06/0.93 tff(144,plain,
% 1.06/0.93 (![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)))))),
% 1.06/0.93 inference(quant_intro,[status(thm)],[143])).
% 1.06/0.93 tff(145,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')).
% 1.06/0.93 tff(146,plain,
% 1.06/0.93 (![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))))))),
% 1.06/0.93 inference(and_elim,[status(thm)],[145])).
% 1.06/0.93 tff(147,plain,
% 1.06/0.93 (![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)))))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[146, 144])).
% 1.06/0.93 tff(148,plain,
% 1.06/0.93 (![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)))))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[147, 142])).
% 1.06/0.93 tff(149,plain,
% 1.06/0.93 (![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)))))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[148, 141])).
% 1.06/0.93 tff(150,plain,(
% 1.06/0.93 ![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)))))),
% 1.06/0.93 inference(skolemize,[status(sab)],[149])).
% 1.06/0.93 tff(151,plain,
% 1.06/0.93 (![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))))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[150, 139])).
% 1.06/0.93 tff(152,plain,
% 1.06/0.93 (![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)))))))))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[151, 137])).
% 1.06/0.93 tff(153,plain,
% 1.06/0.93 (![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)))))))))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[152, 135])).
% 1.06/0.93 tff(154,plain,
% 1.06/0.93 (![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)))))))))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[153, 130])).
% 1.06/0.93 tff(155,plain,
% 1.06/0.93 (((~![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)))))))))),
% 1.06/0.93 inference(rewrite,[status(thm)],[])).
% 1.06/0.93 tff(156,plain,
% 1.06/0.93 (((~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)))))))))),
% 1.06/0.94 inference(rewrite,[status(thm)],[])).
% 1.06/0.94 tff(157,plain,
% 1.06/0.94 ((~((~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))))))))),
% 1.06/0.94 inference(rewrite,[status(thm)],[])).
% 1.06/0.94 tff(158,plain,
% 1.06/0.94 ((~(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))))))))),
% 1.06/0.94 inference(rewrite,[status(thm)],[])).
% 1.06/0.94 tff(159,plain,
% 1.06/0.94 (((~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)))))))) | (~((~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)))))))))),
% 1.06/0.94 inference(monotonicity,[status(thm)],[158, 157])).
% 1.06/0.94 tff(160,plain,
% 1.06/0.94 (((~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)))))))) | (~((~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)))))))))),
% 1.06/0.94 inference(transitivity,[status(thm)],[159, 156])).
% 1.06/0.94 tff(161,plain,
% 1.06/0.94 (((~![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)))))))) | (~((~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))))))))))),
% 1.06/0.94 inference(monotonicity,[status(thm)],[160])).
% 1.06/0.94 tff(162,plain,
% 1.06/0.94 (((~![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)))))))) | (~((~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)))))))))),
% 1.06/0.94 inference(transitivity,[status(thm)],[161, 155])).
% 1.06/0.94 tff(163,plain,
% 1.06/0.94 ((~![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)))))))) | (~((~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)))))))))),
% 1.06/0.94 inference(quant_inst,[status(thm)],[])).
% 1.06/0.94 tff(164,plain,
% 1.06/0.94 ((~![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))))))))),
% 1.06/0.94 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.06/0.94 tff(165,plain,
% 1.06/0.94 ((~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))))))))),
% 1.06/0.94 inference(unit_resolution,[status(thm)],[164, 154, 96])).
% 1.06/0.94 tff(166,plain,
% 1.06/0.94 (~((~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)))))))),
% 1.06/0.94 inference(unit_resolution,[status(thm)],[165, 128, 124])).
% 1.06/0.94 tff(167,plain,
% 1.06/0.94 (((~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))))))),
% 1.06/0.94 inference(tautology,[status(thm)],[])).
% 1.06/0.94 tff(168,plain,
% 1.06/0.94 (![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 1.06/0.94 inference(unit_resolution,[status(thm)],[167, 166])).
% 1.06/0.94 tff(169,plain,
% 1.06/0.94 ((~![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))))))),
% 1.06/0.95 inference(quant_inst,[status(thm)],[])).
% 1.06/0.95 tff(170,plain,
% 1.06/0.95 (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)))))),
% 1.06/0.95 inference(unit_resolution,[status(thm)],[169, 168])).
% 1.06/0.95 tff(171,plain,
% 1.06/0.95 (~aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 1.06/0.95 inference(or_elim,[status(thm)],[29])).
% 1.06/0.95 tff(172,plain,
% 1.06/0.95 (^[W0: $i] : refl(((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))) <=> ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))))),
% 1.06/0.95 inference(bind,[status(th)],[])).
% 1.06/0.95 tff(173,plain,
% 1.06/0.95 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.06/0.95 inference(quant_intro,[status(thm)],[172])).
% 1.06/0.95 tff(174,plain,
% 1.06/0.95 (^[W0: $i] : rewrite(((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))))),
% 1.06/0.95 inference(bind,[status(th)],[])).
% 1.06/0.95 tff(175,plain,
% 1.06/0.95 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.06/0.95 inference(quant_intro,[status(thm)],[174])).
% 1.06/0.95 tff(176,plain,
% 1.06/0.95 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 1.06/0.95 inference(rewrite,[status(thm)],[])).
% 1.06/0.95 tff(177,plain,
% 1.06/0.95 (^[W0: $i] : rewrite((aElementOf0(W0, sdtlpdtrp0(xN, xi)) => aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS)))),
% 1.06/0.95 inference(bind,[status(th)],[])).
% 1.06/0.95 tff(178,plain,
% 1.06/0.95 (![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 1.06/0.95 inference(quant_intro,[status(thm)],[177])).
% 1.06/0.95 tff(179,axiom,(![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => aElementOf0(W0, xS)) & aSubsetOf0(sdtlpdtrp0(xN, xi), xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4037')).
% 1.06/0.95 tff(180,plain,
% 1.06/0.95 (![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => aElementOf0(W0, xS))),
% 1.06/0.95 inference(and_elim,[status(thm)],[179])).
% 1.06/0.95 tff(181,plain,
% 1.06/0.95 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 1.06/0.95 inference(modus_ponens,[status(thm)],[180, 178])).
% 1.06/0.95 tff(182,plain,
% 1.06/0.95 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, xS))),
% 1.06/0.95 inference(modus_ponens,[status(thm)],[181, 176])).
% 1.06/0.95 tff(183,plain,
% 1.06/0.95 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.06/0.95 inference(modus_ponens,[status(thm)],[182, 175])).
% 1.06/0.95 tff(184,plain,(
% 1.06/0.95 ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.06/0.95 inference(skolemize,[status(sab)],[183])).
% 1.06/0.95 tff(185,plain,
% 1.06/0.95 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 1.06/0.95 inference(modus_ponens,[status(thm)],[184, 173])).
% 1.06/0.95 tff(186,plain,
% 1.06/0.95 (((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 1.06/0.95 inference(rewrite,[status(thm)],[])).
% 1.06/0.95 tff(187,plain,
% 1.06/0.95 ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00)))),
% 1.06/0.95 inference(quant_inst,[status(thm)],[])).
% 1.06/0.95 tff(188,plain,
% 1.06/0.95 ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, xi))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | aElementOf0(W0!31, sdtlpdtrp0(xN, sz00))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.09/0.95 tff(189,plain,
% 1.09/0.95 (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[188, 185, 171])).
% 1.09/0.95 tff(190,plain,
% 1.09/0.95 (((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 1.09/0.95 inference(tautology,[status(thm)],[])).
% 1.09/0.95 tff(191,plain,
% 1.09/0.95 ((~aElement0(W0!31)) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[190, 189])).
% 1.09/0.95 tff(192,plain,
% 1.09/0.95 ((~(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)))))),
% 1.09/0.95 inference(tautology,[status(thm)],[])).
% 1.09/0.95 tff(193,plain,
% 1.09/0.95 ((~(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)))))),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[192, 191])).
% 1.09/0.95 tff(194,plain,
% 1.09/0.95 (~aElementOf0(W0!31, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[193, 170])).
% 1.09/0.95 tff(195,plain,
% 1.09/0.95 (((~![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)))))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(196,plain,
% 1.09/0.95 ((~![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)))))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(197,plain,
% 1.09/0.95 ((~![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))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.09/0.95 tff(198,plain,
% 1.09/0.95 (~aElementOf0(W0!31, xQ)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[197, 194, 91])).
% 1.09/0.95 tff(199,plain,
% 1.09/0.95 ((~(aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W0!31, xQ) | (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))),
% 1.09/0.95 inference(tautology,[status(thm)],[])).
% 1.09/0.95 tff(200,plain,
% 1.09/0.95 (W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[199, 198, 35])).
% 1.09/0.95 tff(201,plain,
% 1.09/0.95 (((~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))))) | aSet0(sdtlpdtrp0(xN, xi))),
% 1.09/0.95 inference(tautology,[status(thm)],[])).
% 1.09/0.95 tff(202,plain,
% 1.09/0.95 (aSet0(sdtlpdtrp0(xN, xi))),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[201, 122])).
% 1.09/0.95 tff(203,plain,
% 1.09/0.95 (^[W0: $i] : refl(((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0))) <=> ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(204,plain,
% 1.09/0.95 (![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0))) <=> ![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[203])).
% 1.09/0.95 tff(205,plain,
% 1.09/0.95 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & isCountable0(W0)) <=> (~((~aSet0(W0)) | (~isCountable0(W0))))), ((~(aSet0(W0) & isCountable0(W0))) <=> (~(~((~aSet0(W0)) | (~isCountable0(W0))))))), rewrite((~(~((~aSet0(W0)) | (~isCountable0(W0))))) <=> ((~aSet0(W0)) | (~isCountable0(W0)))), ((~(aSet0(W0) & isCountable0(W0))) <=> ((~aSet0(W0)) | (~isCountable0(W0))))), (((~(W0 = slbdtrb0(sz00))) | (~(aSet0(W0) & isCountable0(W0)))) <=> ((~(W0 = slbdtrb0(sz00))) | ((~aSet0(W0)) | (~isCountable0(W0)))))), rewrite(((~(W0 = slbdtrb0(sz00))) | ((~aSet0(W0)) | (~isCountable0(W0)))) <=> ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))), (((~(W0 = slbdtrb0(sz00))) | (~(aSet0(W0) & isCountable0(W0)))) <=> ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(206,plain,
% 1.09/0.95 (![W0: $i] : ((~(W0 = slbdtrb0(sz00))) | (~(aSet0(W0) & isCountable0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[205])).
% 1.09/0.95 tff(207,plain,
% 1.09/0.95 (^[W0: $i] : rewrite(((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0)))) <=> ((~(W0 = slbdtrb0(sz00))) | (~(aSet0(W0) & isCountable0(W0)))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(208,plain,
% 1.09/0.95 (![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0)))) <=> ![W0: $i] : ((~(W0 = slbdtrb0(sz00))) | (~(aSet0(W0) & isCountable0(W0))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[207])).
% 1.09/0.95 tff(209,plain,
% 1.09/0.95 (![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0)))) <=> ![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(210,plain,
% 1.09/0.95 (^[W0: $i] : rewrite(((aSet0(W0) & isCountable0(W0)) => (~(W0 = slcrc0))) <=> ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0)))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(211,plain,
% 1.09/0.95 (![W0: $i] : ((aSet0(W0) & isCountable0(W0)) => (~(W0 = slcrc0))) <=> ![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[210])).
% 1.09/0.95 tff(212,axiom,(![W0: $i] : ((aSet0(W0) & isCountable0(W0)) => (~(W0 = slcrc0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mCountNFin_01')).
% 1.09/0.95 tff(213,plain,
% 1.09/0.95 (![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.09/0.95 tff(214,plain,
% 1.09/0.95 (![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[213, 209])).
% 1.09/0.95 tff(215,plain,
% 1.09/0.95 (![W0: $i] : ((~(W0 = slbdtrb0(sz00))) | (~(aSet0(W0) & isCountable0(W0))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[214, 208])).
% 1.09/0.95 tff(216,plain,(
% 1.09/0.95 ![W0: $i] : ((~(W0 = slbdtrb0(sz00))) | (~(aSet0(W0) & isCountable0(W0))))),
% 1.09/0.95 inference(skolemize,[status(sab)],[215])).
% 1.09/0.95 tff(217,plain,
% 1.09/0.95 (![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[216, 206])).
% 1.09/0.95 tff(218,plain,
% 1.09/0.95 (![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[217, 204])).
% 1.09/0.95 tff(219,plain,
% 1.09/0.95 (((~![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))) | ((~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))) | (~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(220,plain,
% 1.09/0.95 (((~aSet0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))) | (~isCountable0(sdtlpdtrp0(xN, xi)))) <=> ((~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(221,plain,
% 1.09/0.95 (((~![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))) | ((~aSet0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))) | (~isCountable0(sdtlpdtrp0(xN, xi))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))) | ((~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)))))),
% 1.09/0.95 inference(monotonicity,[status(thm)],[220])).
% 1.09/0.95 tff(222,plain,
% 1.09/0.95 (((~![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))) | ((~aSet0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))) | (~isCountable0(sdtlpdtrp0(xN, xi))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))) | (~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))))),
% 1.09/0.95 inference(transitivity,[status(thm)],[221, 219])).
% 1.09/0.95 tff(223,plain,
% 1.09/0.95 ((~![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))) | ((~aSet0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))) | (~isCountable0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(224,plain,
% 1.09/0.95 ((~![W0: $i] : ((~aSet0(W0)) | (~(W0 = slbdtrb0(sz00))) | (~isCountable0(W0)))) | (~aSet0(sdtlpdtrp0(xN, xi))) | (~isCountable0(sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.09/0.95 tff(225,plain,
% 1.09/0.95 (~(sdtlpdtrp0(xN, xi) = slbdtrb0(sz00))),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[224, 218, 202, 124])).
% 1.09/0.95 tff(226,plain,
% 1.09/0.95 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))) <=> (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))), (![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))), (((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))))))))), rewrite(((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))))))) <=> ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))), (((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(227,plain,
% 1.09/0.95 (![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[226])).
% 1.09/0.95 tff(228,plain,
% 1.09/0.95 (^[W0: $i] : refl(((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(229,plain,
% 1.09/0.95 (![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[228])).
% 1.09/0.95 tff(230,plain,
% 1.09/0.95 (^[W0: $i] : rewrite(((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(231,plain,
% 1.09/0.95 (![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[230])).
% 1.09/0.95 tff(232,plain,
% 1.09/0.95 (![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.09/0.95 inference(transitivity,[status(thm)],[231, 229])).
% 1.09/0.95 tff(233,plain,
% 1.09/0.95 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00)))) <=> (~((~aSubsetOf0(W0, szDzozmdt0(xN))) | (W0 = slbdtrb0(sz00))))), ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) <=> (~(~((~aSubsetOf0(W0, szDzozmdt0(xN))) | (W0 = slbdtrb0(sz00))))))), rewrite((~(~((~aSubsetOf0(W0, szDzozmdt0(xN))) | (W0 = slbdtrb0(sz00))))) <=> ((~aSubsetOf0(W0, szDzozmdt0(xN))) | (W0 = slbdtrb0(sz00)))), ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) <=> ((~aSubsetOf0(W0, szDzozmdt0(xN))) | (W0 = slbdtrb0(sz00))))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite(((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) <=> ((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))), rewrite(((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))) <=> ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))), ((((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) <=> (((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))), rewrite((((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) <=> (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))), ((((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) <=> (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))))), (![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) <=> ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))), (((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))) <=> (((~aSubsetOf0(W0, szDzozmdt0(xN))) | (W0 = slbdtrb0(sz00))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))))), rewrite((((~aSubsetOf0(W0, szDzozmdt0(xN))) | (W0 = slbdtrb0(sz00))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))), (((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))) <=> ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(234,plain,
% 1.09/0.95 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))) <=> ![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[233])).
% 1.09/0.95 tff(235,plain,
% 1.09/0.95 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((W1 = szmzizndt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))) <=> ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(236,plain,
% 1.09/0.95 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((W1 = szmzizndt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[235])).
% 1.09/0.95 tff(237,plain,
% 1.09/0.95 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))) <=> ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(238,plain,
% 1.09/0.95 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[237])).
% 1.09/0.95 tff(239,plain,
% 1.09/0.95 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(240,plain,
% 1.09/0.95 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite(((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2)))) <=> ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))), (![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2)))) <=> ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))), (((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))))) <=> ((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))), rewrite(((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))), (((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(241,plain,
% 1.09/0.95 (![W0: $i] : ((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[240])).
% 1.09/0.95 tff(242,axiom,(![W0: $i] : ((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefMin')).
% 1.09/0.95 tff(243,plain,
% 1.09/0.95 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.09/0.95 tff(244,plain,
% 1.09/0.95 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[243, 239])).
% 1.09/0.95 tff(245,plain,
% 1.09/0.95 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[244, 238])).
% 1.09/0.95 tff(246,plain,(
% 1.09/0.95 ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((W1 = szmzizndt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))),
% 1.09/0.95 inference(skolemize,[status(sab)],[245])).
% 1.09/0.95 tff(247,plain,
% 1.09/0.95 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xN)) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[246, 236])).
% 1.09/0.95 tff(248,plain,
% 1.09/0.95 (![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[247, 234])).
% 1.09/0.95 tff(249,plain,
% 1.09/0.95 (![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[248, 232])).
% 1.09/0.95 tff(250,plain,
% 1.09/0.95 (![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[249, 227])).
% 1.09/0.95 tff(251,plain,
% 1.09/0.95 (((~![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))) <=> ((~![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(252,plain,
% 1.09/0.95 (((sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(253,plain,
% 1.09/0.95 (^[W1: $i] : rewrite((~((~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))) <=> (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(254,plain,
% 1.09/0.95 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))) <=> ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[253])).
% 1.09/0.95 tff(255,plain,
% 1.09/0.95 (((sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))) <=> ((sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.96 inference(monotonicity,[status(thm)],[254])).
% 1.09/0.96 tff(256,plain,
% 1.09/0.96 (((sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.96 inference(transitivity,[status(thm)],[255, 252])).
% 1.09/0.96 tff(257,plain,
% 1.09/0.96 (((~![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))) <=> ((~![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))))),
% 1.09/0.96 inference(monotonicity,[status(thm)],[256])).
% 1.09/0.96 tff(258,plain,
% 1.09/0.96 (((~![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))) <=> ((~![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.96 inference(transitivity,[status(thm)],[257, 251])).
% 1.09/0.96 tff(259,plain,
% 1.09/0.96 ((~![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2))))))))))),
% 1.09/0.96 inference(quant_inst,[status(thm)],[])).
% 1.09/0.96 tff(260,plain,
% 1.09/0.96 ((~![W0: $i] : ((W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.09/0.96 tff(261,plain,
% 1.09/0.96 ((~aSubsetOf0(sdtlpdtrp0(xN, xi), szDzozmdt0(xN))) | (sdtlpdtrp0(xN, xi) = slbdtrb0(sz00)) | ![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[260, 250])).
% 1.09/0.96 tff(262,plain,
% 1.09/0.96 (![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[261, 225, 126])).
% 1.09/0.96 tff(263,plain,
% 1.09/0.96 ((~![W1: $i] : (~((~((W1 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, sdtlpdtrp0(xN, xi))))))) | (~((~(W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W1, W2)))))))))) | (~((~((W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W0!31, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, tptp_fun_W2_6(W0!31, sdtlpdtrp0(xN, xi))))))) | (~((~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2)))))))))),
% 1.09/0.96 inference(quant_inst,[status(thm)],[])).
% 1.09/0.96 tff(264,plain,
% 1.09/0.96 (~((~((W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W0!31, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, tptp_fun_W2_6(W0!31, sdtlpdtrp0(xN, xi))))))) | (~((~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2))))))))),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[263, 262])).
% 1.09/0.96 tff(265,plain,
% 1.09/0.96 (((~((W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))) | (~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~((~aElementOf0(tptp_fun_W2_6(W0!31, sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, tptp_fun_W2_6(W0!31, sdtlpdtrp0(xN, xi))))))) | (~((~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2)))))))) | ((~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2))))))),
% 1.09/0.96 inference(tautology,[status(thm)],[])).
% 1.09/0.96 tff(266,plain,
% 1.09/0.96 ((~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2)))))),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[265, 264])).
% 1.09/0.96 tff(267,plain,
% 1.09/0.96 (((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2)))) | aElementOf0(W0!31, sdtlpdtrp0(xN, xi))),
% 1.09/0.96 inference(tautology,[status(thm)],[])).
% 1.09/0.96 tff(268,plain,
% 1.09/0.96 ((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2)))),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[267, 189])).
% 1.09/0.96 tff(269,plain,
% 1.09/0.96 ((~((~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2))))))) | (~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2)))))),
% 1.09/0.96 inference(tautology,[status(thm)],[])).
% 1.09/0.96 tff(270,plain,
% 1.09/0.96 ((~((~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aElementOf0(W0!31, sdtlpdtrp0(xN, xi))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(W0!31, W2))))))) | (~(W0!31 = szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[269, 268])).
% 1.09/0.96 tff(271,plain,
% 1.09/0.96 ($false),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[270, 266, 200])).
% 1.09/0.97 % SZS output end Proof
%------------------------------------------------------------------------------