TSTP Solution File: NUM601+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM601+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 13:10:48 EDT 2022
% Result : Theorem 27.50s 17.95s
% Output : Proof 27.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM601+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 12:14:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 27.50/17.95 % SZS status Theorem
% 27.50/17.95 % SZS output start Proof
% 27.50/17.95 tff(aElementOf0_type, type, (
% 27.50/17.95 aElementOf0: ( $i * $i ) > $o)).
% 27.50/17.95 tff(sdtlpdtrp0_type, type, (
% 27.50/17.95 sdtlpdtrp0: ( $i * $i ) > $i)).
% 27.50/17.95 tff(tptp_fun_W1_42_type, type, (
% 27.50/17.95 tptp_fun_W1_42: $i > $i)).
% 27.50/17.95 tff(tptp_fun_W0_43_type, type, (
% 27.50/17.95 tptp_fun_W0_43: $i)).
% 27.50/17.95 tff(xN_type, type, (
% 27.50/17.95 xN: $i)).
% 27.50/17.95 tff(xe_type, type, (
% 27.50/17.95 xe: $i)).
% 27.50/17.95 tff(sdtlbdtrb0_type, type, (
% 27.50/17.95 sdtlbdtrb0: ( $i * $i ) > $i)).
% 27.50/17.95 tff(szDzizrdt0_type, type, (
% 27.50/17.95 szDzizrdt0: $i > $i)).
% 27.50/17.95 tff(xd_type, type, (
% 27.50/17.95 xd: $i)).
% 27.50/17.95 tff(szDzozmdt0_type, type, (
% 27.50/17.95 szDzozmdt0: $i > $i)).
% 27.50/17.95 tff(sdtlcdtrc0_type, type, (
% 27.50/17.95 sdtlcdtrc0: ( $i * $i ) > $i)).
% 27.50/17.95 tff(sz00_type, type, (
% 27.50/17.95 sz00: $i)).
% 27.50/17.95 tff(xS_type, type, (
% 27.50/17.95 xS: $i)).
% 27.50/17.95 tff(xO_type, type, (
% 27.50/17.95 xO: $i)).
% 27.50/17.95 tff(aSubsetOf0_type, type, (
% 27.50/17.95 aSubsetOf0: ( $i * $i ) > $o)).
% 27.50/17.95 tff(szNzAzT0_type, type, (
% 27.50/17.95 szNzAzT0: $i)).
% 27.50/17.95 tff(sdtlseqdt0_type, type, (
% 27.50/17.95 sdtlseqdt0: ( $i * $i ) > $o)).
% 27.50/17.95 tff(szmzizndt0_type, type, (
% 27.50/17.95 szmzizndt0: $i > $i)).
% 27.50/17.95 tff(aFunction0_type, type, (
% 27.50/17.95 aFunction0: $i > $o)).
% 27.50/17.95 tff(1,plain,
% 27.50/17.95 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))))),
% 27.50/17.95 inference(rewrite,[status(thm)],[])).
% 27.50/17.95 tff(2,plain,
% 27.50/17.95 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))))),
% 27.50/17.95 inference(rewrite,[status(thm)],[])).
% 27.50/17.95 tff(3,plain,
% 27.50/17.95 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 27.50/17.95 inference(rewrite,[status(thm)],[])).
% 27.50/17.95 tff(4,plain,
% 27.50/17.95 ((~![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 27.50/17.95 inference(rewrite,[status(thm)],[])).
% 27.50/17.95 tff(5,axiom,(~(![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS)) | aSubsetOf0(xO, xS))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 27.50/17.95 tff(6,plain,
% 27.50/17.95 (~![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS))),
% 27.50/17.95 inference(or_elim,[status(thm)],[5])).
% 27.50/17.95 tff(7,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[6, 4])).
% 27.50/17.95 tff(8,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[7, 3])).
% 27.50/17.95 tff(9,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[8, 3])).
% 27.50/17.95 tff(10,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[9, 3])).
% 27.50/17.95 tff(11,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[10, 2])).
% 27.50/17.95 tff(12,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[11, 1])).
% 27.50/17.95 tff(13,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[12, 1])).
% 27.50/17.95 tff(14,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[13, 1])).
% 27.50/17.95 tff(15,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[14, 1])).
% 27.50/17.95 tff(16,plain,
% 27.50/17.95 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 27.50/17.95 inference(modus_ponens,[status(thm)],[15, 1])).
% 27.50/17.95 tff(17,plain,(
% 27.50/17.95 ~((~aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)))),
% 27.50/17.95 inference(skolemize,[status(sab)],[16])).
% 27.64/17.95 tff(18,plain,
% 27.64/17.95 (aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 27.64/17.95 inference(or_elim,[status(thm)],[17])).
% 27.64/17.95 tff(19,plain,
% 27.64/17.95 (((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 27.64/17.95 inference(tautology,[status(thm)],[])).
% 27.64/17.95 tff(20,plain,
% 27.64/17.95 ((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 27.64/17.95 inference(unit_resolution,[status(thm)],[19, 18])).
% 27.64/17.95 tff(21,plain,
% 27.64/17.95 (^[W0: $i] : trans(monotonicity(monotonicity(monotonicity(rewrite((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) <=> (~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))), (((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))))), ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) <=> (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))), rewrite((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) <=> (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))), (((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))))), rewrite(((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))), (((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))))),
% 27.64/17.96 inference(bind,[status(th)],[])).
% 27.64/17.96 tff(22,plain,
% 27.64/17.96 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))),
% 27.64/17.96 inference(quant_intro,[status(thm)],[21])).
% 27.64/17.96 tff(23,plain,
% 27.64/17.96 (^[W0: $i] : refl(((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))))),
% 27.64/17.96 inference(bind,[status(th)],[])).
% 27.64/17.96 tff(24,plain,
% 27.64/17.96 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 27.64/17.96 inference(quant_intro,[status(thm)],[23])).
% 27.64/17.96 tff(25,plain,
% 27.64/17.96 (^[W0: $i] : rewrite(((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))))),
% 27.64/17.96 inference(bind,[status(th)],[])).
% 27.64/17.96 tff(26,plain,
% 27.64/17.96 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 27.64/17.96 inference(quant_intro,[status(thm)],[25])).
% 27.64/17.96 tff(27,plain,
% 27.64/17.96 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 27.64/17.96 inference(transitivity,[status(thm)],[26, 24])).
% 27.64/17.96 tff(28,plain,
% 27.64/17.96 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite((aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) <=> (~((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))), ((~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> (~(~((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))))), rewrite((~(~((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))) <=> ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))), ((~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))))), (![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))))), ((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) <=> (![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))), rewrite((![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) <=> (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))))), ((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) <=> (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))), rewrite((aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)) <=> (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))), (((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))))), rewrite(((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))), (((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))) <=> ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))))),
% 27.64/17.96 inference(bind,[status(th)],[])).
% 27.64/17.96 tff(29,plain,
% 27.64/17.96 (![W0: $i] : ((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0))) <=> ![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 27.64/17.96 inference(quant_intro,[status(thm)],[28])).
% 27.64/17.96 tff(30,plain,
% 27.64/17.96 (^[W0: $i] : rewrite(((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))),
% 27.64/17.96 inference(bind,[status(th)],[])).
% 27.64/17.96 tff(31,plain,
% 27.64/17.96 (![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 27.64/17.96 inference(quant_intro,[status(thm)],[30])).
% 27.64/17.96 tff(32,plain,
% 27.64/17.96 (![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 27.64/17.96 inference(rewrite,[status(thm)],[])).
% 27.64/17.96 tff(33,plain,
% 27.64/17.96 (^[W0: $i] : trans(monotonicity(rewrite((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) <=> (?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite(((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) <=> (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))), ((((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)) <=> ((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))), rewrite(((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)) <=> (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))), ((((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)) <=> (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))), (?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)) <=> ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))), (((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))), rewrite(((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))), (((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))))),
% 27.64/17.96 inference(bind,[status(th)],[])).
% 27.64/17.96 tff(34,plain,
% 27.64/17.96 (![W0: $i] : ((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0))) <=> ![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 27.64/17.96 inference(quant_intro,[status(thm)],[33])).
% 27.64/17.96 tff(35,axiom,(![W0: $i] : ((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO)) => ?[W1: $i] : (((aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4982')).
% 27.64/17.96 tff(36,plain,
% 27.64/17.96 (![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 27.64/17.96 inference(modus_ponens,[status(thm)],[35, 34])).
% 27.64/17.96 tff(37,plain,
% 27.64/17.96 (![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 27.64/17.96 inference(modus_ponens,[status(thm)],[36, 32])).
% 27.64/17.96 tff(38,plain,
% 27.64/17.96 (![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 27.64/17.96 inference(modus_ponens,[status(thm)],[37, 31])).
% 27.64/17.96 tff(39,plain,(
% 27.64/17.96 ![W0: $i] : ((![W1: $i] : (~(aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))) & (~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd)) & aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))),
% 27.64/17.96 inference(skolemize,[status(sab)],[38])).
% 27.64/17.96 tff(40,plain,
% 27.64/17.96 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 27.64/17.96 inference(modus_ponens,[status(thm)],[39, 29])).
% 27.64/17.96 tff(41,plain,
% 27.64/17.96 (![W0: $i] : ((~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))))),
% 27.64/17.96 inference(modus_ponens,[status(thm)],[40, 27])).
% 27.64/17.96 tff(42,plain,
% 27.64/17.96 (![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))),
% 27.64/17.96 inference(modus_ponens,[status(thm)],[41, 22])).
% 27.64/17.96 tff(43,plain,
% 27.64/17.96 (((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))) | ((~((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))) <=> ((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))),
% 27.64/17.96 inference(rewrite,[status(thm)],[])).
% 27.64/17.96 tff(44,plain,
% 27.64/17.96 ((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))) | ((~((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))),
% 27.64/17.96 inference(quant_inst,[status(thm)],[])).
% 27.64/17.96 tff(45,plain,
% 27.64/17.96 ((~![W0: $i] : ((~((~aElementOf0(tptp_fun_W1_42(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0)) = W0)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0)))) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))) | (~((~![W1: $i] : ((~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!43)))) | aElementOf0(W0!43, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))))),
% 27.64/17.96 inference(modus_ponens,[status(thm)],[44, 43])).
% 27.64/17.96 tff(46,plain,
% 27.64/17.96 (~((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)))),
% 27.64/17.96 inference(unit_resolution,[status(thm)],[45, 42, 20])).
% 27.64/17.96 tff(47,plain,
% 27.64/17.96 (((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43))) | (sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43)),
% 27.64/17.96 inference(tautology,[status(thm)],[])).
% 27.64/17.96 tff(48,plain,
% 27.64/17.96 (sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43),
% 27.64/17.96 inference(unit_resolution,[status(thm)],[47, 46])).
% 27.64/17.96 tff(49,plain,
% 27.64/17.96 (W0!43 = sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43))),
% 27.64/17.96 inference(symmetry,[status(thm)],[48])).
% 27.64/17.96 tff(50,plain,
% 27.64/17.96 (aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))) <=> aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 27.64/17.96 inference(monotonicity,[status(thm)],[49])).
% 27.64/17.96 tff(51,plain,
% 27.64/17.96 (aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))) <=> aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 27.64/17.96 inference(symmetry,[status(thm)],[50])).
% 27.64/17.96 tff(52,plain,
% 27.64/17.96 (((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_42(W0!43)) = szDzizrdt0(xd))) | (~aElementOf0(tptp_fun_W1_42(W0!43), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = W0!43))) | aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))),
% 27.64/17.96 inference(tautology,[status(thm)],[])).
% 27.64/17.96 tff(53,plain,
% 27.64/17.96 (aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))),
% 27.64/17.96 inference(unit_resolution,[status(thm)],[52, 46])).
% 27.64/17.96 tff(54,plain,
% 27.64/17.96 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))))))),
% 27.64/17.96 inference(bind,[status(th)],[])).
% 27.64/17.96 tff(55,plain,
% 27.64/17.96 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))),
% 27.64/17.96 inference(quant_intro,[status(thm)],[54])).
% 27.64/17.96 tff(56,plain,
% 27.64/17.96 (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(57,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[56])).
% 27.64/17.97 tff(58,plain,
% 27.64/17.97 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(59,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[58])).
% 27.64/17.97 tff(60,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))))),
% 27.64/17.97 inference(transitivity,[status(thm)],[59, 57])).
% 27.64/17.97 tff(61,plain,
% 27.64/17.97 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(62,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[61])).
% 27.64/17.97 tff(63,plain,
% 27.64/17.97 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(64,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[63])).
% 27.64/17.97 tff(65,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 27.64/17.97 inference(rewrite,[status(thm)],[])).
% 27.64/17.97 tff(66,plain,
% 27.64/17.97 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) <=> (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)))), (((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))), rewrite(((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))), (((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))), ((aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aElementOf0(W0, szNzAzT0) => (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite((aElementOf0(W0, szNzAzT0) => (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))), ((aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(67,plain,
% 27.64/17.97 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[66])).
% 27.64/17.97 tff(68,axiom,((aFunction0(xe) & (szDzozmdt0(xe) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4660')).
% 27.64/17.97 tff(69,plain,
% 27.64/17.97 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 27.64/17.97 inference(and_elim,[status(thm)],[68])).
% 27.64/17.97 tff(70,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[69, 67])).
% 27.64/17.97 tff(71,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[70, 65])).
% 27.64/17.97 tff(72,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[71, 64])).
% 27.64/17.97 tff(73,plain,(
% 27.64/17.97 ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1)) & (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))),
% 27.64/17.97 inference(skolemize,[status(sab)],[72])).
% 27.64/17.97 tff(74,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[73, 62])).
% 27.64/17.97 tff(75,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))))))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[74, 60])).
% 27.64/17.97 tff(76,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[75, 55])).
% 27.64/17.97 tff(77,plain,
% 27.64/17.97 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))))))),
% 27.64/17.97 inference(rewrite,[status(thm)],[])).
% 27.64/17.97 tff(78,plain,
% 27.64/17.97 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))))))),
% 27.64/17.97 inference(quant_inst,[status(thm)],[])).
% 27.64/17.97 tff(79,plain,
% 27.64/17.97 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, W0), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(sdtlpdtrp0(xe, W0), W1))))))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1)))))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[78, 77])).
% 27.64/17.97 tff(80,plain,
% 27.64/17.97 (~((~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1))))),
% 27.64/17.97 inference(unit_resolution,[status(thm)],[79, 76, 53])).
% 27.64/17.97 tff(81,plain,
% 27.64/17.97 (((~aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | (~(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)) = szmzizndt0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | sdtlseqdt0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), W1)))) | aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 27.64/17.97 inference(tautology,[status(thm)],[])).
% 27.64/17.97 tff(82,plain,
% 27.64/17.97 (aElementOf0(sdtlpdtrp0(xe, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 27.64/17.97 inference(unit_resolution,[status(thm)],[81, 80])).
% 27.64/17.97 tff(83,plain,
% 27.64/17.97 (aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[82, 51])).
% 27.64/17.97 tff(84,plain,
% 27.64/17.97 (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0)))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(85,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[84])).
% 27.64/17.97 tff(86,plain,
% 27.64/17.97 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0)))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(87,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[86])).
% 27.64/17.97 tff(88,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(rewrite,[status(thm)],[])).
% 27.64/17.97 tff(89,plain,
% 27.64/17.97 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0)) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0)))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(90,plain,
% 27.64/17.97 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[89])).
% 27.64/17.97 tff(91,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(sz00, W0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mZeroLess')).
% 27.64/17.97 tff(92,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[91, 90])).
% 27.64/17.97 tff(93,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[92, 88])).
% 27.64/17.97 tff(94,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[93, 87])).
% 27.64/17.97 tff(95,plain,(
% 27.64/17.97 ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(skolemize,[status(sab)],[94])).
% 27.64/17.97 tff(96,plain,
% 27.64/17.97 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[95, 85])).
% 27.64/17.97 tff(97,plain,
% 27.64/17.97 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43)))),
% 27.64/17.97 inference(rewrite,[status(thm)],[])).
% 27.64/17.97 tff(98,plain,
% 27.64/17.97 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))) | ((~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43)))),
% 27.64/17.97 inference(quant_inst,[status(thm)],[])).
% 27.64/17.97 tff(99,plain,
% 27.64/17.97 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | sdtlseqdt0(sz00, W0))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))),
% 27.64/17.97 inference(modus_ponens,[status(thm)],[98, 97])).
% 27.64/17.97 tff(100,plain,
% 27.64/17.97 (sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))),
% 27.64/17.97 inference(unit_resolution,[status(thm)],[99, 96, 53])).
% 27.64/17.97 tff(101,plain,
% 27.64/17.97 (^[W0: $i, W1: $i] : rewrite(((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(102,plain,
% 27.64/17.97 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[101])).
% 27.64/17.97 tff(103,plain,
% 27.64/17.97 (^[W0: $i, W1: $i] : refl(((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(104,plain,
% 27.64/17.97 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[103])).
% 27.64/17.97 tff(105,plain,
% 27.64/17.97 (^[W0: $i, W1: $i] : rewrite(((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(106,plain,
% 27.64/17.97 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[105])).
% 27.64/17.97 tff(107,plain,
% 27.64/17.97 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 27.64/17.97 inference(transitivity,[status(thm)],[106, 104])).
% 27.64/17.97 tff(108,plain,
% 27.64/17.97 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), trans(monotonicity(rewrite((aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))) <=> (~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN)))))), ((~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))) <=> (~(~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN)))))))), rewrite((~(~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN)))))) <=> ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))))), ((~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))) <=> ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN)))))), (((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))))) <=> ((~sdtlseqdt0(W1, W0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) | ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))))))), rewrite(((~sdtlseqdt0(W1, W0)) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) | ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))), (((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))))) <=> ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(109,plain,
% 27.64/17.97 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[108])).
% 27.64/17.97 tff(110,plain,
% 27.64/17.97 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN))))), rewrite((![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), rewrite(((~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))))),
% 27.64/17.97 inference(bind,[status(th)],[])).
% 27.64/17.97 tff(111,plain,
% 27.64/17.97 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))),
% 27.64/17.97 inference(quant_intro,[status(thm)],[110])).
% 27.64/17.97 tff(112,plain,
% 27.64/17.97 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 27.64/17.97 inference(rewrite,[status(thm)],[])).
% 27.64/17.97 tff(113,plain,
% 27.64/17.97 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) <=> (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))), ((sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> (sdtlseqdt0(W1, W0) => (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), rewrite((sdtlseqdt0(W1, W0) => (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))), ((sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))) <=> ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))), rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 27.64/17.98 inference(bind,[status(th)],[])).
% 27.64/17.98 tff(114,plain,
% 27.64/17.98 (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 27.64/17.98 inference(quant_intro,[status(thm)],[113])).
% 27.64/17.98 tff(115,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W1, W0) => (![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3754')).
% 27.64/17.98 tff(116,plain,
% 27.64/17.98 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 27.64/17.98 inference(modus_ponens,[status(thm)],[115, 114])).
% 27.64/17.98 tff(117,plain,
% 27.64/17.98 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))),
% 27.64/17.98 inference(modus_ponens,[status(thm)],[116, 112])).
% 27.64/17.98 tff(118,plain,
% 27.64/17.98 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))),
% 27.64/17.98 inference(modus_ponens,[status(thm)],[117, 111])).
% 27.64/17.98 tff(119,plain,(
% 27.64/17.98 ![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1))) & aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~(aElementOf0(W0, szDzozmdt0(xN)) & aElementOf0(W1, szDzozmdt0(xN)))))),
% 27.64/17.98 inference(skolemize,[status(sab)],[118])).
% 27.64/17.98 tff(120,plain,
% 27.64/17.98 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 27.64/17.98 inference(modus_ponens,[status(thm)],[119, 109])).
% 27.64/17.98 tff(121,plain,
% 27.64/17.98 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))) | (~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))))))),
% 27.64/17.98 inference(modus_ponens,[status(thm)],[120, 107])).
% 27.64/17.98 tff(122,plain,
% 27.64/17.98 (![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))),
% 27.64/17.98 inference(modus_ponens,[status(thm)],[121, 102])).
% 27.64/17.98 tff(123,plain,
% 27.64/17.98 (aElementOf0(sz00, szNzAzT0) <=> aElementOf0(sz00, szDzozmdt0(xN))),
% 27.64/17.98 inference(rewrite,[status(thm)],[])).
% 27.64/17.98 tff(124,plain,
% 27.64/17.98 (aElementOf0(sz00, szNzAzT0) <=> aElementOf0(sz00, szNzAzT0)),
% 27.64/17.98 inference(rewrite,[status(thm)],[])).
% 27.64/17.98 tff(125,axiom,(aElementOf0(sz00, szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mZeroNum')).
% 27.64/17.98 tff(126,plain,
% 27.64/17.98 (aElementOf0(sz00, szNzAzT0)),
% 27.64/17.98 inference(modus_ponens,[status(thm)],[125, 124])).
% 27.64/17.98 tff(127,plain,
% 27.64/17.98 (aElementOf0(sz00, szDzozmdt0(xN))),
% 27.64/17.98 inference(modus_ponens,[status(thm)],[126, 123])).
% 27.64/17.98 tff(128,plain,
% 27.64/17.98 (((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 27.64/17.98 inference(rewrite,[status(thm)],[])).
% 27.64/17.98 tff(129,plain,
% 27.64/17.98 (((~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 27.64/17.98 inference(rewrite,[status(thm)],[])).
% 27.64/17.98 tff(130,plain,
% 27.64/17.98 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) <=> (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))),
% 27.64/17.98 inference(rewrite,[status(thm)],[])).
% 27.64/17.98 tff(131,plain,
% 27.64/17.98 (((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))) <=> ((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))),
% 27.64/17.98 inference(monotonicity,[status(thm)],[130])).
% 27.64/17.98 tff(132,plain,
% 27.64/17.98 ((~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) <=> (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))),
% 27.64/17.98 inference(monotonicity,[status(thm)],[131])).
% 27.64/17.98 tff(133,plain,
% 27.64/17.98 (((~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 27.64/17.98 inference(monotonicity,[status(thm)],[132])).
% 27.64/17.98 tff(134,plain,
% 27.64/17.98 (((~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 27.64/17.98 inference(transitivity,[status(thm)],[133, 129])).
% 27.64/17.98 tff(135,plain,
% 27.64/17.98 (((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))))),
% 27.64/17.98 inference(monotonicity,[status(thm)],[134])).
% 27.64/17.98 tff(136,plain,
% 27.64/17.98 (((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 27.64/17.98 inference(transitivity,[status(thm)],[135, 128])).
% 27.64/17.98 tff(137,plain,
% 27.64/17.98 ((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | ((~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 27.64/17.98 inference(quant_inst,[status(thm)],[])).
% 27.67/18.00 tff(138,plain,
% 27.67/18.00 ((~![W0: $i, W1: $i] : ((~sdtlseqdt0(W1, W0)) | (~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, W0), sdtlpdtrp0(xN, W1))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | aElementOf0(W2, sdtlpdtrp0(xN, W1)))))))) | (~aElementOf0(sz00, szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W1_42(W0!43), szDzozmdt0(xN))) | (~sdtlseqdt0(sz00, tptp_fun_W1_42(W0!43))) | (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))),
% 27.67/18.00 inference(modus_ponens,[status(thm)],[137, 136])).
% 27.67/18.00 tff(139,plain,
% 27.67/18.00 (~((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))),
% 27.67/18.00 inference(unit_resolution,[status(thm)],[138, 127, 122, 53, 100])).
% 27.67/18.00 tff(140,plain,
% 27.67/18.00 (((~aSubsetOf0(sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)), sdtlpdtrp0(xN, sz00))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))) | ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))),
% 27.67/18.00 inference(tautology,[status(thm)],[])).
% 27.67/18.00 tff(141,plain,
% 27.67/18.00 (![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))),
% 27.67/18.00 inference(unit_resolution,[status(thm)],[140, 139])).
% 27.67/18.00 tff(142,plain,
% 27.67/18.00 (~aElementOf0(W0!43, sdtlpdtrp0(xN, sz00))),
% 27.67/18.00 inference(or_elim,[status(thm)],[17])).
% 27.67/18.00 tff(143,plain,
% 27.67/18.00 (((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)))),
% 27.67/18.00 inference(rewrite,[status(thm)],[])).
% 27.67/18.00 tff(144,plain,
% 27.67/18.00 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00)))),
% 27.67/18.00 inference(quant_inst,[status(thm)],[])).
% 27.67/18.00 tff(145,plain,
% 27.67/18.00 ((~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!43, sdtlpdtrp0(xN, tptp_fun_W1_42(W0!43)))) | aElementOf0(W0!43, sdtlpdtrp0(xN, sz00))),
% 27.67/18.00 inference(modus_ponens,[status(thm)],[144, 143])).
% 27.67/18.00 tff(146,plain,
% 27.67/18.00 ($false),
% 27.67/18.00 inference(unit_resolution,[status(thm)],[145, 142, 141, 83])).
% 27.67/18.00 % SZS output end Proof
%------------------------------------------------------------------------------