TSTP Solution File: NUM615+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM615+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:55 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM615+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.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 12:34:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(szDzizrdt0_type, type, (
% 0.19/0.48 szDzizrdt0: $i > $i)).
% 0.19/0.48 tff(xd_type, type, (
% 0.19/0.48 xd: $i)).
% 0.19/0.48 tff(sdtlpdtrp0_type, type, (
% 0.19/0.48 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_W0_44_type, type, (
% 0.19/0.48 tptp_fun_W0_44: $i)).
% 0.19/0.48 tff(aElementOf0_type, type, (
% 0.19/0.48 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.48 tff(szDzozmdt0_type, type, (
% 0.19/0.48 szDzozmdt0: $i > $i)).
% 0.19/0.48 tff(xN_type, type, (
% 0.19/0.48 xN: $i)).
% 0.19/0.48 tff(sdtlbdtrb0_type, type, (
% 0.19/0.48 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.19/0.48 tff(szmzizndt0_type, type, (
% 0.19/0.48 szmzizndt0: $i > $i)).
% 0.19/0.48 tff(xQ_type, type, (
% 0.19/0.48 xQ: $i)).
% 0.19/0.48 tff(xe_type, type, (
% 0.19/0.48 xe: $i)).
% 0.19/0.48 tff(xp_type, type, (
% 0.19/0.48 xp: $i)).
% 0.19/0.48 tff(1,plain,
% 0.19/0.48 (^[W0: $i] : rewrite((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp)) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp)) <=> ?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp)) <=> ?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(4,axiom,(?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__5182')).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.48 tff(6,plain,
% 0.19/0.48 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.48 tff(7,plain,(
% 0.19/0.48 aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0!44) = szmzizndt0(xQ))),
% 0.19/0.48 inference(skolemize,[status(sab)],[6])).
% 0.19/0.48 tff(8,plain,
% 0.19/0.48 (aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[7])).
% 0.19/0.48 tff(9,plain,
% 0.19/0.48 ((aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0!44, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd)))))) | (~aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(10,plain,
% 0.19/0.48 (aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0!44, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.48 tff(11,plain,
% 0.19/0.48 (^[W0: $i] : refl(((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))) <=> ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(12,plain,
% 0.19/0.48 (![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))) <=> ![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))), ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))))), rewrite((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))), ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))))), (((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))) <=> ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))), rewrite(((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))) <=> (~((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))))), (((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))) <=> (~((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))))), ((~((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))) <=> (~(~((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))))))), rewrite((~(~((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))))) <=> ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))), ((~((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))) <=> ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(14,plain,
% 0.19/0.48 (![W0: $i] : (~((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))) <=> ![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.48 tff(15,plain,
% 0.19/0.48 ((~?[W0: $i] : ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))) <=> (~?[W0: $i] : ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(16,plain,
% 0.19/0.48 ((~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))) <=> (~?[W0: $i] : ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 ((~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))) <=> (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 ((~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))) <=> (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 ((~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))) <=> (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(20,axiom,(~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.19/0.48 tff(21,plain,
% 0.19/0.48 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.48 tff(22,plain,
% 0.19/0.48 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.19/0.48 tff(27,plain,
% 0.19/0.48 (~?[W0: $i] : ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (~?[W0: $i] : ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[27, 15])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 (~?[W0: $i] : ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[28, 15])).
% 0.19/0.48 tff(30,plain,
% 0.19/0.48 (~?[W0: $i] : ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[29, 15])).
% 0.19/0.48 tff(31,plain,
% 0.19/0.48 (^[W0: $i] : refl($oeq((~((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ)))), (~((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(32,plain,(
% 0.19/0.49 ![W0: $i] : (~((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.49 inference(nnf-neg,[status(sab)],[30, 31])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 (![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[32, 14])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 (![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[33, 12])).
% 0.19/0.49 tff(35,plain,
% 0.19/0.49 (sdtlpdtrp0(xe, W0!44) = szmzizndt0(xQ)),
% 0.19/0.49 inference(and_elim,[status(thm)],[7])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 (((~![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))) | ((~(aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0!44, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0!44) = szmzizndt0(xQ))))) <=> ((~![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))) | (~(aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0!44, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0!44) = szmzizndt0(xQ))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 ((~![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))) | ((~(aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0!44, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0!44) = szmzizndt0(xQ))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 ((~![W0: $i] : ((~(aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0) = szmzizndt0(xQ))))) | (~(aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))) | (~((~aElementOf0(W0!44, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))))))) | (~(sdtlpdtrp0(xe, W0!44) = szmzizndt0(xQ)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[38, 35, 34, 10])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------