TSTP Solution File: NUM618+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM618+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 13:10:56 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM618+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.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 12:47:35 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.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 tff(aElementOf0_type, type, (
% 0.19/0.51 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.51 tff(szDzozmdt0_type, type, (
% 0.19/0.51 szDzozmdt0: $i > $i)).
% 0.19/0.51 tff(xN_type, type, (
% 0.19/0.51 xN: $i)).
% 0.19/0.51 tff(tptp_fun_W0_45_type, type, (
% 0.19/0.51 tptp_fun_W0_45: $i)).
% 0.19/0.51 tff(sdtlpdtrp0_type, type, (
% 0.19/0.51 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.19/0.51 tff(xe_type, type, (
% 0.19/0.51 xe: $i)).
% 0.19/0.51 tff(xx_type, type, (
% 0.19/0.51 xx: $i)).
% 0.19/0.51 tff(sdtlbdtrb0_type, type, (
% 0.19/0.51 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.19/0.51 tff(szDzizrdt0_type, type, (
% 0.19/0.51 szDzizrdt0: $i > $i)).
% 0.19/0.51 tff(xd_type, type, (
% 0.19/0.51 xd: $i)).
% 0.19/0.51 tff(szNzAzT0_type, type, (
% 0.19/0.51 szNzAzT0: $i)).
% 0.19/0.51 tff(aSet0_type, type, (
% 0.19/0.51 aSet0: $i > $o)).
% 0.19/0.51 tff(xT_type, type, (
% 0.19/0.51 xT: $i)).
% 0.19/0.51 tff(1,plain,
% 0.19/0.51 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx)) <=> ?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(2,axiom,(aElementOf0(xx, szNzAzT0) & ?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__5365')).
% 0.19/0.51 tff(3,plain,
% 0.19/0.51 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx))),
% 0.19/0.51 inference(and_elim,[status(thm)],[2])).
% 0.19/0.51 tff(4,plain,
% 0.19/0.51 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xx))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.19/0.51 tff(5,plain,(
% 0.19/0.51 aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0!45) = xx)),
% 0.19/0.51 inference(skolemize,[status(sab)],[4])).
% 0.19/0.51 tff(6,plain,
% 0.19/0.51 (sdtlpdtrp0(xe, W0!45) = xx),
% 0.19/0.51 inference(and_elim,[status(thm)],[5])).
% 0.19/0.51 tff(7,plain,
% 0.19/0.51 (xx = sdtlpdtrp0(xe, W0!45)),
% 0.19/0.51 inference(symmetry,[status(thm)],[6])).
% 0.19/0.51 tff(8,plain,
% 0.19/0.51 (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(9,plain,
% 0.19/0.51 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.51 tff(10,plain,
% 0.19/0.51 (^[W0: $i] : trans(monotonicity(rewrite((aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0)))))), ((~(aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))) <=> (~(~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0)))))))), rewrite((~(~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0)))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))), ((~(aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(11,plain,
% 0.19/0.51 (![W0: $i] : (~(aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.51 tff(12,plain,
% 0.19/0.51 ((~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))) <=> (~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(13,plain,
% 0.19/0.51 ((~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))) <=> (~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(14,plain,
% 0.19/0.51 ((~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))) <=> (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(15,axiom,(~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.19/0.51 tff(16,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.51 tff(17,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.19/0.51 tff(18,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.51 tff(19,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.51 tff(20,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.19/0.51 tff(21,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.19/0.51 tff(22,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.19/0.51 tff(23,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.19/0.51 tff(24,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[23, 12])).
% 0.19/0.51 tff(25,plain,
% 0.19/0.51 (~?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[24, 12])).
% 0.19/0.51 tff(26,plain,
% 0.19/0.51 (^[W0: $i] : refl($oeq((~(aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0)))), (~(aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(27,plain,(
% 0.19/0.51 ![W0: $i] : (~(aElementOf0(W0, szDzozmdt0(xN)) & (xx = sdtlpdtrp0(xe, W0))))),
% 0.19/0.51 inference(nnf-neg,[status(sab)],[25, 26])).
% 0.19/0.51 tff(28,plain,
% 0.19/0.51 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[27, 11])).
% 0.19/0.51 tff(29,plain,
% 0.19/0.51 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[28, 9])).
% 0.19/0.51 tff(30,plain,
% 0.19/0.51 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))) | ((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0!45))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))) | (~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0!45))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(31,plain,
% 0.19/0.51 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))) | ((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0!45))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(32,plain,
% 0.19/0.51 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0))))) | (~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(xx = sdtlpdtrp0(xe, W0!45)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.51 tff(33,plain,
% 0.19/0.51 (~aElementOf0(W0!45, szDzozmdt0(xN))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[32, 29, 7])).
% 0.19/0.51 tff(34,plain,
% 0.19/0.51 (^[W0: $i] : refl((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)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(35,plain,
% 0.19/0.51 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.51 tff(36,plain,
% 0.19/0.51 (^[W0: $i] : 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)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(37,plain,
% 0.19/0.51 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.52 tff(38,plain,
% 0.19/0.52 (^[W0: $i] : rewrite((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(39,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.52 tff(40,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(41,axiom,((aElementOf0(szDzizrdt0(xd), xT) & aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4854')).
% 0.19/0.52 tff(42,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.19/0.52 inference(and_elim,[status(thm)],[41])).
% 0.19/0.52 tff(43,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.19/0.52 tff(44,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.52 tff(45,plain,(
% 0.19/0.52 ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[44])).
% 0.19/0.52 tff(46,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[45, 37])).
% 0.19/0.52 tff(47,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[46, 35])).
% 0.19/0.52 tff(48,plain,
% 0.19/0.52 ((~![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(49,plain,
% 0.19/0.52 (aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.52 tff(50,plain,
% 0.19/0.52 (aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[5])).
% 0.19/0.52 tff(51,plain,
% 0.19/0.52 ((~(aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))))))) | (~aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(52,plain,
% 0.19/0.52 ((~(aElementOf0(W0!45, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))))))) | (~((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.52 tff(53,plain,
% 0.19/0.52 (~((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.19/0.52 tff(54,plain,
% 0.19/0.52 (((~aElementOf0(W0!45, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!45) = szDzizrdt0(xd)))) | aElementOf0(W0!45, szDzozmdt0(xN))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(55,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[54, 53, 33])).
% 0.19/0.52 % SZS output end Proof
%------------------------------------------------------------------------------