%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM293_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n021.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 : Tue May 5 06:23:07 PM UTC 2026
% Result : Theorem 0.29s 0.50s
% Output : Proof 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM293_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n021.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 20:27:27 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.29/0.50 % SZS status Theorem
% 0.29/0.50 % SZS output start Proof
% 0.29/0.50 tff(vtvalue_type, type, (
% 0.29/0.50 vtvalue: vTable > vQuery)).
% 0.29/0.50 tff(tptp_fun_Vt0_307_type, type, (
% 0.29/0.50 tptp_fun_Vt0_307: vTable)).
% 0.29/0.50 tff(vq1_type, type, (
% 0.29/0.50 vq1: vQuery)).
% 0.29/0.50 tff(vptcheck_type, type, (
% 0.29/0.50 vptcheck: ( vTTContext * vQuery * vTType ) > $o)).
% 0.29/0.50 tff(tptp_fun_Vtt_309_type, type, (
% 0.29/0.50 tptp_fun_Vtt_309: vTType)).
% 0.29/0.50 tff(tptp_fun_Vqr_308_type, type, (
% 0.29/0.50 tptp_fun_Vqr_308: vQuery)).
% 0.29/0.50 tff(tptp_fun_Vttc_310_type, type, (
% 0.29/0.50 tptp_fun_Vttc_310: vTTContext)).
% 0.29/0.50 tff(vsomeQuery_type, type, (
% 0.29/0.50 vsomeQuery: vQuery > vOptQuery)).
% 0.29/0.50 tff(vreduce_type, type, (
% 0.29/0.50 vreduce: ( vQuery * vTStore ) > vOptQuery)).
% 0.29/0.50 tff(tptp_fun_Vts_311_type, type, (
% 0.29/0.50 tptp_fun_Vts_311: vTStore)).
% 0.29/0.50 tff(vUnion_type, type, (
% 0.29/0.50 vUnion: ( vQuery * vQuery ) > vQuery)).
% 0.29/0.50 tff(vq2_type, type, (
% 0.29/0.50 vq2: vQuery)).
% 0.29/0.50 tff(vstoreContextConsistent_type, type, (
% 0.29/0.50 vstoreContextConsistent: ( vTStore * vTTContext ) > $o)).
% 0.29/0.50 tff(1,plain,
% 0.29/0.50 ((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))) <=> (~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(2,plain,
% 0.29/0.50 ((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (((vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt))) <=> (~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(3,axiom,(~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (((vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Preservation-Union'')).
% 0.29/0.50 tff(4,plain,
% 0.29/0.50 (~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.29/0.50 tff(5,plain,
% 0.29/0.50 (~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.29/0.50 tff(6,plain,
% 0.29/0.50 (~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.29/0.50 tff(7,plain,
% 0.29/0.50 (~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.29/0.50 tff(8,plain,(
% 0.29/0.50 ~((~(vstoreContextConsistent(Vts!311, Vttc!310) & vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309) & (vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308)))) | vptcheck(Vttc!310, Vqr!308, Vtt!309))),
% 0.29/0.50 inference(skolemize,[status(sab)],[7])).
% 0.29/0.50 tff(9,plain,
% 0.29/0.50 (~vptcheck(Vttc!310, Vqr!308, Vtt!309)),
% 0.29/0.50 inference(or_elim,[status(thm)],[8])).
% 0.29/0.50 tff(10,plain,
% 0.29/0.50 (vstoreContextConsistent(Vts!311, Vttc!310) & vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309) & (vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))),
% 0.29/0.50 inference(or_elim,[status(thm)],[8])).
% 0.29/0.50 tff(11,plain,
% 0.29/0.50 (vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308)),
% 0.29/0.50 inference(and_elim,[status(thm)],[10])).
% 0.29/0.50 tff(12,plain,
% 0.29/0.50 (vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)),
% 0.29/0.50 inference(and_elim,[status(thm)],[10])).
% 0.29/0.50 tff(13,plain,
% 0.29/0.50 (vstoreContextConsistent(Vts!311, Vttc!310)),
% 0.29/0.50 inference(and_elim,[status(thm)],[10])).
% 0.29/0.50 tff(14,plain,
% 0.29/0.50 (^[Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : refl((vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) <=> (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(15,plain,
% 0.29/0.50 (![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) <=> ![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[14])).
% 0.29/0.50 tff(16,plain,
% 0.29/0.50 (^[Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : trans(monotonicity(rewrite(((vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) <=> ((vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))), ((((vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> (((vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)))), rewrite((((vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))), ((((vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(17,plain,
% 0.29/0.50 (![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (((vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> ![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[16])).
% 0.29/0.50 tff(18,plain,
% 0.29/0.50 (![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> ![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(19,plain,
% 0.29/0.50 (^[Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) <=> (![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc))), (((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) <=> ((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)))), rewrite(((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) <=> (![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt))), (((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) <=> (![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)))), ((((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) <=> ((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))), rewrite(((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) <=> (![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))), ((((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) <=> (![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))), (((((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)) <=> ((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)))), rewrite(((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)) <=> ((~(![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))), (((((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)) <=> ((~(![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(20,plain,
% 0.29/0.50 (![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)) <=> ![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[19])).
% 0.29/0.50 tff(21,axiom,(![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((((![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Preservation-Union-q1'')).
% 0.29/0.50 tff(22,plain,
% 0.29/0.50 (![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.29/0.50 tff(23,plain,
% 0.29/0.50 (![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : ((~(![Vt0: vTable] : (~(vq1 = vtvalue(Vt0))) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.29/0.50 tff(24,plain,(
% 0.29/0.50 ![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (((vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.50 inference(skolemize,[status(sab)],[23])).
% 0.29/0.50 tff(25,plain,
% 0.29/0.50 (![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.29/0.50 tff(26,plain,
% 0.29/0.50 (![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.29/0.50 tff(27,plain,
% 0.29/0.50 (((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | ((vq1 = vtvalue(Vt0!307)) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))) <=> ((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vq1 = vtvalue(Vt0!307)) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(28,plain,
% 0.29/0.50 ((vptcheck(Vttc!310, Vqr!308, Vtt!309) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308)))) <=> ((vq1 = vtvalue(Vt0!307)) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(29,plain,
% 0.29/0.50 (((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))) <=> ((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | ((vq1 = vtvalue(Vt0!307)) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308)))))),
% 0.29/0.50 inference(monotonicity,[status(thm)],[28])).
% 0.29/0.50 tff(30,plain,
% 0.29/0.50 (((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))) <=> ((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vq1 = vtvalue(Vt0!307)) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))),
% 0.29/0.50 inference(transitivity,[status(thm)],[29, 27])).
% 0.29/0.50 tff(31,plain,
% 0.29/0.50 ((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))),
% 0.29/0.50 inference(quant_inst,[status(thm)],[])).
% 0.29/0.50 tff(32,plain,
% 0.29/0.50 ((~![Vts: vTStore, Vttc: vTTContext, Vtt: vTType, Vqr: vQuery] : (vptcheck(Vttc, Vqr, Vtt) | (vq1 = vtvalue(Vt0!307)) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vq1 = vtvalue(Vt0!307)) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.29/0.50 tff(33,plain,
% 0.29/0.50 (vq1 = vtvalue(Vt0!307)),
% 0.29/0.50 inference(unit_resolution,[status(thm)],[32, 26, 13, 12, 11, 9])).
% 0.29/0.50 tff(34,plain,
% 0.29/0.50 (^[Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : refl((vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) <=> (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(35,plain,
% 0.29/0.50 (![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) <=> ![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[34])).
% 0.29/0.51 tff(36,plain,
% 0.29/0.51 (^[Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : trans(monotonicity(trans(monotonicity(rewrite(((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) <=> (~((~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))))), ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) <=> (~(~((~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))))))), rewrite((~(~((~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))))) <=> ((~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))), ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) <=> ((~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))))), (((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> (((~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)))), rewrite((((~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))), (((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(37,plain,
% 0.29/0.51 (![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> ![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[36])).
% 0.29/0.51 tff(38,plain,
% 0.29/0.51 (![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt)) <=> ![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(39,plain,
% 0.29/0.51 (^[Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : trans(monotonicity(trans(monotonicity(rewrite((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) <=> ((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt))), (((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) <=> (((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))), rewrite((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) <=> ((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))), (((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) <=> ((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))), ((((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)) <=> (((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)))), rewrite((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)) <=> ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))), ((((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)) <=> ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(40,plain,
% 0.29/0.51 (![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt)) <=> ![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[39])).
% 0.29/0.51 tff(41,axiom,(![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (((((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc)) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))) => vptcheck(Vttc, Vqr, Vtt))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Preservation-Union-tvalue'')).
% 0.29/0.51 tff(42,plain,
% 0.29/0.51 (![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.29/0.51 tff(43,plain,
% 0.29/0.51 (![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.29/0.51 tff(44,plain,(
% 0.29/0.51 ![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : ((~((vq1 = vtvalue(Vt)) & vstoreContextConsistent(Vts, Vttc) & vptcheck(Vttc, vUnion(vq1, vq2), Vtt) & (vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr)))) | vptcheck(Vttc, Vqr, Vtt))),
% 0.29/0.51 inference(skolemize,[status(sab)],[43])).
% 0.29/0.51 tff(45,plain,
% 0.29/0.51 (![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.29/0.51 tff(46,plain,
% 0.29/0.51 (![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.29/0.51 tff(47,plain,
% 0.29/0.51 (((~![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))) | (~(vq1 = vtvalue(Vt0!307))))) <=> ((~![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))) | (~(vq1 = vtvalue(Vt0!307))))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(48,plain,
% 0.29/0.51 ((vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~(vq1 = vtvalue(Vt0!307))) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308)))) <=> (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))) | (~(vq1 = vtvalue(Vt0!307))))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(49,plain,
% 0.29/0.51 (((~![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~(vq1 = vtvalue(Vt0!307))) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))) <=> ((~![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))) | (~(vq1 = vtvalue(Vt0!307)))))),
% 0.29/0.51 inference(monotonicity,[status(thm)],[48])).
% 0.29/0.51 tff(50,plain,
% 0.29/0.51 (((~![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~(vq1 = vtvalue(Vt0!307))) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))) <=> ((~![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))) | (~(vq1 = vtvalue(Vt0!307))))),
% 0.29/0.53 inference(transitivity,[status(thm)],[49, 47])).
% 0.29/0.53 tff(51,plain,
% 0.29/0.53 ((~![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | (vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~(vq1 = vtvalue(Vt0!307))) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))))),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(52,plain,
% 0.29/0.53 ((~![Vqr: vQuery, Vt: vTable, Vttc: vTTContext, Vts: vTStore, Vtt: vTType] : (vptcheck(Vttc, Vqr, Vtt) | (~(vq1 = vtvalue(Vt))) | (~vstoreContextConsistent(Vts, Vttc)) | (~vptcheck(Vttc, vUnion(vq1, vq2), Vtt)) | (~(vreduce(vUnion(vq1, vq2), Vts) = vsomeQuery(Vqr))))) | vptcheck(Vttc!310, Vqr!308, Vtt!309) | (~vstoreContextConsistent(Vts!311, Vttc!310)) | (~vptcheck(Vttc!310, vUnion(vq1, vq2), Vtt!309)) | (~(vreduce(vUnion(vq1, vq2), Vts!311) = vsomeQuery(Vqr!308))) | (~(vq1 = vtvalue(Vt0!307)))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.29/0.53 tff(53,plain,
% 0.29/0.53 ($false),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[52, 46, 13, 12, 11, 9, 33])).
% 0.29/0.53 % SZS output end Proof
% 0.29/0.53 % E exiting
%------------------------------------------------------------------------------