%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM253_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n031.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 06:23:04 PM UTC 2026
% Result : Theorem 0.29s 0.49s
% Output : Proof 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM253_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n031.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 19:48:10 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.29/0.49 % SZS status Theorem
% 0.29/0.49 % SZS output start Proof
% 0.29/0.49 tff(vsomeAType_type, type, (
% 0.29/0.49 vsomeAType: vAType > vOptAType)).
% 0.29/0.49 tff(tptp_fun_Vat_229_type, type, (
% 0.29/0.49 tptp_fun_Vat_229: vAType)).
% 0.29/0.49 tff(vlookupATMap_type, type, (
% 0.29/0.49 vlookupATMap: ( vQID * vATMap ) > vOptAType)).
% 0.29/0.49 tff(vtypeAM_type, type, (
% 0.29/0.49 vtypeAM: vAnsMap > vATMap)).
% 0.29/0.49 tff(vabind_type, type, (
% 0.29/0.49 vabind: ( vQID * vAval * vAnsMap ) > vAnsMap)).
% 0.29/0.49 tff(vam1_type, type, (
% 0.29/0.49 vam1: vAnsMap)).
% 0.29/0.49 tff(tptp_fun_Va_230_type, type, (
% 0.29/0.49 tptp_fun_Va_230: vAval)).
% 0.29/0.49 tff(tptp_fun_Vqid1_231_type, type, (
% 0.29/0.49 tptp_fun_Vqid1_231: vQID)).
% 0.29/0.49 tff(tptp_fun_Vqid_227_type, type, (
% 0.29/0.49 tptp_fun_Vqid_227: vQID)).
% 0.29/0.49 tff(vsomeAval_type, type, (
% 0.29/0.49 vsomeAval: vAval > vOptAval)).
% 0.29/0.49 tff(tptp_fun_Vavr_228_type, type, (
% 0.29/0.49 tptp_fun_Vavr_228: vAval)).
% 0.29/0.49 tff(vlookupAnsMap_type, type, (
% 0.29/0.49 vlookupAnsMap: ( vQID * vAnsMap ) > vOptAval)).
% 0.29/0.49 tff(vtypeOf_type, type, (
% 0.29/0.49 vtypeOf: vAval > vAType)).
% 0.29/0.49 tff(1,plain,
% 0.29/0.49 ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))) <=> (~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)))),
% 0.29/0.49 inference(rewrite,[status(thm)],[])).
% 0.29/0.49 tff(2,plain,
% 0.29/0.49 ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : (((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat))) <=> (~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)))),
% 0.29/0.49 inference(rewrite,[status(thm)],[])).
% 0.29/0.49 tff(3,axiom,(~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : (((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''lookupAnsMapPreservation-abind'')).
% 0.29/0.49 tff(4,plain,
% 0.29/0.49 (~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.29/0.49 tff(5,plain,
% 0.29/0.49 (~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.29/0.49 tff(6,plain,
% 0.29/0.49 (~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.29/0.49 tff(7,plain,
% 0.29/0.49 (~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.29/0.49 tff(8,plain,(
% 0.29/0.49 ~((~((vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)) & (vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228)))) | (vtypeOf(Vavr!228) = Vat!229))),
% 0.29/0.49 inference(skolemize,[status(sab)],[7])).
% 0.29/0.49 tff(9,plain,
% 0.29/0.49 ((vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)) & (vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))),
% 0.29/0.49 inference(or_elim,[status(thm)],[8])).
% 0.29/0.49 tff(10,plain,
% 0.29/0.49 (vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)),
% 0.29/0.49 inference(and_elim,[status(thm)],[9])).
% 0.29/0.49 tff(11,plain,
% 0.29/0.49 (~(vtypeOf(Vavr!228) = Vat!229)),
% 0.29/0.49 inference(or_elim,[status(thm)],[8])).
% 0.29/0.49 tff(12,plain,
% 0.29/0.49 (vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228)),
% 0.29/0.49 inference(and_elim,[status(thm)],[9])).
% 0.29/0.49 tff(13,plain,
% 0.29/0.49 (^[Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : refl(((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) <=> ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))),
% 0.29/0.49 inference(bind,[status(th)],[])).
% 0.29/0.49 tff(14,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) <=> ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))),
% 0.29/0.49 inference(quant_intro,[status(thm)],[13])).
% 0.29/0.49 tff(15,plain,
% 0.29/0.49 (^[Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) <=> (~((Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))), ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) <=> (~(~((Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))))), rewrite((~(~((Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))) <=> ((Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))), ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) <=> ((Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))), (((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> (((Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)))), rewrite((((Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))), (((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))))),
% 0.29/0.49 inference(bind,[status(th)],[])).
% 0.29/0.49 tff(16,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))),
% 0.29/0.49 inference(quant_intro,[status(thm)],[15])).
% 0.29/0.49 tff(17,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(rewrite,[status(thm)],[])).
% 0.29/0.49 tff(18,plain,
% 0.29/0.49 (^[Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : trans(monotonicity(rewrite((((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) <=> ((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))), (((((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat)) <=> (((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat)))), rewrite((((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat)) <=> ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))), (((((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat)) <=> ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))))),
% 0.29/0.49 inference(bind,[status(th)],[])).
% 0.29/0.49 tff(19,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat)) <=> ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(quant_intro,[status(thm)],[18])).
% 0.29/0.49 tff(20,axiom,(![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''lookupAnsMapPreservation-abind-qid-qid1-False'')).
% 0.29/0.49 tff(21,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.29/0.49 tff(22,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.29/0.49 tff(23,plain,(
% 0.29/0.49 ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((~((~(Vqid = Vqid1)) & (vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.49 inference(skolemize,[status(sab)],[22])).
% 0.29/0.49 tff(24,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.29/0.49 tff(25,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.29/0.49 tff(26,plain,
% 0.29/0.49 (((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))))) <=> ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | (vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))))),
% 0.29/0.49 inference(rewrite,[status(thm)],[])).
% 0.29/0.49 tff(27,plain,
% 0.29/0.49 (((vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228)))) <=> ((vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))))),
% 0.29/0.49 inference(rewrite,[status(thm)],[])).
% 0.29/0.49 tff(28,plain,
% 0.29/0.49 (((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))))) <=> ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)))))),
% 0.29/0.49 inference(monotonicity,[status(thm)],[27])).
% 0.29/0.49 tff(29,plain,
% 0.29/0.49 (((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))))) <=> ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | (vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))))),
% 0.29/0.49 inference(transitivity,[status(thm)],[28, 26])).
% 0.29/0.49 tff(30,plain,
% 0.29/0.49 ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))))),
% 0.29/0.49 inference(quant_inst,[status(thm)],[])).
% 0.29/0.49 tff(31,plain,
% 0.29/0.49 ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval, Vqid: vQID] : ((vtypeOf(Vavr) = Vat) | (Vqid = Vqid1) | (~(vlookupATMap(Vqid, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | (vtypeOf(Vavr!228) = Vat!229) | (Vqid!227 = Vqid1!231) | (~(vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)))),
% 0.29/0.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.29/0.49 tff(32,plain,
% 0.29/0.49 (Vqid!227 = Vqid1!231),
% 0.29/0.49 inference(unit_resolution,[status(thm)],[31, 25, 10, 12, 11])).
% 0.29/0.49 tff(33,plain,
% 0.29/0.49 (Vqid1!231 = Vqid!227),
% 0.29/0.49 inference(symmetry,[status(thm)],[32])).
% 0.29/0.49 tff(34,plain,
% 0.29/0.49 (vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vlookupATMap(Vqid!227, vtypeAM(vabind(Vqid1!231, Va!230, vam1)))),
% 0.29/0.49 inference(monotonicity,[status(thm)],[33])).
% 0.29/0.49 tff(35,plain,
% 0.29/0.49 (vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)),
% 0.29/0.49 inference(transitivity,[status(thm)],[34, 10])).
% 0.29/0.49 tff(36,plain,
% 0.29/0.49 (vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1)) = vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1))),
% 0.29/0.49 inference(monotonicity,[status(thm)],[32])).
% 0.29/0.49 tff(37,plain,
% 0.29/0.49 (vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vlookupAnsMap(Vqid!227, vabind(Vqid1!231, Va!230, vam1))),
% 0.29/0.49 inference(symmetry,[status(thm)],[36])).
% 0.29/0.49 tff(38,plain,
% 0.29/0.49 (vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228)),
% 0.29/0.49 inference(transitivity,[status(thm)],[37, 12])).
% 0.29/0.49 tff(39,plain,
% 0.29/0.49 (^[Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : refl(((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) <=> ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))),
% 0.29/0.49 inference(bind,[status(th)],[])).
% 0.29/0.49 tff(40,plain,
% 0.29/0.49 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) <=> ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[39])).
% 0.29/0.50 tff(41,plain,
% 0.29/0.50 (^[Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : trans(monotonicity(trans(monotonicity(rewrite(((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) <=> (~((~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))), ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) <=> (~(~((~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))))), rewrite((~(~((~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))) <=> ((~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))), ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) <=> ((~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))))), (((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> (((~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)))), rewrite((((~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))), (((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(42,plain,
% 0.29/0.50 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[41])).
% 0.29/0.50 tff(43,plain,
% 0.29/0.50 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)) <=> ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(44,plain,
% 0.29/0.50 (^[Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : rewrite((((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat)) <=> ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat)))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(45,plain,
% 0.29/0.50 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : (((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat)) <=> ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.29/0.50 tff(46,axiom,(![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : (((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))) => (vtypeOf(Vavr) = Vat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''lookupAnsMapPreservation-abind-qid-qid1-True'')).
% 0.29/0.50 tff(47,plain,
% 0.29/0.50 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.29/0.50 tff(48,plain,
% 0.29/0.50 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.29/0.50 tff(49,plain,(
% 0.29/0.50 ![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((~((vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat)) & (vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr)))) | (vtypeOf(Vavr) = Vat))),
% 0.29/0.50 inference(skolemize,[status(sab)],[48])).
% 0.29/0.50 tff(50,plain,
% 0.29/0.50 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.29/0.50 tff(51,plain,
% 0.29/0.50 (![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.29/0.50 tff(52,plain,
% 0.29/0.50 (((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))))) <=> ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | (vtypeOf(Vavr!228) = Vat!229) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(53,plain,
% 0.29/0.50 (((vtypeOf(Vavr!228) = Vat!229) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228)))) <=> ((vtypeOf(Vavr!228) = Vat!229) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(54,plain,
% 0.29/0.50 (((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))))) <=> ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)))))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[53])).
% 0.29/0.52 tff(55,plain,
% 0.29/0.52 (((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))))) <=> ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | (vtypeOf(Vavr!228) = Vat!229) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))))),
% 0.29/0.52 inference(transitivity,[status(thm)],[54, 52])).
% 0.29/0.52 tff(56,plain,
% 0.29/0.52 ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | ((vtypeOf(Vavr!228) = Vat!229) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229))) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(57,plain,
% 0.29/0.52 ((~![Vqid1: vQID, Va: vAval, Vat: vAType, Vavr: vAval] : ((vtypeOf(Vavr) = Vat) | (~(vlookupATMap(Vqid1, vtypeAM(vabind(Vqid1, Va, vam1))) = vsomeAType(Vat))) | (~(vlookupAnsMap(Vqid1, vabind(Vqid1, Va, vam1)) = vsomeAval(Vavr))))) | (vtypeOf(Vavr!228) = Vat!229) | (~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.29/0.52 tff(58,plain,
% 0.29/0.52 ((~(vlookupAnsMap(Vqid1!231, vabind(Vqid1!231, Va!230, vam1)) = vsomeAval(Vavr!228))) | (~(vlookupATMap(Vqid1!231, vtypeAM(vabind(Vqid1!231, Va!230, vam1))) = vsomeAType(Vat!229)))),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[57, 51, 11])).
% 0.29/0.52 tff(59,plain,
% 0.29/0.52 ($false),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[58, 38, 35])).
% 0.29/0.52 % SZS output end Proof
% 0.29/0.52 % E exiting
%------------------------------------------------------------------------------