%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM262_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.51s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM262_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n008.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 19:55:45 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.29/0.51 % SZS status Theorem
% 0.29/0.51 % SZS output start Proof
% 0.29/0.51 tff(vsomeExp_type, type, (
% 0.29/0.51 vsomeExp: vExp > vOptExp)).
% 0.29/0.51 tff(tptp_fun_VwildcardName0_100_type, type, (
% 0.29/0.51 tptp_fun_VwildcardName0_100: vOptExp > vExp)).
% 0.29/0.51 tff(vreduceExp_type, type, (
% 0.29/0.51 vreduceExp: ( vExp * vAnsMap ) > vOptExp)).
% 0.29/0.51 tff(tptp_fun_Vam_231_type, type, (
% 0.29/0.51 tptp_fun_Vam_231: vAnsMap)).
% 0.29/0.51 tff(tptp_fun_Vexp_228_type, type, (
% 0.29/0.51 tptp_fun_Vexp_228: vExp)).
% 0.29/0.51 tff(tptp_fun_Vamr_233_type, type, (
% 0.29/0.51 tptp_fun_Vamr_233: vAnsMap)).
% 0.29/0.51 tff(visSomeExp_type, type, (
% 0.29/0.51 visSomeExp: vOptExp > $o)).
% 0.29/0.51 tff(vsomeQConf_type, type, (
% 0.29/0.51 vsomeQConf: vQConf > vOptQConf)).
% 0.29/0.51 tff(vQC_type, type, (
% 0.29/0.51 vQC: ( vAnsMap * vQMap * vQuestionnaire ) > vQConf)).
% 0.29/0.51 tff(tptp_fun_Vqr_236_type, type, (
% 0.29/0.51 tptp_fun_Vqr_236: vQuestionnaire)).
% 0.29/0.51 tff(tptp_fun_Vqmr_230_type, type, (
% 0.29/0.51 tptp_fun_Vqmr_230: vQMap)).
% 0.29/0.51 tff(vreduce_type, type, (
% 0.29/0.51 vreduce: ( vQuestionnaire * vAnsMap * vQMap ) > vOptQConf)).
% 0.29/0.51 tff(tptp_fun_Vqm_235_type, type, (
% 0.29/0.51 tptp_fun_Vqm_235: vQMap)).
% 0.29/0.51 tff(vqsingle_type, type, (
% 0.29/0.51 vqsingle: vEntry > vQuestionnaire)).
% 0.29/0.51 tff(vvalue_type, type, (
% 0.29/0.51 vvalue: ( vQID * vAType * vExp ) > vEntry)).
% 0.29/0.51 tff(tptp_fun_Vt_234_type, type, (
% 0.29/0.51 tptp_fun_Vt_234: vAType)).
% 0.29/0.51 tff(tptp_fun_Vqid_229_type, type, (
% 0.29/0.51 tptp_fun_Vqid_229: vQID)).
% 0.29/0.51 tff(vptcheck_type, type, (
% 0.29/0.51 vptcheck: ( vMapConf * vQuestionnaire * vMapConf ) > $o)).
% 0.29/0.51 tff(vMC_type, type, (
% 0.29/0.51 vMC: ( vATMap * vATMap ) > vMapConf)).
% 0.29/0.51 tff(tptp_fun_Vqtm1_237_type, type, (
% 0.29/0.51 tptp_fun_Vqtm1_237: vATMap)).
% 0.29/0.51 tff(tptp_fun_Vatm1_232_type, type, (
% 0.29/0.51 tptp_fun_Vatm1_232: vATMap)).
% 0.29/0.51 tff(vtypeQM_type, type, (
% 0.29/0.51 vtypeQM: vQMap > vATMap)).
% 0.29/0.51 tff(vtypeAM_type, type, (
% 0.29/0.51 vtypeAM: vAnsMap > vATMap)).
% 0.29/0.51 tff(vexpIsValue_type, type, (
% 0.29/0.51 vexpIsValue: vExp > $o)).
% 0.29/0.51 tff(vgetAM_type, type, (
% 0.29/0.51 vgetAM: vQConf > vAnsMap)).
% 0.29/0.51 tff(vgetExp_type, type, (
% 0.29/0.51 vgetExp: vOptExp > vExp)).
% 0.29/0.51 tff(vgetQC_type, type, (
% 0.29/0.51 vgetQC: vOptQConf > vQConf)).
% 0.29/0.51 tff(vsomeAType_type, type, (
% 0.29/0.51 vsomeAType: vAType > vOptAType)).
% 0.29/0.51 tff(vecheck_type, type, (
% 0.29/0.51 vecheck: ( vATMap * vExp ) > vOptAType)).
% 0.29/0.51 tff(vatmbind_type, type, (
% 0.29/0.51 vatmbind: ( vQID * vAType * vATMap ) > vATMap)).
% 0.29/0.51 tff(vgetQuest_type, type, (
% 0.29/0.51 vgetQuest: vQConf > vQuestionnaire)).
% 0.29/0.51 tff(vgetQM_type, type, (
% 0.29/0.51 vgetQM: vQConf > vQMap)).
% 0.29/0.51 tff(vnoAType_type, type, (
% 0.29/0.51 vnoAType: vOptAType)).
% 0.29/0.51 tff(vlookupATMap_type, type, (
% 0.29/0.51 vlookupATMap: ( vQID * vATMap ) > vOptAType)).
% 0.29/0.51 tff(1,plain,
% 0.29/0.51 ((~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((~(visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp)) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1)) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))) <=> (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((~(visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp)) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1)) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1))))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(2,plain,
% 0.29/0.51 ((~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((((visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp))) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1))) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr)))) => vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))) <=> (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((~(visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp)) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1)) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1))))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(3,axiom,(~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((((visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp))) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1))) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr)))) => vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Preservation-qsingle-value-expIsValue-False-isSomeExp-True'')).
% 0.29/0.52 tff(4,plain,
% 0.29/0.52 (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((~(visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp)) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1)) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.29/0.52 tff(5,plain,
% 0.29/0.52 (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((~(visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp)) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1)) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.29/0.52 tff(6,plain,
% 0.29/0.52 (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((~(visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp)) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1)) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.29/0.52 tff(7,plain,
% 0.29/0.52 (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vt: vAType, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap, Vqid: vQID, Vexp: vExp] : ((~(visSomeExp(vreduceExp(Vexp, Vam)) & (~vexpIsValue(Vexp)) & vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqsingle(vvalue(Vqid, Vt, Vexp)), vMC(Vatm1, Vqtm1)) & (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.29/0.52 tff(8,plain,(
% 0.29/0.52 ~((~(visSomeExp(vreduceExp(Vexp!228, Vam!231)) & (~vexpIsValue(Vexp!228)) & vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237)) & (vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235) = vsomeQConf(vQC(Vamr!233, Vqmr!230, Vqr!236))))) | vptcheck(vMC(vtypeAM(Vamr!233), vtypeQM(Vqmr!230)), Vqr!236, vMC(Vatm1!232, Vqtm1!237)))),
% 0.29/0.52 inference(skolemize,[status(sab)],[7])).
% 0.29/0.52 tff(9,plain,
% 0.29/0.52 (visSomeExp(vreduceExp(Vexp!228, Vam!231)) & (~vexpIsValue(Vexp!228)) & vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237)) & (vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235) = vsomeQConf(vQC(Vamr!233, Vqmr!230, Vqr!236)))),
% 0.29/0.52 inference(or_elim,[status(thm)],[8])).
% 0.29/0.52 tff(10,plain,
% 0.29/0.52 (visSomeExp(vreduceExp(Vexp!228, Vam!231))),
% 0.29/0.52 inference(and_elim,[status(thm)],[9])).
% 0.29/0.52 tff(11,plain,
% 0.29/0.52 (^[VOptExp0: vOptExp] : refl(((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0)))) <=> ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0)))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(12,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0)))) <=> ![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0))))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[11])).
% 0.29/0.52 tff(13,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0))) <=> ![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0)))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(14,plain,
% 0.29/0.52 (^[VOptExp0: vOptExp] : rewrite((visSomeExp(VOptExp0) => ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0))) <=> ((~visSomeExp(VOptExp0)) | ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(15,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) => ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0))) <=> ![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0)))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[14])).
% 0.29/0.52 tff(16,axiom,(![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) => ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''isSomeExp-true-INV'')).
% 0.29/0.52 tff(17,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.29/0.52 tff(18,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | ?[VwildcardName0: vExp] : (VOptExp0 = vsomeExp(VwildcardName0)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.29/0.52 tff(19,plain,(
% 0.29/0.52 ![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0))))),
% 0.29/0.52 inference(skolemize,[status(sab)],[18])).
% 0.29/0.52 tff(20,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.29/0.52 tff(21,plain,
% 0.29/0.52 (((~![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0))))) | ((~visSomeExp(vreduceExp(Vexp!228, Vam!231))) | (vreduceExp(Vexp!228, Vam!231) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))))) <=> ((~![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0))))) | (~visSomeExp(vreduceExp(Vexp!228, Vam!231))) | (vreduceExp(Vexp!228, Vam!231) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(22,plain,
% 0.29/0.52 ((~![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0))))) | ((~visSomeExp(vreduceExp(Vexp!228, Vam!231))) | (vreduceExp(Vexp!228, Vam!231) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(23,plain,
% 0.29/0.52 ((~![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) | (VOptExp0 = vsomeExp(tptp_fun_VwildcardName0_100(VOptExp0))))) | (~visSomeExp(vreduceExp(Vexp!228, Vam!231))) | (vreduceExp(Vexp!228, Vam!231) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.29/0.52 tff(24,plain,
% 0.29/0.52 (vreduceExp(Vexp!228, Vam!231) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.29/0.52 tff(25,plain,
% 0.29/0.52 (^[Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : refl((vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam) <=> (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(26,plain,
% 0.29/0.52 (![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam) <=> ![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam)),
% 0.29/0.52 inference(quant_intro,[status(thm)],[25])).
% 0.29/0.52 tff(27,plain,
% 0.29/0.52 (![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam) <=> ![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam)),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(28,axiom,(![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''getAM-0'')).
% 0.29/0.52 tff(29,plain,
% 0.29/0.52 (![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam)),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.29/0.52 tff(30,plain,(
% 0.29/0.52 ![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam)),
% 0.29/0.52 inference(skolemize,[status(sab)],[29])).
% 0.29/0.52 tff(31,plain,
% 0.29/0.52 (![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam)),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.29/0.52 tff(32,plain,
% 0.29/0.52 ((~![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam)) | (vgetAM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = Vam!231)),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(33,plain,
% 0.29/0.52 (vgetAM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = Vam!231),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.29/0.52 tff(34,plain,
% 0.29/0.52 (![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc) <=> ![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc)),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(35,plain,
% 0.29/0.52 (![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc) <=> ![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc)),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(36,axiom,(![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''getQC-0'')).
% 0.29/0.52 tff(37,plain,
% 0.29/0.52 (![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc)),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.29/0.52 tff(38,plain,(
% 0.29/0.52 ![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc)),
% 0.29/0.52 inference(skolemize,[status(sab)],[37])).
% 0.29/0.52 tff(39,plain,
% 0.29/0.52 (![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc)),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.29/0.52 tff(40,plain,
% 0.29/0.52 ((~![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc)) | (vgetQC(vsomeQConf(vQC(Vamr!233, Vqmr!230, Vqr!236))) = vQC(Vamr!233, Vqmr!230, Vqr!236))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(41,plain,
% 0.29/0.52 (vgetQC(vsomeQConf(vQC(Vamr!233, Vqmr!230, Vqr!236))) = vQC(Vamr!233, Vqmr!230, Vqr!236)),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.29/0.52 tff(42,plain,
% 0.29/0.52 (vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235) = vsomeQConf(vQC(Vamr!233, Vqmr!230, Vqr!236))),
% 0.29/0.52 inference(and_elim,[status(thm)],[9])).
% 0.29/0.52 tff(43,plain,
% 0.29/0.52 (~vexpIsValue(Vexp!228)),
% 0.29/0.52 inference(and_elim,[status(thm)],[9])).
% 0.29/0.52 tff(44,plain,
% 0.29/0.52 (^[Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : refl((vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(45,plain,
% 0.29/0.52 (![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> ![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[44])).
% 0.29/0.52 tff(46,plain,
% 0.29/0.52 (^[Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : trans(monotonicity(trans(monotonicity(rewrite(((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam))) <=> (~(vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam)))))), ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) <=> (~(~(vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam)))))))), rewrite((~(~(vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam)))))) <=> (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))))), ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) <=> (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam)))))), (((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> ((vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))))), rewrite(((vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))), (((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(47,plain,
% 0.29/0.52 (![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> ![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[46])).
% 0.29/0.52 tff(48,plain,
% 0.29/0.52 (![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> ![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(49,plain,
% 0.29/0.52 (^[Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : rewrite((((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam))) => (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(50,plain,
% 0.29/0.52 (![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam))) => (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam)))))))) <=> ![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[49])).
% 0.29/0.52 tff(51,axiom,(![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam))) => (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduce-3'')).
% 0.29/0.52 tff(52,plain,
% 0.29/0.52 (![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.29/0.52 tff(53,plain,
% 0.29/0.52 (![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.29/0.52 tff(54,plain,(
% 0.29/0.52 ![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : ((~((~vexpIsValue(Vexp)) & visSomeExp(vreduceExp(Vexp, Vam)))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(skolemize,[status(sab)],[53])).
% 0.29/0.52 tff(55,plain,
% 0.29/0.52 (![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.29/0.52 tff(56,plain,
% 0.29/0.52 (![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.29/0.52 tff(57,plain,
% 0.29/0.52 (((~![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))) | (vexpIsValue(Vexp!228) | (~visSomeExp(vreduceExp(Vexp!228, Vam!231))) | (vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235) = vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))))) <=> ((~![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))) | vexpIsValue(Vexp!228) | (~visSomeExp(vreduceExp(Vexp!228, Vam!231))) | (vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235) = vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(58,plain,
% 0.29/0.52 ((~![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))) | (vexpIsValue(Vexp!228) | (~visSomeExp(vreduceExp(Vexp!228, Vam!231))) | (vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235) = vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(59,plain,
% 0.29/0.52 ((~![Vqm: vQMap, Vt: vAType, Vam: vAnsMap, Vqid: vQID, Vexp: vExp] : (vexpIsValue(Vexp) | (~visSomeExp(vreduceExp(Vexp, Vam))) | (vreduce(vqsingle(vvalue(Vqid, Vt, Vexp)), Vam, Vqm) = vsomeQConf(vQC(Vam, Vqm, vqsingle(vvalue(Vqid, Vt, vgetExp(vreduceExp(Vexp, Vam))))))))) | vexpIsValue(Vexp!228) | (~visSomeExp(vreduceExp(Vexp!228, Vam!231))) | (vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235) = vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.29/0.52 tff(60,plain,
% 0.29/0.52 (vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235) = vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[59, 56, 10, 43])).
% 0.29/0.52 tff(61,plain,
% 0.29/0.52 (vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = vreduce(vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), Vam!231, Vqm!235)),
% 0.29/0.52 inference(symmetry,[status(thm)],[60])).
% 0.29/0.52 tff(62,plain,
% 0.29/0.52 (vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = vsomeQConf(vQC(Vamr!233, Vqmr!230, Vqr!236))),
% 0.29/0.52 inference(transitivity,[status(thm)],[61, 42])).
% 0.29/0.52 tff(63,plain,
% 0.29/0.52 (vgetQC(vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))) = vgetQC(vsomeQConf(vQC(Vamr!233, Vqmr!230, Vqr!236)))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[62])).
% 0.29/0.52 tff(64,plain,
% 0.29/0.52 ((~![Vqc: vQConf] : (vgetQC(vsomeQConf(Vqc)) = Vqc)) | (vgetQC(vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))) = vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(65,plain,
% 0.29/0.52 (vgetQC(vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))) = vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[64, 39])).
% 0.29/0.52 tff(66,plain,
% 0.29/0.52 (vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))) = vgetQC(vsomeQConf(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))))),
% 0.29/0.52 inference(symmetry,[status(thm)],[65])).
% 0.29/0.52 tff(67,plain,
% 0.29/0.52 (vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))) = vQC(Vamr!233, Vqmr!230, Vqr!236)),
% 0.29/0.52 inference(transitivity,[status(thm)],[66, 63, 41])).
% 0.29/0.52 tff(68,plain,
% 0.29/0.52 (vgetAM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = vgetAM(vQC(Vamr!233, Vqmr!230, Vqr!236))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[67])).
% 0.29/0.52 tff(69,plain,
% 0.29/0.52 (vgetAM(vQC(Vamr!233, Vqmr!230, Vqr!236)) = vgetAM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.52 inference(symmetry,[status(thm)],[68])).
% 0.29/0.52 tff(70,plain,
% 0.29/0.52 ((~![Vam: vAnsMap, VwildcardName0: vQMap, VwildcardName1: vQuestionnaire] : (vgetAM(vQC(Vam, VwildcardName0, VwildcardName1)) = Vam)) | (vgetAM(vQC(Vamr!233, Vqmr!230, Vqr!236)) = Vamr!233)),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(71,plain,
% 0.29/0.52 (vgetAM(vQC(Vamr!233, Vqmr!230, Vqr!236)) = Vamr!233),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[70, 31])).
% 0.29/0.52 tff(72,plain,
% 0.29/0.52 (Vamr!233 = vgetAM(vQC(Vamr!233, Vqmr!230, Vqr!236))),
% 0.29/0.52 inference(symmetry,[status(thm)],[71])).
% 0.29/0.52 tff(73,plain,
% 0.29/0.52 (Vamr!233 = Vam!231),
% 0.29/0.52 inference(transitivity,[status(thm)],[72, 69, 33])).
% 0.29/0.52 tff(74,plain,
% 0.29/0.52 (vreduceExp(Vexp!228, Vamr!233) = vreduceExp(Vexp!228, Vam!231)),
% 0.29/0.52 inference(monotonicity,[status(thm)],[73])).
% 0.29/0.52 tff(75,plain,
% 0.29/0.52 (vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))),
% 0.29/0.52 inference(transitivity,[status(thm)],[74, 24])).
% 0.29/0.52 tff(76,plain,
% 0.29/0.52 (vgetExp(vreduceExp(Vexp!228, Vam!231)) = vgetExp(vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[24])).
% 0.29/0.52 tff(77,plain,
% 0.29/0.52 (vgetExp(vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))) = vgetExp(vreduceExp(Vexp!228, Vam!231))),
% 0.29/0.52 inference(symmetry,[status(thm)],[76])).
% 0.29/0.52 tff(78,plain,
% 0.29/0.52 (![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve) <=> ![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve)),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(79,plain,
% 0.29/0.52 (![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve) <=> ![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve)),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(80,axiom,(![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''getExp-0'')).
% 0.29/0.52 tff(81,plain,
% 0.29/0.52 (![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve)),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.29/0.52 tff(82,plain,(
% 0.29/0.52 ![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve)),
% 0.29/0.52 inference(skolemize,[status(sab)],[81])).
% 0.29/0.52 tff(83,plain,
% 0.29/0.52 (![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve)),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.29/0.52 tff(84,plain,
% 0.29/0.52 ((~![Ve: vExp] : (vgetExp(vsomeExp(Ve)) = Ve)) | (vgetExp(vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))) = tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(85,plain,
% 0.29/0.52 (vgetExp(vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))) = tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.29/0.52 tff(86,plain,
% 0.29/0.52 (tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)) = vgetExp(vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))),
% 0.29/0.52 inference(symmetry,[status(thm)],[85])).
% 0.29/0.52 tff(87,plain,
% 0.29/0.52 (tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)) = vgetExp(vreduceExp(Vexp!228, Vam!231))),
% 0.29/0.52 inference(transitivity,[status(thm)],[86, 77])).
% 0.29/0.52 tff(88,plain,
% 0.29/0.52 (vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vecheck(vtypeAM(Vamr!233), vgetExp(vreduceExp(Vexp!228, Vam!231)))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[87])).
% 0.29/0.52 tff(89,plain,
% 0.29/0.52 ((vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) <=> (vecheck(vtypeAM(Vamr!233), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[88])).
% 0.29/0.52 tff(90,plain,
% 0.29/0.52 ((vecheck(vtypeAM(Vamr!233), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) <=> (vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))),
% 0.29/0.52 inference(symmetry,[status(thm)],[89])).
% 0.29/0.52 tff(91,plain,
% 0.29/0.52 ((~(vecheck(vtypeAM(Vamr!233), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))) <=> (~(vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[90])).
% 0.29/0.52 tff(92,plain,
% 0.29/0.52 (Vam!231 = vgetAM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.52 inference(symmetry,[status(thm)],[33])).
% 0.29/0.52 tff(93,plain,
% 0.29/0.52 (Vam!231 = Vamr!233),
% 0.29/0.52 inference(transitivity,[status(thm)],[92, 68, 71])).
% 0.29/0.52 tff(94,plain,
% 0.29/0.52 (vtypeAM(Vam!231) = vtypeAM(Vamr!233)),
% 0.29/0.52 inference(monotonicity,[status(thm)],[93])).
% 0.29/0.52 tff(95,plain,
% 0.29/0.52 (vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vecheck(vtypeAM(Vamr!233), vgetExp(vreduceExp(Vexp!228, Vam!231)))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[94])).
% 0.29/0.52 tff(96,plain,
% 0.29/0.52 ((vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) <=> (vecheck(vtypeAM(Vamr!233), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[95])).
% 0.29/0.52 tff(97,plain,
% 0.29/0.52 ((~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))) <=> (~(vecheck(vtypeAM(Vamr!233), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[96])).
% 0.29/0.52 tff(98,plain,
% 0.29/0.52 (vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))),
% 0.29/0.52 inference(and_elim,[status(thm)],[9])).
% 0.29/0.52 tff(99,plain,
% 0.29/0.52 (^[Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : refl(((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm)) <=> ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm)))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(100,plain,
% 0.29/0.52 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm)) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[99])).
% 0.29/0.52 tff(101,plain,
% 0.29/0.52 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm)) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(102,plain,
% 0.29/0.52 (^[Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : rewrite((vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (Vqm1 = Vqm)) <=> ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm)))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(103,plain,
% 0.29/0.52 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (Vqm1 = Vqm)) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[102])).
% 0.29/0.52 tff(104,axiom,(![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (Vqm1 = Vqm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Tvalue_inv4'')).
% 0.29/0.52 tff(105,plain,
% 0.29/0.52 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.29/0.52 tff(106,plain,
% 0.29/0.52 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.29/0.52 tff(107,plain,(
% 0.29/0.52 ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))),
% 0.29/0.52 inference(skolemize,[status(sab)],[106])).
% 0.29/0.52 tff(108,plain,
% 0.29/0.52 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.29/0.53 tff(109,plain,
% 0.29/0.53 (((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))) | ((~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (Vqtm1!237 = vtypeQM(Vqm!235)))) <=> ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))) | (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (Vqtm1!237 = vtypeQM(Vqm!235)))),
% 0.29/0.53 inference(rewrite,[status(thm)],[])).
% 0.29/0.53 tff(110,plain,
% 0.29/0.53 ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))) | ((~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (Vqtm1!237 = vtypeQM(Vqm!235)))),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(111,plain,
% 0.29/0.53 ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vqm1 = Vqm))) | (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (Vqtm1!237 = vtypeQM(Vqm!235))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.29/0.53 tff(112,plain,
% 0.29/0.53 (Vqtm1!237 = vtypeQM(Vqm!235)),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[111, 108, 98])).
% 0.29/0.53 tff(113,plain,
% 0.29/0.53 (vtypeQM(Vqm!235) = Vqtm1!237),
% 0.29/0.53 inference(symmetry,[status(thm)],[112])).
% 0.29/0.53 tff(114,plain,
% 0.29/0.53 (^[Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : refl(((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm))) <=> ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm))))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(115,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm))) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))),
% 0.29/0.53 inference(quant_intro,[status(thm)],[114])).
% 0.29/0.53 tff(116,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm))) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))),
% 0.29/0.53 inference(rewrite,[status(thm)],[])).
% 0.29/0.53 tff(117,plain,
% 0.29/0.53 (^[Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : rewrite((vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (Vatm1 = vatmbind(Vqid, Vat, Vatm))) <=> ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm))))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(118,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (Vatm1 = vatmbind(Vqid, Vat, Vatm))) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))),
% 0.29/0.53 inference(quant_intro,[status(thm)],[117])).
% 0.29/0.53 tff(119,axiom,(![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (Vatm1 = vatmbind(Vqid, Vat, Vatm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Tvalue_inv3'')).
% 0.29/0.53 tff(120,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.29/0.53 tff(121,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.29/0.53 tff(122,plain,(
% 0.29/0.53 ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))),
% 0.29/0.53 inference(skolemize,[status(sab)],[121])).
% 0.29/0.53 tff(123,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.29/0.53 tff(124,plain,
% 0.29/0.53 (((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))) | ((~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (Vatm1!232 = vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231))))) <=> ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))) | (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (Vatm1!232 = vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231))))),
% 0.29/0.53 inference(rewrite,[status(thm)],[])).
% 0.29/0.53 tff(125,plain,
% 0.29/0.53 ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))) | ((~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (Vatm1!232 = vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231))))),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(126,plain,
% 0.29/0.53 ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (Vatm1 = vatmbind(Vqid, Vat, Vatm)))) | (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (Vatm1!232 = vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.29/0.53 tff(127,plain,
% 0.29/0.53 (Vatm1!232 = vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231))),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[126, 123, 98])).
% 0.29/0.53 tff(128,plain,
% 0.29/0.53 (vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)) = Vatm1!232),
% 0.29/0.53 inference(symmetry,[status(thm)],[127])).
% 0.29/0.53 tff(129,plain,
% 0.29/0.53 (vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235)) = vMC(Vatm1!232, Vqtm1!237)),
% 0.29/0.53 inference(monotonicity,[status(thm)],[128, 113])).
% 0.29/0.53 tff(130,plain,
% 0.29/0.53 (^[VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : refl((vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq) <=> (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(131,plain,
% 0.29/0.53 (![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq) <=> ![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq)),
% 0.29/0.53 inference(quant_intro,[status(thm)],[130])).
% 0.29/0.53 tff(132,plain,
% 0.29/0.53 (![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq) <=> ![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq)),
% 0.29/0.53 inference(rewrite,[status(thm)],[])).
% 0.29/0.53 tff(133,axiom,(![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''getQuest-0'')).
% 0.29/0.53 tff(134,plain,
% 0.29/0.53 (![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq)),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.29/0.53 tff(135,plain,(
% 0.29/0.53 ![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq)),
% 0.29/0.53 inference(skolemize,[status(sab)],[134])).
% 0.29/0.53 tff(136,plain,
% 0.29/0.53 (![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq)),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.29/0.53 tff(137,plain,
% 0.29/0.53 ((~![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq)) | (vgetQuest(vQC(Vamr!233, Vqmr!230, Vqr!236)) = Vqr!236)),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(138,plain,
% 0.29/0.53 (vgetQuest(vQC(Vamr!233, Vqmr!230, Vqr!236)) = Vqr!236),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.29/0.53 tff(139,plain,
% 0.29/0.53 (vgetQuest(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = vgetQuest(vQC(Vamr!233, Vqmr!230, Vqr!236))),
% 0.29/0.53 inference(monotonicity,[status(thm)],[67])).
% 0.29/0.53 tff(140,plain,
% 0.29/0.53 ((~![VwildcardName0: vAnsMap, VwildcardName1: vQMap, Vq: vQuestionnaire] : (vgetQuest(vQC(VwildcardName0, VwildcardName1, Vq)) = Vq)) | (vgetQuest(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(141,plain,
% 0.29/0.53 (vgetQuest(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[140, 136])).
% 0.29/0.53 tff(142,plain,
% 0.29/0.53 (vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))) = vgetQuest(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.53 inference(symmetry,[status(thm)],[141])).
% 0.29/0.53 tff(143,plain,
% 0.29/0.53 (vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))) = Vqr!236),
% 0.29/0.53 inference(transitivity,[status(thm)],[142, 139, 138])).
% 0.29/0.53 tff(144,plain,
% 0.29/0.53 (^[VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : refl((vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm) <=> (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(145,plain,
% 0.29/0.53 (![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm) <=> ![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm)),
% 0.29/0.53 inference(quant_intro,[status(thm)],[144])).
% 0.29/0.53 tff(146,plain,
% 0.29/0.53 (![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm) <=> ![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm)),
% 0.29/0.53 inference(rewrite,[status(thm)],[])).
% 0.29/0.53 tff(147,axiom,(![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''getQM-0'')).
% 0.29/0.53 tff(148,plain,
% 0.29/0.53 (![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm)),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.29/0.53 tff(149,plain,(
% 0.29/0.53 ![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm)),
% 0.29/0.53 inference(skolemize,[status(sab)],[148])).
% 0.29/0.53 tff(150,plain,
% 0.29/0.53 (![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm)),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.29/0.53 tff(151,plain,
% 0.29/0.53 ((~![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm)) | (vgetQM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = Vqm!235)),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(152,plain,
% 0.29/0.53 (vgetQM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = Vqm!235),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.29/0.53 tff(153,plain,
% 0.29/0.53 (vgetQM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))))) = vgetQM(vQC(Vamr!233, Vqmr!230, Vqr!236))),
% 0.29/0.53 inference(monotonicity,[status(thm)],[67])).
% 0.29/0.53 tff(154,plain,
% 0.29/0.53 (vgetQM(vQC(Vamr!233, Vqmr!230, Vqr!236)) = vgetQM(vQC(Vam!231, Vqm!235, vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.53 inference(symmetry,[status(thm)],[153])).
% 0.29/0.53 tff(155,plain,
% 0.29/0.53 ((~![VwildcardName0: vAnsMap, Vqm: vQMap, VwildcardName1: vQuestionnaire] : (vgetQM(vQC(VwildcardName0, Vqm, VwildcardName1)) = Vqm)) | (vgetQM(vQC(Vamr!233, Vqmr!230, Vqr!236)) = Vqmr!230)),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(156,plain,
% 0.29/0.53 (vgetQM(vQC(Vamr!233, Vqmr!230, Vqr!236)) = Vqmr!230),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[155, 150])).
% 0.29/0.53 tff(157,plain,
% 0.29/0.53 (Vqmr!230 = vgetQM(vQC(Vamr!233, Vqmr!230, Vqr!236))),
% 0.29/0.53 inference(symmetry,[status(thm)],[156])).
% 0.29/0.53 tff(158,plain,
% 0.29/0.53 (Vqmr!230 = Vqm!235),
% 0.29/0.53 inference(transitivity,[status(thm)],[157, 154, 152])).
% 0.29/0.53 tff(159,plain,
% 0.29/0.53 (vtypeQM(Vqmr!230) = vtypeQM(Vqm!235)),
% 0.29/0.53 inference(monotonicity,[status(thm)],[158])).
% 0.29/0.53 tff(160,plain,
% 0.29/0.53 (vtypeQM(Vqm!235) = vtypeQM(Vqmr!230)),
% 0.29/0.53 inference(symmetry,[status(thm)],[159])).
% 0.29/0.53 tff(161,plain,
% 0.29/0.53 (vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)) = vMC(vtypeAM(Vamr!233), vtypeQM(Vqmr!230))),
% 0.29/0.53 inference(monotonicity,[status(thm)],[94, 160])).
% 0.29/0.53 tff(162,plain,
% 0.29/0.53 (vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) <=> vptcheck(vMC(vtypeAM(Vamr!233), vtypeQM(Vqmr!230)), Vqr!236, vMC(Vatm1!232, Vqtm1!237))),
% 0.29/0.53 inference(monotonicity,[status(thm)],[161, 143, 129])).
% 0.29/0.53 tff(163,plain,
% 0.29/0.53 (vptcheck(vMC(vtypeAM(Vamr!233), vtypeQM(Vqmr!230)), Vqr!236, vMC(Vatm1!232, Vqtm1!237)) <=> vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235)))),
% 0.29/0.53 inference(symmetry,[status(thm)],[162])).
% 0.29/0.53 tff(164,plain,
% 0.29/0.53 ((~vptcheck(vMC(vtypeAM(Vamr!233), vtypeQM(Vqmr!230)), Vqr!236, vMC(Vatm1!232, Vqtm1!237))) <=> (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))))),
% 0.29/0.53 inference(monotonicity,[status(thm)],[163])).
% 0.29/0.53 tff(165,plain,
% 0.29/0.53 (~vptcheck(vMC(vtypeAM(Vamr!233), vtypeQM(Vqmr!230)), Vqr!236, vMC(Vatm1!232, Vqtm1!237))),
% 0.29/0.53 inference(or_elim,[status(thm)],[8])).
% 0.29/0.53 tff(166,plain,
% 0.29/0.53 (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235)))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.29/0.53 tff(167,plain,
% 0.29/0.53 (^[Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : refl(((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType)) <=> ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType)))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(168,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType)) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))),
% 0.29/0.53 inference(quant_intro,[status(thm)],[167])).
% 0.29/0.53 tff(169,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType)) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))),
% 0.29/0.53 inference(rewrite,[status(thm)],[])).
% 0.29/0.53 tff(170,plain,
% 0.29/0.53 (^[Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : rewrite((vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (vlookupATMap(Vqid, Vatm) = vnoAType)) <=> ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType)))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(171,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (vlookupATMap(Vqid, Vatm) = vnoAType)) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))),
% 0.29/0.53 inference(quant_intro,[status(thm)],[170])).
% 0.29/0.53 tff(172,axiom,(![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (vlookupATMap(Vqid, Vatm) = vnoAType))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Tvalue_inv1'')).
% 0.29/0.53 tff(173,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.29/0.53 tff(174,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.29/0.53 tff(175,plain,(
% 0.29/0.53 ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))),
% 0.29/0.53 inference(skolemize,[status(sab)],[174])).
% 0.29/0.53 tff(176,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.29/0.53 tff(177,plain,
% 0.29/0.53 (((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))) | ((~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType))) <=> ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))) | (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType))),
% 0.29/0.53 inference(rewrite,[status(thm)],[])).
% 0.29/0.53 tff(178,plain,
% 0.29/0.53 ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))) | ((~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType))),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(179,plain,
% 0.29/0.53 ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vlookupATMap(Vqid, Vatm) = vnoAType))) | (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.29/0.53 tff(180,plain,
% 0.29/0.53 (vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[179, 176, 98])).
% 0.29/0.53 tff(181,plain,
% 0.29/0.53 (^[Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : refl((vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))) <=> (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(182,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))) <=> ![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))),
% 0.29/0.53 inference(quant_intro,[status(thm)],[181])).
% 0.29/0.53 tff(183,plain,
% 0.29/0.53 (^[Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : trans(monotonicity(trans(monotonicity(rewrite(((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat))) <=> (~((~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))))), ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) <=> (~(~((~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))))))), rewrite((~(~((~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))))) <=> ((~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))), ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) <=> ((~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))))), (((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))) <=> (((~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))))), rewrite((((~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))) <=> (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))), (((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))) <=> (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(184,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))) <=> ![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))),
% 0.29/0.53 inference(quant_intro,[status(thm)],[183])).
% 0.29/0.53 tff(185,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))) <=> ![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)))),
% 0.29/0.53 inference(rewrite,[status(thm)],[])).
% 0.29/0.53 tff(186,plain,
% 0.29/0.53 (^[Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : rewrite((((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat))) => vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))) <=> ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))))),
% 0.29/0.53 inference(bind,[status(th)],[])).
% 0.29/0.53 tff(187,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat))) => vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm))) <=> ![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)))),
% 0.29/0.53 inference(quant_intro,[status(thm)],[186])).
% 0.29/0.53 tff(188,axiom,(![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat))) => vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Tvalue'')).
% 0.29/0.53 tff(189,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.29/0.53 tff(190,plain,
% 0.29/0.53 (![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.29/0.54 tff(191,plain,(
% 0.29/0.54 ![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : ((~((vlookupATMap(Vqid, Vatm) = vnoAType) & (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)))),
% 0.29/0.54 inference(skolemize,[status(sab)],[190])).
% 0.29/0.54 tff(192,plain,
% 0.29/0.54 (![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.29/0.54 tff(193,plain,
% 0.29/0.54 (![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[192, 182])).
% 0.29/0.54 tff(194,plain,
% 0.29/0.54 (((~![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))) | ((~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))))) <=> ((~![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))) | (~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))))),
% 0.29/0.54 inference(rewrite,[status(thm)],[])).
% 0.29/0.54 tff(195,plain,
% 0.29/0.54 ((vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)))) <=> ((~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))))),
% 0.29/0.54 inference(rewrite,[status(thm)],[])).
% 0.29/0.54 tff(196,plain,
% 0.29/0.54 (((~![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))) | (vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))))) <=> ((~![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))) | ((~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)))))),
% 0.29/0.54 inference(monotonicity,[status(thm)],[195])).
% 0.29/0.54 tff(197,plain,
% 0.29/0.54 (((~![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))) | (vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))))) <=> ((~![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))) | (~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))))),
% 0.29/0.54 inference(transitivity,[status(thm)],[196, 194])).
% 0.29/0.54 tff(198,plain,
% 0.29/0.54 ((~![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))) | (vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))))),
% 0.29/0.54 inference(quant_inst,[status(thm)],[])).
% 0.29/0.54 tff(199,plain,
% 0.29/0.54 ((~![Vqm: vATMap, Vatm: vATMap, Vat: vAType, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(vatmbind(Vqid, Vat, Vatm), Vqm)) | (~(vlookupATMap(Vqid, Vatm) = vnoAType)) | (~(vecheck(Vatm, Vexp) = vsomeAType(Vat))))) | (~(vlookupATMap(Vqid!229, vtypeAM(Vam!231)) = vnoAType)) | vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.29/0.54 tff(200,plain,
% 0.29/0.54 (vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, vgetExp(vreduceExp(Vexp!228, Vam!231)))), vMC(vatmbind(Vqid!229, Vt!234, vtypeAM(Vam!231)), vtypeQM(Vqm!235))) | (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)))),
% 0.29/0.54 inference(unit_resolution,[status(thm)],[199, 193, 180])).
% 0.29/0.54 tff(201,plain,
% 0.29/0.54 (~(vecheck(vtypeAM(Vam!231), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))),
% 0.29/0.54 inference(unit_resolution,[status(thm)],[200, 166])).
% 0.29/0.54 tff(202,plain,
% 0.29/0.54 (~(vecheck(vtypeAM(Vamr!233), vgetExp(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[201, 97])).
% 0.29/0.54 tff(203,plain,
% 0.29/0.54 (~(vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[202, 91])).
% 0.29/0.54 tff(204,plain,
% 0.29/0.54 (^[Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : refl(((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat))) <=> ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat))))),
% 0.29/0.54 inference(bind,[status(th)],[])).
% 0.29/0.54 tff(205,plain,
% 0.29/0.54 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat))) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))),
% 0.29/0.54 inference(quant_intro,[status(thm)],[204])).
% 0.29/0.54 tff(206,plain,
% 0.29/0.54 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat))) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))),
% 0.29/0.54 inference(rewrite,[status(thm)],[])).
% 0.29/0.54 tff(207,plain,
% 0.29/0.54 (^[Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : rewrite((vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (vecheck(Vatm, Vexp) = vsomeAType(Vat))) <=> ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat))))),
% 0.29/0.54 inference(bind,[status(th)],[])).
% 0.29/0.54 tff(208,plain,
% 0.29/0.54 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (vecheck(Vatm, Vexp) = vsomeAType(Vat))) <=> ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))),
% 0.29/0.54 inference(quant_intro,[status(thm)],[207])).
% 0.29/0.54 tff(209,axiom,(![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : (vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1)) => (vecheck(Vatm, Vexp) = vsomeAType(Vat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Tvalue_inv2'')).
% 0.29/0.54 tff(210,plain,
% 0.29/0.54 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.29/0.54 tff(211,plain,
% 0.29/0.54 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.29/0.54 tff(212,plain,(
% 0.29/0.54 ![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))),
% 0.29/0.54 inference(skolemize,[status(sab)],[211])).
% 0.29/0.54 tff(213,plain,
% 0.29/0.54 (![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.29/0.54 tff(214,plain,
% 0.29/0.54 (((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | ((~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (vecheck(vtypeAM(Vam!231), Vexp!228) = vsomeAType(Vt!234)))) <=> ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (vecheck(vtypeAM(Vam!231), Vexp!228) = vsomeAType(Vt!234)))),
% 0.29/0.54 inference(rewrite,[status(thm)],[])).
% 0.29/0.54 tff(215,plain,
% 0.29/0.54 ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | ((~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (vecheck(vtypeAM(Vam!231), Vexp!228) = vsomeAType(Vt!234)))),
% 0.29/0.54 inference(quant_inst,[status(thm)],[])).
% 0.29/0.54 tff(216,plain,
% 0.29/0.54 ((~![Vqm: vATMap, Vatm: vATMap, Vqm1: vATMap, Vat: vAType, Vatm1: vATMap, Vqid: vQID, Vexp: vExp] : ((~vptcheck(vMC(Vatm, Vqm), vqsingle(vvalue(Vqid, Vat, Vexp)), vMC(Vatm1, Vqm1))) | (vecheck(Vatm, Vexp) = vsomeAType(Vat)))) | (~vptcheck(vMC(vtypeAM(Vam!231), vtypeQM(Vqm!235)), vqsingle(vvalue(Vqid!229, Vt!234, Vexp!228)), vMC(Vatm1!232, Vqtm1!237))) | (vecheck(vtypeAM(Vam!231), Vexp!228) = vsomeAType(Vt!234))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.29/0.54 tff(217,plain,
% 0.29/0.54 (vecheck(vtypeAM(Vam!231), Vexp!228) = vsomeAType(Vt!234)),
% 0.29/0.54 inference(unit_resolution,[status(thm)],[216, 213, 98])).
% 0.29/0.54 tff(218,plain,
% 0.29/0.54 (vtypeAM(Vamr!233) = vtypeAM(Vam!231)),
% 0.29/0.54 inference(symmetry,[status(thm)],[94])).
% 0.29/0.54 tff(219,plain,
% 0.29/0.54 (vecheck(vtypeAM(Vamr!233), Vexp!228) = vecheck(vtypeAM(Vam!231), Vexp!228)),
% 0.29/0.54 inference(monotonicity,[status(thm)],[218])).
% 0.29/0.54 tff(220,plain,
% 0.29/0.54 (vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234)),
% 0.29/0.54 inference(transitivity,[status(thm)],[219, 217])).
% 0.29/0.54 tff(221,plain,
% 0.29/0.54 (^[Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : refl(((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))) <=> ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))))),
% 0.29/0.54 inference(bind,[status(th)],[])).
% 0.29/0.54 tff(222,plain,
% 0.29/0.54 (![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))) <=> ![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))),
% 0.29/0.54 inference(quant_intro,[status(thm)],[221])).
% 0.29/0.54 tff(223,plain,
% 0.29/0.54 (^[Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : trans(monotonicity(trans(monotonicity(rewrite(((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver))) <=> (~((~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))))), ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) <=> (~(~((~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))))))), rewrite((~(~((~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))))) <=> ((~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))), ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) <=> ((~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))))), (((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))) <=> (((~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))))), rewrite((((~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))) <=> ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))), (((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))) <=> ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))))),
% 0.29/0.54 inference(bind,[status(th)],[])).
% 0.29/0.54 tff(224,plain,
% 0.29/0.54 (![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))) <=> ![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))),
% 0.29/0.54 inference(quant_intro,[status(thm)],[223])).
% 0.29/0.54 tff(225,plain,
% 0.29/0.54 (![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))) <=> ![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.29/0.54 inference(rewrite,[status(thm)],[])).
% 0.29/0.54 tff(226,plain,
% 0.29/0.54 (^[Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : rewrite((((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver))) => (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))) <=> ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))))),
% 0.29/0.54 inference(bind,[status(th)],[])).
% 0.29/0.54 tff(227,plain,
% 0.29/0.54 (![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : (((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver))) => (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))) <=> ![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.29/0.54 inference(quant_intro,[status(thm)],[226])).
% 0.29/0.54 tff(228,axiom,(![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : (((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver))) => (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExpPreservation')).
% 0.29/0.54 tff(229,plain,
% 0.29/0.54 (![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.29/0.54 tff(230,plain,
% 0.29/0.54 (![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.29/0.54 tff(231,plain,(
% 0.29/0.54 ![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((~((vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat)) & (vreduceExp(Ve, Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.29/0.54 inference(skolemize,[status(sab)],[230])).
% 0.29/0.54 tff(232,plain,
% 0.29/0.54 (![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.29/0.54 tff(233,plain,
% 0.29/0.54 (![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[232, 222])).
% 0.29/0.54 tff(234,plain,
% 0.29/0.54 (((~![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))) | ((~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))))) <=> ((~![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))) | (~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.54 inference(rewrite,[status(thm)],[])).
% 0.29/0.54 tff(235,plain,
% 0.29/0.54 (((vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))))) <=> ((~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.54 inference(rewrite,[status(thm)],[])).
% 0.29/0.54 tff(236,plain,
% 0.29/0.54 (((~![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))) | ((vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))))) <=> ((~![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))) | ((~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))))))),
% 0.29/0.54 inference(monotonicity,[status(thm)],[235])).
% 0.29/0.54 tff(237,plain,
% 0.29/0.54 (((~![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))) | ((vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))))) <=> ((~![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))) | (~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))))),
% 0.29/0.54 inference(transitivity,[status(thm)],[236, 234])).
% 0.29/0.54 tff(238,plain,
% 0.29/0.54 ((~![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))) | ((vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))))))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(239,plain,
% 0.39/0.56 ((~![Vam: vAnsMap, Ve: vExp, Vat: vAType, Ver: vExp] : ((vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)) | (~(vecheck(vtypeAM(Vam), Ve) = vsomeAType(Vat))) | (~(vreduceExp(Ve, Vam) = vsomeExp(Ver))))) | (~(vecheck(vtypeAM(Vamr!233), Vexp!228) = vsomeAType(Vt!234))) | (vecheck(vtypeAM(Vamr!233), tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231))) = vsomeAType(Vt!234)) | (~(vreduceExp(Vexp!228, Vamr!233) = vsomeExp(tptp_fun_VwildcardName0_100(vreduceExp(Vexp!228, Vam!231)))))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.39/0.56 tff(240,plain,
% 0.39/0.56 ($false),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[239, 233, 220, 203, 75])).
% 0.39/0.56 % SZS output end Proof
% 0.39/0.56 % E exiting
%------------------------------------------------------------------------------