%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM256_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n028.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 0.27s 0.52s
% Output : Proof 0.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COM256_1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 19:50:02 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.27/0.52 % SZS status Theorem
% 0.27/0.52 % SZS output start Proof
% 0.27/0.52 tff(vsomeQConf_type, type, (
% 0.27/0.52 vsomeQConf: vQConf > vOptQConf)).
% 0.27/0.52 tff(vQC_type, type, (
% 0.27/0.52 vQC: ( vAnsMap * vQMap * vQuestionnaire ) > vQConf)).
% 0.27/0.52 tff(tptp_fun_Vqr_232_type, type, (
% 0.27/0.52 tptp_fun_Vqr_232: vQuestionnaire)).
% 0.27/0.52 tff(tptp_fun_Vqmr_227_type, type, (
% 0.27/0.52 tptp_fun_Vqmr_227: vQMap)).
% 0.27/0.52 tff(tptp_fun_Vamr_230_type, type, (
% 0.27/0.52 tptp_fun_Vamr_230: vAnsMap)).
% 0.27/0.52 tff(vnoQConf_type, type, (
% 0.27/0.52 vnoQConf: vOptQConf)).
% 0.27/0.52 tff(vreduce_type, type, (
% 0.27/0.52 vreduce: ( vQuestionnaire * vAnsMap * vQMap ) > vOptQConf)).
% 0.27/0.52 tff(tptp_fun_Vqm_231_type, type, (
% 0.27/0.52 tptp_fun_Vqm_231: vQMap)).
% 0.27/0.52 tff(tptp_fun_Vam_228_type, type, (
% 0.27/0.52 tptp_fun_Vam_228: vAnsMap)).
% 0.27/0.52 tff(vqempty_type, type, (
% 0.27/0.52 vqempty: vQuestionnaire)).
% 0.27/0.52 tff(vptcheck_type, type, (
% 0.27/0.52 vptcheck: ( vMapConf * vQuestionnaire * vMapConf ) > $o)).
% 0.27/0.52 tff(vMC_type, type, (
% 0.27/0.52 vMC: ( vATMap * vATMap ) > vMapConf)).
% 0.27/0.52 tff(tptp_fun_Vqtm1_233_type, type, (
% 0.27/0.52 tptp_fun_Vqtm1_233: vATMap)).
% 0.27/0.52 tff(tptp_fun_Vatm1_229_type, type, (
% 0.27/0.52 tptp_fun_Vatm1_229: vATMap)).
% 0.27/0.52 tff(vtypeQM_type, type, (
% 0.27/0.52 vtypeQM: vQMap > vATMap)).
% 0.27/0.52 tff(vtypeAM_type, type, (
% 0.27/0.52 vtypeAM: vAnsMap > vATMap)).
% 0.27/0.52 tff(1,plain,
% 0.27/0.52 ((~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((~(vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))) <=> (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((~(vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1))))),
% 0.27/0.52 inference(rewrite,[status(thm)],[])).
% 0.27/0.52 tff(2,plain,
% 0.27/0.52 ((~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr)))) => vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))) <=> (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((~(vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1))))),
% 0.27/0.52 inference(rewrite,[status(thm)],[])).
% 0.27/0.52 tff(3,axiom,(~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr)))) => vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Preservation-qempty'')).
% 0.27/0.52 tff(4,plain,
% 0.27/0.52 (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((~(vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))),
% 0.27/0.52 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.27/0.52 tff(5,plain,
% 0.27/0.52 (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((~(vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))),
% 0.27/0.52 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.27/0.52 tff(6,plain,
% 0.27/0.52 (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((~(vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))),
% 0.27/0.52 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.27/0.52 tff(7,plain,
% 0.27/0.52 (~![Vqtm1: vATMap, Vqr: vQuestionnaire, Vqm: vQMap, Vamr: vAnsMap, Vatm1: vATMap, Vam: vAnsMap, Vqmr: vQMap] : ((~(vptcheck(vMC(vtypeAM(Vam), vtypeQM(Vqm)), vqempty, vMC(Vatm1, Vqtm1)) & (vreduce(vqempty, Vam, Vqm) = vsomeQConf(vQC(Vamr, Vqmr, Vqr))))) | vptcheck(vMC(vtypeAM(Vamr), vtypeQM(Vqmr)), Vqr, vMC(Vatm1, Vqtm1)))),
% 0.27/0.52 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.27/0.52 tff(8,plain,(
% 0.27/0.52 ~((~(vptcheck(vMC(vtypeAM(Vam!228), vtypeQM(Vqm!231)), vqempty, vMC(Vatm1!229, Vqtm1!233)) & (vreduce(vqempty, Vam!228, Vqm!231) = vsomeQConf(vQC(Vamr!230, Vqmr!227, Vqr!232))))) | vptcheck(vMC(vtypeAM(Vamr!230), vtypeQM(Vqmr!227)), Vqr!232, vMC(Vatm1!229, Vqtm1!233)))),
% 0.27/0.52 inference(skolemize,[status(sab)],[7])).
% 0.27/0.52 tff(9,plain,
% 0.27/0.52 (vptcheck(vMC(vtypeAM(Vam!228), vtypeQM(Vqm!231)), vqempty, vMC(Vatm1!229, Vqtm1!233)) & (vreduce(vqempty, Vam!228, Vqm!231) = vsomeQConf(vQC(Vamr!230, Vqmr!227, Vqr!232)))),
% 0.27/0.52 inference(or_elim,[status(thm)],[8])).
% 0.27/0.52 tff(10,plain,
% 0.27/0.52 (vreduce(vqempty, Vam!228, Vqm!231) = vsomeQConf(vQC(Vamr!230, Vqmr!227, Vqr!232))),
% 0.27/0.52 inference(and_elim,[status(thm)],[9])).
% 0.27/0.52 tff(11,plain,
% 0.27/0.52 (^[VwildcardName0: vAnsMap, VwildcardName1: vQMap] : refl((vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf) <=> (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf))),
% 0.27/0.52 inference(bind,[status(th)],[])).
% 0.27/0.52 tff(12,plain,
% 0.27/0.52 (![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf) <=> ![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf)),
% 0.27/0.52 inference(quant_intro,[status(thm)],[11])).
% 0.27/0.52 tff(13,plain,
% 0.27/0.52 (![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf) <=> ![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf)),
% 0.27/0.52 inference(rewrite,[status(thm)],[])).
% 0.27/0.52 tff(14,axiom,(![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''reduce-0'')).
% 0.27/0.52 tff(15,plain,
% 0.27/0.52 (![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf)),
% 0.27/0.52 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.27/0.52 tff(16,plain,(
% 0.27/0.52 ![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf)),
% 0.27/0.52 inference(skolemize,[status(sab)],[15])).
% 0.27/0.52 tff(17,plain,
% 0.27/0.52 (![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf)),
% 0.27/0.52 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.27/0.52 tff(18,plain,
% 0.27/0.52 ((~![VwildcardName0: vAnsMap, VwildcardName1: vQMap] : (vreduce(vqempty, VwildcardName0, VwildcardName1) = vnoQConf)) | (vreduce(vqempty, Vam!228, Vqm!231) = vnoQConf)),
% 0.27/0.52 inference(quant_inst,[status(thm)],[])).
% 0.27/0.52 tff(19,plain,
% 0.27/0.52 (vreduce(vqempty, Vam!228, Vqm!231) = vnoQConf),
% 0.27/0.52 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.27/0.52 tff(20,plain,
% 0.27/0.52 (vnoQConf = vreduce(vqempty, Vam!228, Vqm!231)),
% 0.27/0.52 inference(symmetry,[status(thm)],[19])).
% 0.27/0.52 tff(21,plain,
% 0.27/0.52 (vnoQConf = vsomeQConf(vQC(Vamr!230, Vqmr!227, Vqr!232))),
% 0.27/0.52 inference(transitivity,[status(thm)],[20, 10])).
% 0.27/0.52 tff(22,plain,
% 0.27/0.52 (^[VQConf0: vQConf] : refl((~(vnoQConf = vsomeQConf(VQConf0))) <=> (~(vnoQConf = vsomeQConf(VQConf0))))),
% 0.27/0.52 inference(bind,[status(th)],[])).
% 0.27/0.52 tff(23,plain,
% 0.27/0.52 (![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0))) <=> ![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0)))),
% 0.27/0.52 inference(quant_intro,[status(thm)],[22])).
% 0.27/0.52 tff(24,plain,
% 0.27/0.52 (![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0))) <=> ![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0)))),
% 0.27/0.52 inference(rewrite,[status(thm)],[])).
% 0.27/0.52 tff(25,axiom,(![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''DIFF-noQConf-someQConf'')).
% 0.27/0.52 tff(26,plain,
% 0.27/0.52 (![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0)))),
% 0.27/0.54 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.27/0.54 tff(27,plain,(
% 0.27/0.54 ![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0)))),
% 0.27/0.54 inference(skolemize,[status(sab)],[26])).
% 0.27/0.54 tff(28,plain,
% 0.27/0.54 (![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0)))),
% 0.27/0.54 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.27/0.54 tff(29,plain,
% 0.27/0.54 ((~![VQConf0: vQConf] : (~(vnoQConf = vsomeQConf(VQConf0)))) | (~(vnoQConf = vsomeQConf(vQC(Vamr!230, Vqmr!227, Vqr!232))))),
% 0.27/0.54 inference(quant_inst,[status(thm)],[])).
% 0.27/0.54 tff(30,plain,
% 0.27/0.54 (~(vnoQConf = vsomeQConf(vQC(Vamr!230, Vqmr!227, Vqr!232)))),
% 0.27/0.54 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.27/0.54 tff(31,plain,
% 0.27/0.54 ($false),
% 0.27/0.54 inference(unit_resolution,[status(thm)],[30, 21])).
% 0.27/0.54 % SZS output end Proof
% 0.27/0.54 % E exiting
%------------------------------------------------------------------------------