%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM273_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n025.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 06:23:05 PM UTC 2026
% Result : Theorem 0.30s 0.52s
% Output : Proof 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM273_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 20:07:44 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.30/0.52 % SZS status Theorem
% 0.30/0.52 % SZS output start Proof
% 0.30/0.52 tff(vsomeExp_type, type, (
% 0.30/0.52 vsomeExp: vExp > vOptExp)).
% 0.30/0.52 tff(tptp_fun_Ver_228_type, type, (
% 0.30/0.52 tptp_fun_Ver_228: vExp)).
% 0.30/0.52 tff(vevalUnOp_type, type, (
% 0.30/0.52 vevalUnOp: ( vUnOpT * vAval ) > vOptExp)).
% 0.30/0.52 tff(tptp_fun_VwildcardName00_101_type, type, (
% 0.30/0.52 tptp_fun_VwildcardName00_101: vExp > vAval)).
% 0.30/0.52 tff(ve1_type, type, (
% 0.30/0.52 ve1: vExp)).
% 0.30/0.52 tff(tptp_fun_Vuot_230_type, type, (
% 0.30/0.52 tptp_fun_Vuot_230: vUnOpT)).
% 0.30/0.52 tff(vreduceExp_type, type, (
% 0.30/0.52 vreduceExp: ( vExp * vAnsMap ) > vOptExp)).
% 0.30/0.52 tff(tptp_fun_Vam_231_type, type, (
% 0.30/0.52 tptp_fun_Vam_231: vAnsMap)).
% 0.30/0.52 tff(vunop_type, type, (
% 0.30/0.52 vunop: ( vUnOpT * vExp ) > vExp)).
% 0.30/0.52 tff(vsomeAType_type, type, (
% 0.30/0.52 vsomeAType: vAType > vOptAType)).
% 0.30/0.52 tff(tptp_fun_Vat_229_type, type, (
% 0.30/0.52 tptp_fun_Vat_229: vAType)).
% 0.30/0.52 tff(vecheck_type, type, (
% 0.30/0.52 vecheck: ( vATMap * vExp ) > vOptAType)).
% 0.30/0.52 tff(vtypeAM_type, type, (
% 0.30/0.52 vtypeAM: vAnsMap > vATMap)).
% 0.30/0.52 tff(vexpIsValue_type, type, (
% 0.30/0.52 vexpIsValue: vExp > $o)).
% 0.30/0.52 tff(vgetExpValue_type, type, (
% 0.30/0.52 vgetExpValue: vExp > vAval)).
% 0.30/0.52 tff(vconstant_type, type, (
% 0.30/0.52 vconstant: vAval > vExp)).
% 0.30/0.52 tff(1,plain,
% 0.30/0.52 ((~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : ((~(vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))) <=> (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : ((~(vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(2,plain,
% 0.30/0.52 ((~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : (((vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat))) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver))) => (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))) <=> (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : ((~(vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat))))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(3,axiom,(~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : (((vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat))) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver))) => (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduceExpPreservation-unop-expIsValue-True'')).
% 0.30/0.52 tff(4,plain,
% 0.30/0.52 (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : ((~(vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.30/0.52 tff(5,plain,
% 0.30/0.52 (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : ((~(vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.30/0.52 tff(6,plain,
% 0.30/0.52 (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : ((~(vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.30/0.52 tff(7,plain,
% 0.30/0.52 (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType, Ver: vExp] : ((~(vexpIsValue(ve1) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)) & (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Ver)))) | (vecheck(vtypeAM(Vam), Ver) = vsomeAType(Vat)))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.30/0.52 tff(8,plain,(
% 0.30/0.52 ~((~(vexpIsValue(ve1) & (vecheck(vtypeAM(Vam!231), vunop(Vuot!230, ve1)) = vsomeAType(Vat!229)) & (vreduceExp(vunop(Vuot!230, ve1), Vam!231) = vsomeExp(Ver!228)))) | (vecheck(vtypeAM(Vam!231), Ver!228) = vsomeAType(Vat!229)))),
% 0.30/0.52 inference(skolemize,[status(sab)],[7])).
% 0.30/0.52 tff(9,plain,
% 0.30/0.52 (vexpIsValue(ve1) & (vecheck(vtypeAM(Vam!231), vunop(Vuot!230, ve1)) = vsomeAType(Vat!229)) & (vreduceExp(vunop(Vuot!230, ve1), Vam!231) = vsomeExp(Ver!228))),
% 0.30/0.52 inference(or_elim,[status(thm)],[8])).
% 0.30/0.52 tff(10,plain,
% 0.30/0.52 (vreduceExp(vunop(Vuot!230, ve1), Vam!231) = vsomeExp(Ver!228)),
% 0.30/0.52 inference(and_elim,[status(thm)],[9])).
% 0.30/0.52 tff(11,plain,
% 0.30/0.52 (vexpIsValue(ve1)),
% 0.30/0.52 inference(and_elim,[status(thm)],[9])).
% 0.30/0.52 tff(12,plain,
% 0.30/0.52 (^[Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : refl(((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1)))) <=> ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1)))))),
% 0.30/0.52 inference(bind,[status(th)],[])).
% 0.30/0.52 tff(13,plain,
% 0.30/0.52 (![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1)))) <=> ![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))),
% 0.30/0.52 inference(quant_intro,[status(thm)],[12])).
% 0.30/0.52 tff(14,plain,
% 0.30/0.52 (![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1)))) <=> ![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(15,plain,
% 0.30/0.52 (^[Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : rewrite((vexpIsValue(Ve1) => (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1)))) <=> ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1)))))),
% 0.30/0.52 inference(bind,[status(th)],[])).
% 0.30/0.52 tff(16,plain,
% 0.30/0.52 (![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : (vexpIsValue(Ve1) => (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1)))) <=> ![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))),
% 0.30/0.52 inference(quant_intro,[status(thm)],[15])).
% 0.30/0.52 tff(17,axiom,(![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : (vexpIsValue(Ve1) => (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduceExp-8'')).
% 0.30/0.52 tff(18,plain,
% 0.30/0.52 (![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.30/0.52 tff(19,plain,
% 0.30/0.52 (![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.30/0.52 tff(20,plain,(
% 0.30/0.52 ![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))),
% 0.30/0.52 inference(skolemize,[status(sab)],[19])).
% 0.30/0.52 tff(21,plain,
% 0.30/0.52 (![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.30/0.52 tff(22,plain,
% 0.30/0.52 (((~![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))) | ((~vexpIsValue(ve1)) | (vreduceExp(vunop(Vuot!230, ve1), Vam!231) = vevalUnOp(Vuot!230, vgetExpValue(ve1))))) <=> ((~![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))) | (~vexpIsValue(ve1)) | (vreduceExp(vunop(Vuot!230, ve1), Vam!231) = vevalUnOp(Vuot!230, vgetExpValue(ve1))))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(23,plain,
% 0.30/0.52 ((~![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))) | ((~vexpIsValue(ve1)) | (vreduceExp(vunop(Vuot!230, ve1), Vam!231) = vevalUnOp(Vuot!230, vgetExpValue(ve1))))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(24,plain,
% 0.30/0.52 ((~![Ve1: vExp, Vop: vUnOpT, Vam: vAnsMap] : ((~vexpIsValue(Ve1)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vevalUnOp(Vop, vgetExpValue(Ve1))))) | (~vexpIsValue(ve1)) | (vreduceExp(vunop(Vuot!230, ve1), Vam!231) = vevalUnOp(Vuot!230, vgetExpValue(ve1)))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.30/0.52 tff(25,plain,
% 0.30/0.52 (vreduceExp(vunop(Vuot!230, ve1), Vam!231) = vevalUnOp(Vuot!230, vgetExpValue(ve1))),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.30/0.52 tff(26,plain,
% 0.30/0.52 (vevalUnOp(Vuot!230, vgetExpValue(ve1)) = vreduceExp(vunop(Vuot!230, ve1), Vam!231)),
% 0.30/0.52 inference(symmetry,[status(thm)],[25])).
% 0.30/0.52 tff(27,plain,
% 0.30/0.52 (^[Ve: vExp] : refl(((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve)))) <=> ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve)))))),
% 0.30/0.52 inference(bind,[status(th)],[])).
% 0.30/0.52 tff(28,plain,
% 0.30/0.52 (![Ve: vExp] : ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve)))) <=> ![Ve: vExp] : ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve))))),
% 0.30/0.52 inference(quant_intro,[status(thm)],[27])).
% 0.30/0.52 tff(29,plain,
% 0.30/0.52 (![Ve: vExp] : ((~vexpIsValue(Ve)) | (~![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00))))) <=> ![Ve: vExp] : ((~vexpIsValue(Ve)) | (~![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00)))))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(30,plain,
% 0.30/0.52 (^[Ve: vExp] : rewrite((![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00))) => (~vexpIsValue(Ve))) <=> ((~vexpIsValue(Ve)) | (~![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00))))))),
% 0.30/0.52 inference(bind,[status(th)],[])).
% 0.30/0.52 tff(31,plain,
% 0.30/0.52 (![Ve: vExp] : (![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00))) => (~vexpIsValue(Ve))) <=> ![Ve: vExp] : ((~vexpIsValue(Ve)) | (~![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00)))))),
% 0.30/0.52 inference(quant_intro,[status(thm)],[30])).
% 0.30/0.52 tff(32,axiom,(![Ve: vExp] : (![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00))) => (~vexpIsValue(Ve)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''expIsValue-1'')).
% 0.30/0.52 tff(33,plain,
% 0.30/0.52 (![Ve: vExp] : ((~vexpIsValue(Ve)) | (~![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00)))))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.30/0.52 tff(34,plain,
% 0.30/0.52 (![Ve: vExp] : ((~vexpIsValue(Ve)) | (~![VwildcardName00: vAval] : (~(Ve = vconstant(VwildcardName00)))))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.30/0.52 tff(35,plain,(
% 0.30/0.52 ![Ve: vExp] : ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve))))),
% 0.30/0.52 inference(skolemize,[status(sab)],[34])).
% 0.30/0.52 tff(36,plain,
% 0.30/0.52 (![Ve: vExp] : ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve))))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.30/0.52 tff(37,plain,
% 0.30/0.52 (((~![Ve: vExp] : ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve))))) | ((~vexpIsValue(ve1)) | (ve1 = vconstant(tptp_fun_VwildcardName00_101(ve1))))) <=> ((~![Ve: vExp] : ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve))))) | (~vexpIsValue(ve1)) | (ve1 = vconstant(tptp_fun_VwildcardName00_101(ve1))))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(38,plain,
% 0.30/0.52 ((~![Ve: vExp] : ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve))))) | ((~vexpIsValue(ve1)) | (ve1 = vconstant(tptp_fun_VwildcardName00_101(ve1))))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(39,plain,
% 0.30/0.52 ((~![Ve: vExp] : ((~vexpIsValue(Ve)) | (Ve = vconstant(tptp_fun_VwildcardName00_101(Ve))))) | (~vexpIsValue(ve1)) | (ve1 = vconstant(tptp_fun_VwildcardName00_101(ve1)))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.30/0.52 tff(40,plain,
% 0.30/0.52 (ve1 = vconstant(tptp_fun_VwildcardName00_101(ve1))),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[39, 36, 11])).
% 0.30/0.52 tff(41,plain,
% 0.30/0.52 (vgetExpValue(ve1) = vgetExpValue(vconstant(tptp_fun_VwildcardName00_101(ve1)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[40])).
% 0.30/0.52 tff(42,plain,
% 0.30/0.52 (vgetExpValue(vconstant(tptp_fun_VwildcardName00_101(ve1))) = vgetExpValue(ve1)),
% 0.30/0.52 inference(symmetry,[status(thm)],[41])).
% 0.30/0.52 tff(43,plain,
% 0.30/0.53 (![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav) <=> ![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav)),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(44,plain,
% 0.30/0.53 (![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav) <=> ![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav)),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(45,axiom,(![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''getExpValue-0'')).
% 0.30/0.53 tff(46,plain,
% 0.30/0.53 (![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.30/0.53 tff(47,plain,(
% 0.30/0.53 ![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav)),
% 0.30/0.53 inference(skolemize,[status(sab)],[46])).
% 0.30/0.53 tff(48,plain,
% 0.30/0.53 (![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.30/0.53 tff(49,plain,
% 0.30/0.53 ((~![Vav: vAval] : (vgetExpValue(vconstant(Vav)) = Vav)) | (vgetExpValue(vconstant(tptp_fun_VwildcardName00_101(ve1))) = tptp_fun_VwildcardName00_101(ve1))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(50,plain,
% 0.30/0.53 (vgetExpValue(vconstant(tptp_fun_VwildcardName00_101(ve1))) = tptp_fun_VwildcardName00_101(ve1)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.30/0.53 tff(51,plain,
% 0.30/0.53 (tptp_fun_VwildcardName00_101(ve1) = vgetExpValue(vconstant(tptp_fun_VwildcardName00_101(ve1)))),
% 0.30/0.53 inference(symmetry,[status(thm)],[50])).
% 0.30/0.53 tff(52,plain,
% 0.30/0.53 (tptp_fun_VwildcardName00_101(ve1) = vgetExpValue(ve1)),
% 0.30/0.53 inference(transitivity,[status(thm)],[51, 42])).
% 0.30/0.53 tff(53,plain,
% 0.30/0.53 (vevalUnOp(Vuot!230, tptp_fun_VwildcardName00_101(ve1)) = vevalUnOp(Vuot!230, vgetExpValue(ve1))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[52])).
% 0.30/0.53 tff(54,plain,
% 0.30/0.53 (vevalUnOp(Vuot!230, tptp_fun_VwildcardName00_101(ve1)) = vsomeExp(Ver!228)),
% 0.30/0.53 inference(transitivity,[status(thm)],[53, 26, 10])).
% 0.30/0.53 tff(55,plain,
% 0.30/0.53 (vecheck(vtypeAM(Vam!231), vunop(Vuot!230, ve1)) = vsomeAType(Vat!229)),
% 0.30/0.53 inference(and_elim,[status(thm)],[9])).
% 0.30/0.53 tff(56,plain,
% 0.30/0.53 (vconstant(tptp_fun_VwildcardName00_101(ve1)) = ve1),
% 0.30/0.53 inference(symmetry,[status(thm)],[40])).
% 0.30/0.53 tff(57,plain,
% 0.30/0.53 (vunop(Vuot!230, vconstant(tptp_fun_VwildcardName00_101(ve1))) = vunop(Vuot!230, ve1)),
% 0.30/0.53 inference(monotonicity,[status(thm)],[56])).
% 0.30/0.53 tff(58,plain,
% 0.30/0.53 (vecheck(vtypeAM(Vam!231), vunop(Vuot!230, vconstant(tptp_fun_VwildcardName00_101(ve1)))) = vecheck(vtypeAM(Vam!231), vunop(Vuot!230, ve1))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[57])).
% 0.30/0.53 tff(59,plain,
% 0.30/0.53 (vecheck(vtypeAM(Vam!231), vunop(Vuot!230, vconstant(tptp_fun_VwildcardName00_101(ve1)))) = vsomeAType(Vat!229)),
% 0.30/0.53 inference(transitivity,[status(thm)],[58, 55])).
% 0.30/0.53 tff(60,plain,
% 0.30/0.53 (~(vecheck(vtypeAM(Vam!231), Ver!228) = vsomeAType(Vat!229))),
% 0.30/0.53 inference(or_elim,[status(thm)],[8])).
% 0.30/0.53 tff(61,plain,
% 0.30/0.53 (^[Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : refl(((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) <=> ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))))),
% 0.30/0.53 inference(bind,[status(th)],[])).
% 0.30/0.53 tff(62,plain,
% 0.30/0.53 (![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) <=> ![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))),
% 0.30/0.53 inference(quant_intro,[status(thm)],[61])).
% 0.30/0.53 tff(63,plain,
% 0.30/0.53 (^[Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : trans(monotonicity(trans(monotonicity(rewrite(((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres))) <=> (~((~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))))), ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) <=> (~(~((~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))))))), rewrite((~(~((~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))))) <=> ((~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))), ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) <=> ((~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))))), (((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat))) <=> (((~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat))))), rewrite((((~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat))) <=> ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))), (((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat))) <=> ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))))),
% 0.30/0.53 inference(bind,[status(th)],[])).
% 0.30/0.53 tff(64,plain,
% 0.30/0.53 (![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat))) <=> ![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))),
% 0.30/0.53 inference(quant_intro,[status(thm)],[63])).
% 0.30/0.53 tff(65,plain,
% 0.30/0.53 (![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat))) <=> ![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(66,plain,
% 0.30/0.53 (^[Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : rewrite((((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres))) => (vecheck(Vatm, Veres) = vsomeAType(Vat))) <=> ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat))))),
% 0.30/0.53 inference(bind,[status(th)],[])).
% 0.30/0.53 tff(67,plain,
% 0.30/0.53 (![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : (((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres))) => (vecheck(Vatm, Veres) = vsomeAType(Vat))) <=> ![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat)))),
% 0.30/0.53 inference(quant_intro,[status(thm)],[66])).
% 0.30/0.53 tff(68,axiom,(![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : (((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres))) => (vecheck(Vatm, Veres) = vsomeAType(Vat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','evalUnOpPreservation')).
% 0.30/0.55 tff(69,plain,
% 0.30/0.55 (![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat)))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.30/0.55 tff(70,plain,
% 0.30/0.55 (![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat)))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.30/0.55 tff(71,plain,(
% 0.30/0.55 ![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((~((vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat)) & (vevalUnOp(Vuot, Vav) = vsomeExp(Veres)))) | (vecheck(Vatm, Veres) = vsomeAType(Vat)))),
% 0.30/0.55 inference(skolemize,[status(sab)],[70])).
% 0.30/0.55 tff(72,plain,
% 0.30/0.55 (![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.30/0.55 tff(73,plain,
% 0.30/0.55 (![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.30/0.55 tff(74,plain,
% 0.30/0.55 (((~![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))) | ((vecheck(vtypeAM(Vam!231), Ver!228) = vsomeAType(Vat!229)) | (~(vecheck(vtypeAM(Vam!231), vunop(Vuot!230, vconstant(tptp_fun_VwildcardName00_101(ve1)))) = vsomeAType(Vat!229))) | (~(vevalUnOp(Vuot!230, tptp_fun_VwildcardName00_101(ve1)) = vsomeExp(Ver!228))))) <=> ((~![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))) | (vecheck(vtypeAM(Vam!231), Ver!228) = vsomeAType(Vat!229)) | (~(vecheck(vtypeAM(Vam!231), vunop(Vuot!230, vconstant(tptp_fun_VwildcardName00_101(ve1)))) = vsomeAType(Vat!229))) | (~(vevalUnOp(Vuot!230, tptp_fun_VwildcardName00_101(ve1)) = vsomeExp(Ver!228))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(75,plain,
% 0.30/0.55 ((~![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))) | ((vecheck(vtypeAM(Vam!231), Ver!228) = vsomeAType(Vat!229)) | (~(vecheck(vtypeAM(Vam!231), vunop(Vuot!230, vconstant(tptp_fun_VwildcardName00_101(ve1)))) = vsomeAType(Vat!229))) | (~(vevalUnOp(Vuot!230, tptp_fun_VwildcardName00_101(ve1)) = vsomeExp(Ver!228))))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(76,plain,
% 0.30/0.55 ((~![Veres: vExp, Vatm: vATMap, Vat: vAType, Vav: vAval, Vuot: vUnOpT] : ((vecheck(Vatm, Veres) = vsomeAType(Vat)) | (~(vecheck(Vatm, vunop(Vuot, vconstant(Vav))) = vsomeAType(Vat))) | (~(vevalUnOp(Vuot, Vav) = vsomeExp(Veres))))) | (vecheck(vtypeAM(Vam!231), Ver!228) = vsomeAType(Vat!229)) | (~(vecheck(vtypeAM(Vam!231), vunop(Vuot!230, vconstant(tptp_fun_VwildcardName00_101(ve1)))) = vsomeAType(Vat!229))) | (~(vevalUnOp(Vuot!230, tptp_fun_VwildcardName00_101(ve1)) = vsomeExp(Ver!228)))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.30/0.55 tff(77,plain,
% 0.30/0.55 ((~(vecheck(vtypeAM(Vam!231), vunop(Vuot!230, vconstant(tptp_fun_VwildcardName00_101(ve1)))) = vsomeAType(Vat!229))) | (~(vevalUnOp(Vuot!230, tptp_fun_VwildcardName00_101(ve1)) = vsomeExp(Ver!228)))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[76, 73, 60])).
% 0.30/0.55 tff(78,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[77, 59, 54])).
% 0.30/0.55 % SZS output end Proof
% 0.30/0.55 % E exiting
%------------------------------------------------------------------------------