%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM277_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n027.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 0.29s 0.50s
% Output : Proof 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM277_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:11:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.29/0.50 % SZS status Theorem
% 0.29/0.50 % SZS output start Proof
% 0.29/0.50 tff(vsomeExp_type, type, (
% 0.29/0.50 vsomeExp: vExp > vOptExp)).
% 0.29/0.50 tff(tptp_fun_Veres00_227_type, type, (
% 0.29/0.50 tptp_fun_Veres00_227: vAnsMap > vExp)).
% 0.29/0.50 tff(tptp_fun_Vam_230_type, type, (
% 0.29/0.50 tptp_fun_Vam_230: vAnsMap)).
% 0.29/0.50 tff(vreduceExp_type, type, (
% 0.29/0.50 vreduceExp: ( vExp * vAnsMap ) > vOptExp)).
% 0.29/0.50 tff(vunop_type, type, (
% 0.29/0.50 vunop: ( vUnOpT * vExp ) > vExp)).
% 0.29/0.50 tff(ve1_type, type, (
% 0.29/0.50 ve1: vExp)).
% 0.29/0.50 tff(tptp_fun_Vuot_229_type, type, (
% 0.29/0.50 tptp_fun_Vuot_229: vUnOpT)).
% 0.29/0.50 tff(vsomeAType_type, type, (
% 0.29/0.50 vsomeAType: vAType > vOptAType)).
% 0.29/0.50 tff(tptp_fun_VwildcardName0_66_type, type, (
% 0.29/0.50 tptp_fun_VwildcardName0_66: vOptAType > vAType)).
% 0.29/0.50 tff(vecheck_type, type, (
% 0.29/0.50 vecheck: ( vATMap * vExp ) > vOptAType)).
% 0.29/0.50 tff(vtypeAM_type, type, (
% 0.29/0.50 vtypeAM: vAnsMap > vATMap)).
% 0.29/0.50 tff(visSomeAType_type, type, (
% 0.29/0.50 visSomeAType: vOptAType > $o)).
% 0.29/0.50 tff(vnoAType_type, type, (
% 0.29/0.50 vnoAType: vOptAType)).
% 0.29/0.50 tff(tptp_fun_Vat_228_type, type, (
% 0.29/0.50 tptp_fun_Vat_228: vAType)).
% 0.29/0.50 tff(vexpIsValue_type, type, (
% 0.29/0.50 vexpIsValue: vExp > $o)).
% 0.29/0.50 tff(visSomeExp_type, type, (
% 0.29/0.50 visSomeExp: vOptExp > $o)).
% 0.29/0.50 tff(vnoExp_type, type, (
% 0.29/0.50 vnoExp: vOptExp)).
% 0.29/0.50 tff(1,plain,
% 0.29/0.50 ((vsomeAType(Vat!228) = vnoAType) <=> (vnoAType = vsomeAType(Vat!228))),
% 0.29/0.50 inference(commutativity,[status(thm)],[])).
% 0.29/0.50 tff(2,plain,
% 0.29/0.50 ((((~visSomeExp(vreduceExp(ve1, Vam!230))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot!229, ve1))) & (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vsomeAType(Vat!228))) & ![Veres000: vExp] : (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000)))) <=> ((~visSomeExp(vreduceExp(ve1, Vam!230))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot!229, ve1))) & (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vsomeAType(Vat!228)) & ![Veres000: vExp] : (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(3,plain,
% 0.29/0.50 ((~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot, ve1))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000)))) <=> (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot, ve1))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(4,plain,
% 0.29/0.50 ((~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : (((((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1))) & (~vexpIsValue(vunop(Vuot, ve1)))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat))) => ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000)))) <=> (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot, ve1))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(5,axiom,(~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : (((((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1))) & (~vexpIsValue(vunop(Vuot, ve1)))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat))) => ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''reduceExpProgress-unop-expIsValue-False-isSomeExp-False'')).
% 0.29/0.50 tff(6,plain,
% 0.29/0.50 (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot, ve1))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.29/0.50 tff(7,plain,
% 0.29/0.50 (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot, ve1))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.29/0.50 tff(8,plain,
% 0.29/0.50 (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot, ve1))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.29/0.50 tff(9,plain,
% 0.29/0.50 (~![Vam: vAnsMap, Vuot: vUnOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot, ve1))) & (vecheck(vtypeAM(Vam), vunop(Vuot, ve1)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vunop(Vuot, ve1), Vam) = vsomeExp(Veres000)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.29/0.50 tff(10,plain,
% 0.29/0.50 ((~visSomeExp(vreduceExp(ve1, Vam!230))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vunop(Vuot!229, ve1))) & (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vsomeAType(Vat!228)) & ![Veres000: vExp] : (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.29/0.50 tff(11,plain,
% 0.29/0.50 (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vsomeAType(Vat!228)),
% 0.29/0.50 inference(and_elim,[status(thm)],[10])).
% 0.29/0.50 tff(12,plain,
% 0.29/0.50 ((vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType) <=> (vsomeAType(Vat!228) = vnoAType)),
% 0.29/0.50 inference(monotonicity,[status(thm)],[11])).
% 0.29/0.50 tff(13,plain,
% 0.29/0.50 ((vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType) <=> (vnoAType = vsomeAType(Vat!228))),
% 0.29/0.50 inference(transitivity,[status(thm)],[12, 1])).
% 0.29/0.50 tff(14,plain,
% 0.29/0.50 ((vnoAType = vsomeAType(Vat!228)) <=> (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType)),
% 0.29/0.50 inference(symmetry,[status(thm)],[13])).
% 0.29/0.50 tff(15,plain,
% 0.29/0.50 ((~(vnoAType = vsomeAType(Vat!228))) <=> (~(vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType))),
% 0.29/0.50 inference(monotonicity,[status(thm)],[14])).
% 0.29/0.50 tff(16,plain,
% 0.29/0.50 (^[VAType0: vAType] : refl((~(vnoAType = vsomeAType(VAType0))) <=> (~(vnoAType = vsomeAType(VAType0))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(17,plain,
% 0.29/0.50 (![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0))) <=> ![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[16])).
% 0.29/0.50 tff(18,plain,
% 0.29/0.50 (![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0))) <=> ![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(19,axiom,(![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''DIFF-noAType-someAType'')).
% 0.29/0.50 tff(20,plain,
% 0.29/0.50 (![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.29/0.50 tff(21,plain,(
% 0.29/0.50 ![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.50 inference(skolemize,[status(sab)],[20])).
% 0.29/0.50 tff(22,plain,
% 0.29/0.50 (![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.29/0.50 tff(23,plain,
% 0.29/0.50 ((~![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))) | (~(vnoAType = vsomeAType(Vat!228)))),
% 0.29/0.50 inference(quant_inst,[status(thm)],[])).
% 0.29/0.50 tff(24,plain,
% 0.29/0.50 (~(vnoAType = vsomeAType(Vat!228))),
% 0.29/0.50 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.29/0.50 tff(25,plain,
% 0.29/0.50 (~(vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType)),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.29/0.50 tff(26,plain,
% 0.29/0.50 (^[Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : refl((visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType)) <=> (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType)))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(27,plain,
% 0.29/0.50 (![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType)) <=> ![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[26])).
% 0.29/0.50 tff(28,plain,
% 0.29/0.50 (![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType)) <=> ![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(29,plain,
% 0.29/0.50 (^[Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : rewrite(((~visSomeAType(vecheck(Vatm, Ve))) => (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType)) <=> (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType)))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(30,plain,
% 0.29/0.50 (![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : ((~visSomeAType(vecheck(Vatm, Ve))) => (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType)) <=> ![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[29])).
% 0.29/0.50 tff(31,axiom,(![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : ((~visSomeAType(vecheck(Vatm, Ve))) => (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''echeck-7'')).
% 0.29/0.50 tff(32,plain,
% 0.29/0.50 (![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.29/0.50 tff(33,plain,
% 0.29/0.50 (![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.29/0.50 tff(34,plain,(
% 0.29/0.50 ![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))),
% 0.29/0.50 inference(skolemize,[status(sab)],[33])).
% 0.29/0.50 tff(35,plain,
% 0.29/0.50 (![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.29/0.50 tff(36,plain,
% 0.29/0.50 (((~![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))) | (visSomeAType(vecheck(vtypeAM(Vam!230), ve1)) | (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType))) <=> ((~![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))) | visSomeAType(vecheck(vtypeAM(Vam!230), ve1)) | (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(37,plain,
% 0.29/0.50 ((~![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))) | (visSomeAType(vecheck(vtypeAM(Vam!230), ve1)) | (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType))),
% 0.29/0.50 inference(quant_inst,[status(thm)],[])).
% 0.29/0.50 tff(38,plain,
% 0.29/0.50 ((~![Vatm: vATMap, Ve: vExp, Vop: vUnOpT] : (visSomeAType(vecheck(Vatm, Ve)) | (vecheck(Vatm, vunop(Vop, Ve)) = vnoAType))) | visSomeAType(vecheck(vtypeAM(Vam!230), ve1)) | (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType)),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.29/0.50 tff(39,plain,
% 0.29/0.50 (visSomeAType(vecheck(vtypeAM(Vam!230), ve1)) | (vecheck(vtypeAM(Vam!230), vunop(Vuot!229, ve1)) = vnoAType)),
% 0.29/0.50 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.29/0.50 tff(40,plain,
% 0.29/0.50 (visSomeAType(vecheck(vtypeAM(Vam!230), ve1))),
% 0.29/0.50 inference(unit_resolution,[status(thm)],[39, 25])).
% 0.29/0.50 tff(41,plain,
% 0.29/0.50 (^[VOptAType0: vOptAType] : refl(((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0)))) <=> ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0)))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(42,plain,
% 0.29/0.50 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0)))) <=> ![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[41])).
% 0.29/0.50 tff(43,plain,
% 0.29/0.50 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0))) <=> ![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(44,plain,
% 0.29/0.50 (^[VOptAType0: vOptAType] : rewrite((visSomeAType(VOptAType0) => ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0))) <=> ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(45,plain,
% 0.29/0.50 (![VOptAType0: vOptAType] : (visSomeAType(VOptAType0) => ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0))) <=> ![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.29/0.50 tff(46,axiom,(![VOptAType0: vOptAType] : (visSomeAType(VOptAType0) => ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''isSomeAType-true-INV'')).
% 0.29/0.50 tff(47,plain,
% 0.29/0.50 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.29/0.50 tff(48,plain,
% 0.29/0.50 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.29/0.50 tff(49,plain,(
% 0.29/0.50 ![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))),
% 0.29/0.50 inference(skolemize,[status(sab)],[48])).
% 0.29/0.50 tff(50,plain,
% 0.29/0.50 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.29/0.50 tff(51,plain,
% 0.29/0.50 (((~![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))) | ((~visSomeAType(vecheck(vtypeAM(Vam!230), ve1))) | (vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1)))))) <=> ((~![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))) | (~visSomeAType(vecheck(vtypeAM(Vam!230), ve1))) | (vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1)))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(52,plain,
% 0.29/0.50 ((~![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))) | ((~visSomeAType(vecheck(vtypeAM(Vam!230), ve1))) | (vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1)))))),
% 0.29/0.50 inference(quant_inst,[status(thm)],[])).
% 0.29/0.50 tff(53,plain,
% 0.29/0.50 ((~![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))) | (~visSomeAType(vecheck(vtypeAM(Vam!230), ve1))) | (vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.29/0.50 tff(54,plain,
% 0.29/0.50 (vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1)))),
% 0.29/0.50 inference(unit_resolution,[status(thm)],[53, 50, 40])).
% 0.29/0.50 tff(55,plain,
% 0.29/0.50 (~vexpIsValue(ve1)),
% 0.29/0.50 inference(and_elim,[status(thm)],[10])).
% 0.29/0.50 tff(56,plain,
% 0.29/0.50 (^[Vam: vAnsMap, Vat: vAType] : refl((vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) <=> (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(57,plain,
% 0.29/0.50 (![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) <=> ![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[56])).
% 0.29/0.50 tff(58,plain,
% 0.29/0.50 (^[Vam: vAnsMap, Vat: vAType] : trans(monotonicity(trans(monotonicity(rewrite(((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))) <=> (~(vexpIsValue(ve1) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))))), ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) <=> (~(~(vexpIsValue(ve1) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))))))), rewrite((~(~(vexpIsValue(ve1) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))))) <=> (vexpIsValue(ve1) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))), ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) <=> (vexpIsValue(ve1) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))))), (((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam)))) <=> ((vexpIsValue(ve1) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam)))))), rewrite(((vexpIsValue(ve1) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam)))) <=> (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))), (((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam)))) <=> (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(59,plain,
% 0.29/0.50 (![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam)))) <=> ![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[58])).
% 0.29/0.50 tff(60,plain,
% 0.29/0.50 (![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00))) <=> ![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00)))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(61,plain,
% 0.29/0.50 (^[Vam: vAnsMap, Vat: vAType] : rewrite((((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))) => ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00))) <=> ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(62,plain,
% 0.29/0.50 (![Vam: vAnsMap, Vat: vAType] : (((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))) => ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00))) <=> ![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00)))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[61])).
% 0.29/0.50 tff(63,axiom,(![Vam: vAnsMap, Vat: vAType] : (((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))) => ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''reduceExpProgress-unop-IH0'')).
% 0.29/0.50 tff(64,plain,
% 0.29/0.50 (![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.29/0.50 tff(65,plain,
% 0.29/0.50 (![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00)))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.29/0.50 tff(66,plain,(
% 0.29/0.50 ![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))))),
% 0.29/0.50 inference(skolemize,[status(sab)],[65])).
% 0.29/0.50 tff(67,plain,
% 0.29/0.50 (![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.29/0.50 tff(68,plain,
% 0.29/0.50 (![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.29/0.50 tff(69,plain,
% 0.29/0.50 (((~![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))) | (vexpIsValue(ve1) | (vreduceExp(ve1, Vam!230) = vsomeExp(tptp_fun_Veres00_227(Vam!230))) | (~(vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1))))))) <=> ((~![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))) | vexpIsValue(ve1) | (vreduceExp(ve1, Vam!230) = vsomeExp(tptp_fun_Veres00_227(Vam!230))) | (~(vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1))))))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(70,plain,
% 0.29/0.50 ((~![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))) | (vexpIsValue(ve1) | (vreduceExp(ve1, Vam!230) = vsomeExp(tptp_fun_Veres00_227(Vam!230))) | (~(vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1))))))),
% 0.29/0.50 inference(quant_inst,[status(thm)],[])).
% 0.29/0.50 tff(71,plain,
% 0.29/0.50 ((~![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))) | vexpIsValue(ve1) | (vreduceExp(ve1, Vam!230) = vsomeExp(tptp_fun_Veres00_227(Vam!230))) | (~(vecheck(vtypeAM(Vam!230), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!230), ve1)))))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.29/0.50 tff(72,plain,
% 0.29/0.50 (vreduceExp(ve1, Vam!230) = vsomeExp(tptp_fun_Veres00_227(Vam!230))),
% 0.29/0.50 inference(unit_resolution,[status(thm)],[71, 68, 55, 54])).
% 0.29/0.50 tff(73,plain,
% 0.29/0.50 (~visSomeExp(vreduceExp(ve1, Vam!230))),
% 0.29/0.50 inference(and_elim,[status(thm)],[10])).
% 0.29/0.50 tff(74,plain,
% 0.29/0.50 (^[VOptExp0: vOptExp] : refl((visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)) <=> (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(75,plain,
% 0.29/0.50 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)) <=> ![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[74])).
% 0.29/0.50 tff(76,plain,
% 0.29/0.50 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)) <=> ![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(77,plain,
% 0.29/0.50 (^[VOptExp0: vOptExp] : rewrite(((~visSomeExp(VOptExp0)) => (VOptExp0 = vnoExp)) <=> (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(78,plain,
% 0.29/0.50 (![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) => (VOptExp0 = vnoExp)) <=> ![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[77])).
% 0.29/0.50 tff(79,axiom,(![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) => (VOptExp0 = vnoExp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''isSomeExp-false-INV'')).
% 0.29/0.50 tff(80,plain,
% 0.29/0.50 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.29/0.50 tff(81,plain,
% 0.29/0.50 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.29/0.50 tff(82,plain,(
% 0.29/0.50 ![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.50 inference(skolemize,[status(sab)],[81])).
% 0.29/0.50 tff(83,plain,
% 0.29/0.50 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.29/0.50 tff(84,plain,
% 0.29/0.50 (((~![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))) | (visSomeExp(vreduceExp(ve1, Vam!230)) | (vreduceExp(ve1, Vam!230) = vnoExp))) <=> ((~![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))) | visSomeExp(vreduceExp(ve1, Vam!230)) | (vreduceExp(ve1, Vam!230) = vnoExp))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.50 tff(85,plain,
% 0.29/0.50 ((~![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))) | (visSomeExp(vreduceExp(ve1, Vam!230)) | (vreduceExp(ve1, Vam!230) = vnoExp))),
% 0.29/0.50 inference(quant_inst,[status(thm)],[])).
% 0.29/0.50 tff(86,plain,
% 0.29/0.50 ((~![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))) | visSomeExp(vreduceExp(ve1, Vam!230)) | (vreduceExp(ve1, Vam!230) = vnoExp)),
% 0.29/0.50 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.29/0.50 tff(87,plain,
% 0.29/0.50 (vreduceExp(ve1, Vam!230) = vnoExp),
% 0.29/0.50 inference(unit_resolution,[status(thm)],[86, 83, 73])).
% 0.29/0.50 tff(88,plain,
% 0.29/0.50 (vnoExp = vreduceExp(ve1, Vam!230)),
% 0.29/0.50 inference(symmetry,[status(thm)],[87])).
% 0.29/0.50 tff(89,plain,
% 0.29/0.50 (^[Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : refl((vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(90,plain,
% 0.29/0.50 (![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> ![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[89])).
% 0.29/0.50 tff(91,plain,
% 0.29/0.50 (^[Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : trans(monotonicity(trans(monotonicity(rewrite(((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam)))) <=> (~(vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))))), ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) <=> (~(~(vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))))))), rewrite((~(~(vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))))) <=> (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))), ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) <=> (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))))), (((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> ((vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)))), rewrite(((vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))), (((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))))),
% 0.29/0.50 inference(bind,[status(th)],[])).
% 0.29/0.50 tff(92,plain,
% 0.29/0.50 (![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> ![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.50 inference(quant_intro,[status(thm)],[91])).
% 0.29/0.50 tff(93,plain,
% 0.29/0.50 (![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> ![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.50 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(94,plain,
% 0.29/0.51 (^[Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : rewrite((((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam)))) => (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(95,plain,
% 0.29/0.51 (![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam)))) => (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp)) <=> ![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[94])).
% 0.29/0.51 tff(96,axiom,(![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam)))) => (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''reduceExp-10'')).
% 0.29/0.51 tff(97,plain,
% 0.29/0.51 (![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.29/0.51 tff(98,plain,
% 0.29/0.51 (![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.29/0.51 tff(99,plain,(
% 0.29/0.51 ![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.51 inference(skolemize,[status(sab)],[98])).
% 0.29/0.51 tff(100,plain,
% 0.29/0.51 (![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.29/0.51 tff(101,plain,
% 0.29/0.51 (![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.29/0.51 tff(102,plain,
% 0.29/0.51 (((~![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))) | (vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!230)) | (vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vnoExp))) <=> ((~![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!230)) | (vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vnoExp))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(103,plain,
% 0.29/0.51 ((~![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))) | (vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!230)) | (vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vnoExp))),
% 0.29/0.51 inference(quant_inst,[status(thm)],[])).
% 0.29/0.51 tff(104,plain,
% 0.29/0.51 ((~![Ve1: vExp, Vam: vAnsMap, Vop: vUnOpT] : (vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)) | (vreduceExp(vunop(Vop, Ve1), Vam) = vnoExp))) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!230)) | (vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vnoExp)),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.29/0.51 tff(105,plain,
% 0.29/0.51 (vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vnoExp),
% 0.29/0.51 inference(unit_resolution,[status(thm)],[104, 101, 73, 55])).
% 0.29/0.51 tff(106,plain,
% 0.29/0.51 (vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(tptp_fun_Veres00_227(Vam!230))),
% 0.29/0.51 inference(transitivity,[status(thm)],[105, 88, 72])).
% 0.29/0.51 tff(107,plain,
% 0.29/0.51 (^[Veres000: vExp] : refl((~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000))) <=> (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(108,plain,
% 0.29/0.51 (![Veres000: vExp] : (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000))) <=> ![Veres000: vExp] : (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000)))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[107])).
% 0.29/0.53 tff(109,plain,
% 0.29/0.53 (![Veres000: vExp] : (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000)))),
% 0.29/0.53 inference(and_elim,[status(thm)],[10])).
% 0.29/0.53 tff(110,plain,
% 0.29/0.53 (![Veres000: vExp] : (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000)))),
% 0.29/0.53 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.29/0.53 tff(111,plain,
% 0.29/0.53 ((~![Veres000: vExp] : (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(Veres000)))) | (~(vreduceExp(vunop(Vuot!229, ve1), Vam!230) = vsomeExp(tptp_fun_Veres00_227(Vam!230))))),
% 0.29/0.53 inference(quant_inst,[status(thm)],[])).
% 0.29/0.53 tff(112,plain,
% 0.29/0.53 ($false),
% 0.29/0.53 inference(unit_resolution,[status(thm)],[111, 110, 106])).
% 0.29/0.53 % SZS output end Proof
% 0.29/0.53 % E exiting
%------------------------------------------------------------------------------