%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM274_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.51s
% Output : Proof 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM274_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.33 % Computer : n006.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 20:08:03 EDT 2026
% 0.16/0.33 % 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_Veres00_227_type, type, (
% 0.29/0.51 tptp_fun_Veres00_227: vAnsMap > vExp)).
% 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(vreduceExp_type, type, (
% 0.29/0.51 vreduceExp: ( vExp * vAnsMap ) > vOptExp)).
% 0.29/0.51 tff(vbinop_type, type, (
% 0.29/0.51 vbinop: ( vExp * vBinOpT * vExp ) > vExp)).
% 0.29/0.51 tff(ve2_type, type, (
% 0.29/0.51 ve2: vExp)).
% 0.29/0.51 tff(tptp_fun_Vbot_230_type, type, (
% 0.29/0.51 tptp_fun_Vbot_230: vBinOpT)).
% 0.29/0.51 tff(ve1_type, type, (
% 0.29/0.51 ve1: vExp)).
% 0.29/0.51 tff(vsomeAType_type, type, (
% 0.29/0.51 vsomeAType: vAType > vOptAType)).
% 0.29/0.51 tff(tptp_fun_VwildcardName0_66_type, type, (
% 0.29/0.51 tptp_fun_VwildcardName0_66: vOptAType > vAType)).
% 0.29/0.51 tff(vecheck_type, type, (
% 0.29/0.51 vecheck: ( vATMap * vExp ) > vOptAType)).
% 0.29/0.51 tff(vtypeAM_type, type, (
% 0.29/0.51 vtypeAM: vAnsMap > vATMap)).
% 0.29/0.51 tff(visSomeAType_type, type, (
% 0.29/0.51 visSomeAType: vOptAType > $o)).
% 0.29/0.51 tff(vnoAType_type, type, (
% 0.29/0.51 vnoAType: vOptAType)).
% 0.29/0.51 tff(tptp_fun_Vat_229_type, type, (
% 0.29/0.51 tptp_fun_Vat_229: vAType)).
% 0.29/0.51 tff(vexpIsValue_type, type, (
% 0.29/0.51 vexpIsValue: vExp > $o)).
% 0.29/0.51 tff(visSomeExp_type, type, (
% 0.29/0.51 visSomeExp: vOptExp > $o)).
% 0.29/0.51 tff(vnoExp_type, type, (
% 0.29/0.51 vnoExp: vOptExp)).
% 0.29/0.51 tff(1,plain,
% 0.29/0.51 ((vsomeAType(Vat!229) = vnoAType) <=> (vnoAType = vsomeAType(Vat!229))),
% 0.29/0.51 inference(commutativity,[status(thm)],[])).
% 0.29/0.51 tff(2,plain,
% 0.29/0.51 ((((~visSomeExp(vreduceExp(ve1, Vam!231))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot!230, ve2))) & (vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vsomeAType(Vat!229))) & ![Veres000: vExp] : (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000)))) <=> ((~visSomeExp(vreduceExp(ve1, Vam!231))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot!230, ve2))) & (vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vsomeAType(Vat!229)) & ![Veres000: vExp] : (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000))))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(3,plain,
% 0.29/0.51 ((~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot, ve2))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000)))) <=> (~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot, ve2))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000))))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(4,plain,
% 0.29/0.51 ((~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : (((((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1))) & (~vexpIsValue(vbinop(ve1, Vbot, ve2)))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat))) => ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000)))) <=> (~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot, ve2))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000))))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(5,axiom,(~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : (((((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1))) & (~vexpIsValue(vbinop(ve1, Vbot, ve2)))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat))) => ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduceExpProgress-binop-expIsValue-False-isSomeExp-False'')).
% 0.29/0.51 tff(6,plain,
% 0.29/0.51 (~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot, ve2))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000)))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.29/0.51 tff(7,plain,
% 0.29/0.51 (~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot, ve2))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000)))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.29/0.51 tff(8,plain,
% 0.29/0.51 (~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot, ve2))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000)))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.29/0.51 tff(9,plain,
% 0.29/0.51 (~![Vam: vAnsMap, Vbot: vBinOpT, Vat: vAType] : ((~((~visSomeExp(vreduceExp(ve1, Vam))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot, ve2))) & (vecheck(vtypeAM(Vam), vbinop(ve1, Vbot, ve2)) = vsomeAType(Vat)))) | ?[Veres000: vExp] : (vreduceExp(vbinop(ve1, Vbot, ve2), Vam) = vsomeExp(Veres000)))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.29/0.51 tff(10,plain,
% 0.29/0.51 ((~visSomeExp(vreduceExp(ve1, Vam!231))) & (~vexpIsValue(ve1)) & (~vexpIsValue(vbinop(ve1, Vbot!230, ve2))) & (vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vsomeAType(Vat!229)) & ![Veres000: vExp] : (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000)))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.29/0.51 tff(11,plain,
% 0.29/0.51 (vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vsomeAType(Vat!229)),
% 0.29/0.51 inference(and_elim,[status(thm)],[10])).
% 0.29/0.51 tff(12,plain,
% 0.29/0.51 ((vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType) <=> (vsomeAType(Vat!229) = vnoAType)),
% 0.29/0.51 inference(monotonicity,[status(thm)],[11])).
% 0.29/0.51 tff(13,plain,
% 0.29/0.51 ((vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType) <=> (vnoAType = vsomeAType(Vat!229))),
% 0.29/0.51 inference(transitivity,[status(thm)],[12, 1])).
% 0.29/0.51 tff(14,plain,
% 0.29/0.51 ((vnoAType = vsomeAType(Vat!229)) <=> (vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType)),
% 0.29/0.51 inference(symmetry,[status(thm)],[13])).
% 0.29/0.51 tff(15,plain,
% 0.29/0.51 ((~(vnoAType = vsomeAType(Vat!229))) <=> (~(vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType))),
% 0.29/0.51 inference(monotonicity,[status(thm)],[14])).
% 0.29/0.51 tff(16,plain,
% 0.29/0.51 (^[VAType0: vAType] : refl((~(vnoAType = vsomeAType(VAType0))) <=> (~(vnoAType = vsomeAType(VAType0))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(17,plain,
% 0.29/0.51 (![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0))) <=> ![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[16])).
% 0.29/0.51 tff(18,plain,
% 0.29/0.51 (![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0))) <=> ![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(19,axiom,(![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-noAType-someAType'')).
% 0.29/0.51 tff(20,plain,
% 0.29/0.51 (![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.29/0.51 tff(21,plain,(
% 0.29/0.51 ![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.51 inference(skolemize,[status(sab)],[20])).
% 0.29/0.51 tff(22,plain,
% 0.29/0.51 (![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.29/0.51 tff(23,plain,
% 0.29/0.51 ((~![VAType0: vAType] : (~(vnoAType = vsomeAType(VAType0)))) | (~(vnoAType = vsomeAType(Vat!229)))),
% 0.29/0.51 inference(quant_inst,[status(thm)],[])).
% 0.29/0.51 tff(24,plain,
% 0.29/0.51 (~(vnoAType = vsomeAType(Vat!229))),
% 0.29/0.51 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.29/0.51 tff(25,plain,
% 0.29/0.51 (~(vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType)),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.29/0.51 tff(26,plain,
% 0.29/0.51 (^[Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : refl(((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2)))))) <=> ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2)))))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(27,plain,
% 0.29/0.51 (![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2)))))) <=> ![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[26])).
% 0.29/0.51 tff(28,plain,
% 0.29/0.51 (^[Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : trans(monotonicity(rewrite((visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2))) <=> (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2)))))), (((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2)))) <=> ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2)))))))), rewrite(((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2)))))) <=> ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))), (((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2)))) <=> ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(29,plain,
% 0.29/0.51 (![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2)))) <=> ![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[28])).
% 0.29/0.51 tff(30,plain,
% 0.29/0.51 (![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2)))) <=> ![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2))))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(31,plain,
% 0.29/0.51 (^[Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : rewrite(((~(visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2)))) => (vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType)) <=> ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2)))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(32,plain,
% 0.29/0.51 (![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((~(visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2)))) => (vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType)) <=> ![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2))))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[31])).
% 0.29/0.51 tff(33,axiom,(![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((~(visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2)))) => (vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''echeck-5'')).
% 0.29/0.51 tff(34,plain,
% 0.29/0.51 (![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2))))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.29/0.51 tff(35,plain,
% 0.29/0.51 (![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2))))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.29/0.51 tff(36,plain,(
% 0.29/0.51 ![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (visSomeAType(vecheck(Vatm, Ve1)) & visSomeAType(vecheck(Vatm, Ve2))))),
% 0.29/0.51 inference(skolemize,[status(sab)],[35])).
% 0.29/0.51 tff(37,plain,
% 0.29/0.51 (![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.29/0.51 tff(38,plain,
% 0.29/0.51 (![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.29/0.51 tff(39,plain,
% 0.29/0.51 (((~![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))) | ((vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType) | (~((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve2))))))) <=> ((~![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))) | (vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType) | (~((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve2))))))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(40,plain,
% 0.29/0.51 ((~![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))) | ((vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType) | (~((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve2))))))),
% 0.29/0.51 inference(quant_inst,[status(thm)],[])).
% 0.29/0.51 tff(41,plain,
% 0.29/0.51 ((~![Vatm: vATMap, Ve1: vExp, Ve2: vExp, Vop: vBinOpT] : ((vecheck(Vatm, vbinop(Ve1, Vop, Ve2)) = vnoAType) | (~((~visSomeAType(vecheck(Vatm, Ve1))) | (~visSomeAType(vecheck(Vatm, Ve2))))))) | (vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType) | (~((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve2)))))),
% 0.29/0.51 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.29/0.51 tff(42,plain,
% 0.29/0.51 ((vecheck(vtypeAM(Vam!231), vbinop(ve1, Vbot!230, ve2)) = vnoAType) | (~((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve2)))))),
% 0.29/0.51 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.29/0.51 tff(43,plain,
% 0.29/0.51 (~((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve2))))),
% 0.29/0.51 inference(unit_resolution,[status(thm)],[42, 25])).
% 0.29/0.51 tff(44,plain,
% 0.29/0.51 (((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve2)))) | visSomeAType(vecheck(vtypeAM(Vam!231), ve1))),
% 0.29/0.51 inference(tautology,[status(thm)],[])).
% 0.29/0.51 tff(45,plain,
% 0.29/0.51 (visSomeAType(vecheck(vtypeAM(Vam!231), ve1))),
% 0.29/0.51 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.29/0.51 tff(46,plain,
% 0.29/0.51 (^[VOptAType0: vOptAType] : refl(((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0)))) <=> ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0)))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(47,plain,
% 0.29/0.51 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0)))) <=> ![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[46])).
% 0.29/0.51 tff(48,plain,
% 0.29/0.51 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0))) <=> ![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))),
% 0.29/0.51 inference(rewrite,[status(thm)],[])).
% 0.29/0.51 tff(49,plain,
% 0.29/0.51 (^[VOptAType0: vOptAType] : rewrite((visSomeAType(VOptAType0) => ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0))) <=> ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0))))),
% 0.29/0.51 inference(bind,[status(th)],[])).
% 0.29/0.51 tff(50,plain,
% 0.29/0.51 (![VOptAType0: vOptAType] : (visSomeAType(VOptAType0) => ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0))) <=> ![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))),
% 0.29/0.51 inference(quant_intro,[status(thm)],[49])).
% 0.29/0.51 tff(51,axiom,(![VOptAType0: vOptAType] : (visSomeAType(VOptAType0) => ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''isSomeAType-true-INV'')).
% 0.29/0.51 tff(52,plain,
% 0.29/0.51 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.29/0.52 tff(53,plain,
% 0.29/0.52 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | ?[VwildcardName0: vAType] : (VOptAType0 = vsomeAType(VwildcardName0)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.29/0.52 tff(54,plain,(
% 0.29/0.52 ![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))),
% 0.29/0.52 inference(skolemize,[status(sab)],[53])).
% 0.29/0.52 tff(55,plain,
% 0.29/0.52 (![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.29/0.52 tff(56,plain,
% 0.29/0.52 (((~![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))) | ((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), ve1)))))) <=> ((~![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), ve1)))))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(57,plain,
% 0.29/0.52 ((~![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))) | ((~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), ve1)))))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(58,plain,
% 0.29/0.52 ((~![VOptAType0: vOptAType] : ((~visSomeAType(VOptAType0)) | (VOptAType0 = vsomeAType(tptp_fun_VwildcardName0_66(VOptAType0))))) | (~visSomeAType(vecheck(vtypeAM(Vam!231), ve1))) | (vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), ve1))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.29/0.52 tff(59,plain,
% 0.29/0.52 (vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), ve1)))),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[58, 55, 45])).
% 0.29/0.52 tff(60,plain,
% 0.29/0.52 (~vexpIsValue(ve1)),
% 0.29/0.52 inference(and_elim,[status(thm)],[10])).
% 0.29/0.52 tff(61,plain,
% 0.29/0.52 (^[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)))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(62,plain,
% 0.29/0.52 (![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))))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[61])).
% 0.29/0.52 tff(63,plain,
% 0.29/0.52 (^[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))))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(64,plain,
% 0.29/0.52 (![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))))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[63])).
% 0.29/0.52 tff(65,plain,
% 0.29/0.52 (![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)))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(66,plain,
% 0.29/0.52 (^[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))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(67,plain,
% 0.29/0.52 (![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)))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[66])).
% 0.29/0.52 tff(68,axiom,(![Vam: vAnsMap, Vat: vAType] : (((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))) => ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduceExpProgress-binop-IH0'')).
% 0.29/0.52 tff(69,plain,
% 0.29/0.52 (![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.29/0.52 tff(70,plain,
% 0.29/0.52 (![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | ?[Veres00: vExp] : (vreduceExp(ve1, Vam) = vsomeExp(Veres00)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.29/0.52 tff(71,plain,(
% 0.29/0.52 ![Vam: vAnsMap, Vat: vAType] : ((~((~vexpIsValue(ve1)) & (vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat)))) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))))),
% 0.29/0.52 inference(skolemize,[status(sab)],[70])).
% 0.29/0.52 tff(72,plain,
% 0.29/0.52 (![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.29/0.52 tff(73,plain,
% 0.29/0.52 (![Vam: vAnsMap, Vat: vAType] : (vexpIsValue(ve1) | (vreduceExp(ve1, Vam) = vsomeExp(tptp_fun_Veres00_227(Vam))) | (~(vecheck(vtypeAM(Vam), ve1) = vsomeAType(Vat))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.29/0.52 tff(74,plain,
% 0.29/0.52 (((~![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!231) = vsomeExp(tptp_fun_Veres00_227(Vam!231))) | (~(vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), 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!231) = vsomeExp(tptp_fun_Veres00_227(Vam!231))) | (~(vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), ve1))))))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(75,plain,
% 0.29/0.52 ((~![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!231) = vsomeExp(tptp_fun_Veres00_227(Vam!231))) | (~(vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), ve1))))))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(76,plain,
% 0.29/0.52 ((~![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!231) = vsomeExp(tptp_fun_Veres00_227(Vam!231))) | (~(vecheck(vtypeAM(Vam!231), ve1) = vsomeAType(tptp_fun_VwildcardName0_66(vecheck(vtypeAM(Vam!231), ve1)))))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.29/0.52 tff(77,plain,
% 0.29/0.52 (vreduceExp(ve1, Vam!231) = vsomeExp(tptp_fun_Veres00_227(Vam!231))),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[76, 73, 60, 59])).
% 0.29/0.52 tff(78,plain,
% 0.29/0.52 (~visSomeExp(vreduceExp(ve1, Vam!231))),
% 0.29/0.52 inference(and_elim,[status(thm)],[10])).
% 0.29/0.52 tff(79,plain,
% 0.29/0.52 (^[VOptExp0: vOptExp] : refl((visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)) <=> (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(80,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)) <=> ![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[79])).
% 0.29/0.52 tff(81,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)) <=> ![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(82,plain,
% 0.29/0.52 (^[VOptExp0: vOptExp] : rewrite(((~visSomeExp(VOptExp0)) => (VOptExp0 = vnoExp)) <=> (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp)))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(83,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) => (VOptExp0 = vnoExp)) <=> ![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[82])).
% 0.29/0.52 tff(84,axiom,(![VOptExp0: vOptExp] : ((~visSomeExp(VOptExp0)) => (VOptExp0 = vnoExp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''isSomeExp-false-INV'')).
% 0.29/0.52 tff(85,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.29/0.52 tff(86,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.29/0.52 tff(87,plain,(
% 0.29/0.52 ![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.52 inference(skolemize,[status(sab)],[86])).
% 0.29/0.52 tff(88,plain,
% 0.29/0.52 (![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.29/0.52 tff(89,plain,
% 0.29/0.52 (((~![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))) | (visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(ve1, Vam!231) = vnoExp))) <=> ((~![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))) | visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(ve1, Vam!231) = vnoExp))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(90,plain,
% 0.29/0.52 ((~![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))) | (visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(ve1, Vam!231) = vnoExp))),
% 0.29/0.52 inference(quant_inst,[status(thm)],[])).
% 0.29/0.52 tff(91,plain,
% 0.29/0.52 ((~![VOptExp0: vOptExp] : (visSomeExp(VOptExp0) | (VOptExp0 = vnoExp))) | visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(ve1, Vam!231) = vnoExp)),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.29/0.52 tff(92,plain,
% 0.29/0.52 (vreduceExp(ve1, Vam!231) = vnoExp),
% 0.29/0.52 inference(unit_resolution,[status(thm)],[91, 88, 78])).
% 0.29/0.52 tff(93,plain,
% 0.29/0.52 (vnoExp = vreduceExp(ve1, Vam!231)),
% 0.29/0.52 inference(symmetry,[status(thm)],[92])).
% 0.29/0.52 tff(94,plain,
% 0.29/0.52 (^[Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : refl(((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))) <=> ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(95,plain,
% 0.29/0.52 (![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))) <=> ![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[94])).
% 0.29/0.52 tff(96,plain,
% 0.29/0.52 (^[Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : 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(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)) <=> ((vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)))), rewrite(((vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)) <=> ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))), (((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)) <=> ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(97,plain,
% 0.29/0.52 (![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)) <=> ![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[96])).
% 0.29/0.52 tff(98,plain,
% 0.29/0.52 (![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)) <=> ![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(99,plain,
% 0.29/0.52 (^[Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : rewrite((((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam)))) => (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)) <=> ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)))),
% 0.29/0.52 inference(bind,[status(th)],[])).
% 0.29/0.52 tff(100,plain,
% 0.29/0.52 (![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : (((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam)))) => (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp)) <=> ![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp))),
% 0.29/0.52 inference(quant_intro,[status(thm)],[99])).
% 0.29/0.52 tff(101,axiom,(![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : (((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam)))) => (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduceExp-7'')).
% 0.29/0.52 tff(102,plain,
% 0.29/0.52 (![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.29/0.52 tff(103,plain,
% 0.29/0.52 (![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.29/0.52 tff(104,plain,(
% 0.29/0.52 ![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((~((~vexpIsValue(Ve1)) & (~visSomeExp(vreduceExp(Ve1, Vam))))) | (vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp))),
% 0.29/0.52 inference(skolemize,[status(sab)],[103])).
% 0.29/0.52 tff(105,plain,
% 0.29/0.52 (![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.29/0.52 tff(106,plain,
% 0.29/0.52 (![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))),
% 0.29/0.52 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.29/0.52 tff(107,plain,
% 0.29/0.52 (((~![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))) | (vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp))) <=> ((~![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(108,plain,
% 0.29/0.52 (((vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231))) <=> (vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp))),
% 0.29/0.52 inference(rewrite,[status(thm)],[])).
% 0.29/0.52 tff(109,plain,
% 0.29/0.52 (((~![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))) | ((vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)))) <=> ((~![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))) | (vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp)))),
% 0.29/0.52 inference(monotonicity,[status(thm)],[108])).
% 0.29/0.52 tff(110,plain,
% 0.29/0.52 (((~![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))) | ((vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)))) <=> ((~![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp))),
% 0.29/0.54 inference(transitivity,[status(thm)],[109, 107])).
% 0.29/0.54 tff(111,plain,
% 0.29/0.54 ((~![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))) | ((vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)))),
% 0.29/0.54 inference(quant_inst,[status(thm)],[])).
% 0.29/0.54 tff(112,plain,
% 0.29/0.54 ((~![Ve1: vExp, Vam: vAnsMap, Vop: vBinOpT, Ve2: vExp] : ((vreduceExp(vbinop(Ve1, Vop, Ve2), Vam) = vnoExp) | vexpIsValue(Ve1) | visSomeExp(vreduceExp(Ve1, Vam)))) | vexpIsValue(ve1) | visSomeExp(vreduceExp(ve1, Vam!231)) | (vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp)),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.29/0.54 tff(113,plain,
% 0.29/0.54 (vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vnoExp),
% 0.29/0.54 inference(unit_resolution,[status(thm)],[112, 106, 78, 60])).
% 0.29/0.54 tff(114,plain,
% 0.29/0.54 (vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(tptp_fun_Veres00_227(Vam!231))),
% 0.29/0.54 inference(transitivity,[status(thm)],[113, 93, 77])).
% 0.29/0.54 tff(115,plain,
% 0.29/0.54 (^[Veres000: vExp] : refl((~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000))) <=> (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000))))),
% 0.29/0.54 inference(bind,[status(th)],[])).
% 0.29/0.54 tff(116,plain,
% 0.29/0.54 (![Veres000: vExp] : (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000))) <=> ![Veres000: vExp] : (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000)))),
% 0.29/0.54 inference(quant_intro,[status(thm)],[115])).
% 0.29/0.54 tff(117,plain,
% 0.29/0.54 (![Veres000: vExp] : (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000)))),
% 0.29/0.54 inference(and_elim,[status(thm)],[10])).
% 0.29/0.54 tff(118,plain,
% 0.29/0.54 (![Veres000: vExp] : (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000)))),
% 0.29/0.54 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.29/0.54 tff(119,plain,
% 0.29/0.54 ((~![Veres000: vExp] : (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(Veres000)))) | (~(vreduceExp(vbinop(ve1, Vbot!230, ve2), Vam!231) = vsomeExp(tptp_fun_Veres00_227(Vam!231))))),
% 0.29/0.54 inference(quant_inst,[status(thm)],[])).
% 0.29/0.54 tff(120,plain,
% 0.29/0.54 ($false),
% 0.29/0.54 inference(unit_resolution,[status(thm)],[119, 118, 114])).
% 0.29/0.54 % SZS output end Proof
% 0.29/0.55 % E exiting
%------------------------------------------------------------------------------