%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM233_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 06:23:02 PM UTC 2026
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM233_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:15:57 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(vsomeTerm_type, type, (
% 0.19/0.43 vsomeTerm: vTerm > vOptTerm)).
% 0.19/0.43 tff(vPlus_type, type, (
% 0.19/0.43 vPlus: ( vTerm * vTerm ) > vTerm)).
% 0.19/0.43 tff(vt2_type, type, (
% 0.19/0.43 vt2: vTerm)).
% 0.19/0.43 tff(vgetTerm_type, type, (
% 0.19/0.43 vgetTerm: vOptTerm > vTerm)).
% 0.19/0.43 tff(vreduce_type, type, (
% 0.19/0.43 vreduce: vTerm > vOptTerm)).
% 0.19/0.43 tff(vt1_type, type, (
% 0.19/0.43 vt1: vTerm)).
% 0.19/0.43 tff(vnoTerm_type, type, (
% 0.19/0.43 vnoTerm: vOptTerm)).
% 0.19/0.43 tff(visNV_type, type, (
% 0.19/0.43 visNV: vTerm > $o)).
% 0.19/0.43 tff(visValue_type, type, (
% 0.19/0.43 visValue: vTerm > $o)).
% 0.19/0.43 tff(vptchecksimple_type, type, (
% 0.19/0.43 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.19/0.43 tff(tptp_fun_VT_62_type, type, (
% 0.19/0.43 tptp_fun_VT_62: vTy)).
% 0.19/0.43 tff(visSomeTerm_type, type, (
% 0.19/0.43 visSomeTerm: vOptTerm > $o)).
% 0.19/0.43 tff(1,plain,
% 0.19/0.43 ((~![VT: vTy] : ((~(vreduce(vPlus(vt1, vt2)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (~visValue(vPlus(vt1, vt2))))))) <=> (~![VT: vTy] : ((~(vreduce(vPlus(vt1, vt2)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (~visValue(vPlus(vt1, vt2)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 ((~![VT: vTy] : ((((visSomeTerm(vreduce(vt1)) & (~visNV(vt1))) & vptchecksimple(vPlus(vt1, vt2), VT)) & (~visValue(vPlus(vt1, vt2)))) => (~(vreduce(vPlus(vt1, vt2)) = vnoTerm)))) <=> (~![VT: vTy] : ((~(vreduce(vPlus(vt1, vt2)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (~visValue(vPlus(vt1, vt2)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(3,axiom,(~![VT: vTy] : ((((visSomeTerm(vreduce(vt1)) & (~visNV(vt1))) & vptchecksimple(vPlus(vt1, vt2), VT)) & (~visValue(vPlus(vt1, vt2)))) => (~(vreduce(vPlus(vt1, vt2)) = vnoTerm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Progress-Plus-isNV-False-isSomeTerm-True'')).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (~![VT: vTy] : ((~(vreduce(vPlus(vt1, vt2)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (~visValue(vPlus(vt1, vt2))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (~![VT: vTy] : ((~(vreduce(vPlus(vt1, vt2)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (~visValue(vPlus(vt1, vt2))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (~![VT: vTy] : ((~(vreduce(vPlus(vt1, vt2)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (~visValue(vPlus(vt1, vt2))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (~![VT: vTy] : ((~(vreduce(vPlus(vt1, vt2)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (~visValue(vPlus(vt1, vt2))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.43 tff(8,plain,(
% 0.19/0.43 ~((~(vreduce(vPlus(vt1, vt2)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT!62) & (~visValue(vPlus(vt1, vt2))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[7])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (visSomeTerm(vreduce(vt1)) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT!62) & (~visValue(vPlus(vt1, vt2)))),
% 0.19/0.43 inference(or_elim,[status(thm)],[8])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (~visNV(vt1)),
% 0.19/0.43 inference(and_elim,[status(thm)],[9])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (visSomeTerm(vreduce(vt1))),
% 0.19/0.43 inference(and_elim,[status(thm)],[9])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (^[Vt1: vTerm, Vt2: vTerm] : refl((visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> ![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (^[Vt1: vTerm, Vt2: vTerm] : trans(monotonicity(trans(monotonicity(rewrite(((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1))) <=> (~(visNV(Vt1) | (~visSomeTerm(vreduce(Vt1)))))), ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) <=> (~(~(visNV(Vt1) | (~visSomeTerm(vreduce(Vt1)))))))), rewrite((~(~(visNV(Vt1) | (~visSomeTerm(vreduce(Vt1)))))) <=> (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))))), ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) <=> (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1)))))), (((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> ((visNV(Vt1) | (~visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))))), rewrite(((visNV(Vt1) | (~visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))), (((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> ![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> ![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (^[Vt1: vTerm, Vt2: vTerm] : rewrite((((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1))) => (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![Vt1: vTerm, Vt2: vTerm] : (((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1))) => (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2)))) <=> ![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.43 tff(19,axiom,(![Vt1: vTerm, Vt2: vTerm] : (((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1))) => (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduce-21'')).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.43 tff(22,plain,(
% 0.19/0.43 ![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[21])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))) | (visNV(vt1) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vPlus(vt1, vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(vt1)), vt2))))) <=> ((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))) | visNV(vt1) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vPlus(vt1, vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(vt1)), vt2))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 ((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))) | (visNV(vt1) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vPlus(vt1, vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(vt1)), vt2))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 ((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(Vt1)), Vt2))))) | visNV(vt1) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vPlus(vt1, vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(vt1)), vt2)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (vreduce(vPlus(vt1, vt2)) = vsomeTerm(vPlus(vgetTerm(vreduce(vt1)), vt2))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[27, 24, 11, 10])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (vreduce(vPlus(vt1, vt2)) = vnoTerm),
% 0.19/0.44 inference(or_elim,[status(thm)],[8])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (vnoTerm = vreduce(vPlus(vt1, vt2))),
% 0.19/0.44 inference(symmetry,[status(thm)],[29])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (vnoTerm = vsomeTerm(vPlus(vgetTerm(vreduce(vt1)), vt2))),
% 0.19/0.44 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (^[VTerm0: vTerm] : refl((~(vnoTerm = vsomeTerm(VTerm0))) <=> (~(vnoTerm = vsomeTerm(VTerm0))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(35,axiom,(![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-noTerm-someTerm'')).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.44 tff(37,plain,(
% 0.19/0.44 ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[36])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 ((~![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))) | (~(vnoTerm = vsomeTerm(vPlus(vgetTerm(vreduce(vt1)), vt2))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[39, 38, 31])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------