%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM222_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 06:23:01 PM UTC 2026
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM222_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n006.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 19:05:02 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(vsomeTerm_type, type, (
% 0.19/0.41 vsomeTerm: vTerm > vOptTerm)).
% 0.19/0.41 tff(tptp_fun_Vtres_62_type, type, (
% 0.19/0.41 tptp_fun_Vtres_62: vTerm)).
% 0.19/0.41 tff(vnoTerm_type, type, (
% 0.19/0.41 vnoTerm: vOptTerm)).
% 0.19/0.41 tff(vreduce_type, type, (
% 0.19/0.41 vreduce: vTerm > vOptTerm)).
% 0.19/0.41 tff(vPlus_type, type, (
% 0.19/0.41 vPlus: ( vTerm * vTerm ) > vTerm)).
% 0.19/0.41 tff(vt2_type, type, (
% 0.19/0.41 vt2: vTerm)).
% 0.19/0.41 tff(vt1_type, type, (
% 0.19/0.41 vt1: vTerm)).
% 0.19/0.41 tff(vptchecksimple_type, type, (
% 0.19/0.41 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.19/0.41 tff(tptp_fun_VT_63_type, type, (
% 0.19/0.41 tptp_fun_VT_63: vTy)).
% 0.19/0.41 tff(visNV_type, type, (
% 0.19/0.41 visNV: vTerm > $o)).
% 0.19/0.41 tff(visSomeTerm_type, type, (
% 0.19/0.41 visSomeTerm: vOptTerm > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 ((~![VT: vTy, Vtres: vTerm] : ((~((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))) <=> (~![VT: vTy, Vtres: vTerm] : ((~((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 ((~![VT: vTy, Vtres: vTerm] : (((((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1))) & vptchecksimple(vPlus(vt1, vt2), VT)) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT))) <=> (~![VT: vTy, Vtres: vTerm] : ((~((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(3,axiom,(~![VT: vTy, Vtres: vTerm] : (((((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1))) & vptchecksimple(vPlus(vt1, vt2), VT)) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Preservation-Plus-isNV-False-isSomeTerm-False'')).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (~![VT: vTy, Vtres: vTerm] : ((~((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (~![VT: vTy, Vtres: vTerm] : ((~((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (~![VT: vTy, Vtres: vTerm] : ((~((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (~![VT: vTy, Vtres: vTerm] : ((~((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.41 tff(8,plain,(
% 0.19/0.41 ~((~((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT!63) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres!62)))) | vptchecksimple(Vtres!62, VT!63))),
% 0.19/0.41 inference(skolemize,[status(sab)],[7])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 ((~visSomeTerm(vreduce(vt1))) & (~visNV(vt1)) & vptchecksimple(vPlus(vt1, vt2), VT!63) & (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres!62))),
% 0.19/0.41 inference(or_elim,[status(thm)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (vreduce(vPlus(vt1, vt2)) = vsomeTerm(Vtres!62)),
% 0.19/0.41 inference(and_elim,[status(thm)],[9])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (~visNV(vt1)),
% 0.19/0.41 inference(and_elim,[status(thm)],[9])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (~visSomeTerm(vreduce(vt1))),
% 0.19/0.41 inference(and_elim,[status(thm)],[9])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (^[Vt1: vTerm, Vt2: vTerm] : refl((visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1))) <=> (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1))) <=> ![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (^[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)) = vnoTerm)) <=> ((visNV(Vt1) | visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm)))), rewrite(((visNV(Vt1) | visSomeTerm(vreduce(Vt1))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm)) <=> (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))), (((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm)) <=> (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm)) <=> ![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm)) <=> ![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (^[Vt1: vTerm, Vt2: vTerm] : rewrite((((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1)))) => (vreduce(vPlus(Vt1, Vt2)) = vnoTerm)) <=> ((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![Vt1: vTerm, Vt2: vTerm] : (((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1)))) => (vreduce(vPlus(Vt1, Vt2)) = vnoTerm)) <=> ![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.41 tff(20,axiom,(![Vt1: vTerm, Vt2: vTerm] : (((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1)))) => (vreduce(vPlus(Vt1, Vt2)) = vnoTerm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduce-22'')).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.41 tff(23,plain,(
% 0.19/0.41 ![Vt1: vTerm, Vt2: vTerm] : ((~((~visNV(Vt1)) & (~visSomeTerm(vreduce(Vt1))))) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm))),
% 0.19/0.41 inference(skolemize,[status(sab)],[22])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))) | (visSomeTerm(vreduce(vt1)) | visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm))) <=> ((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))) | visSomeTerm(vreduce(vt1)) | visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm) | visSomeTerm(vreduce(vt1))) <=> (visSomeTerm(vreduce(vt1)) | visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))) | (visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm) | visSomeTerm(vreduce(vt1)))) <=> ((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))) | (visSomeTerm(vreduce(vt1)) | visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[27])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))) | (visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm) | visSomeTerm(vreduce(vt1)))) <=> ((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))) | visSomeTerm(vreduce(vt1)) | visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm))),
% 0.19/0.42 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 ((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))) | (visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm) | visSomeTerm(vreduce(vt1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 ((~![Vt1: vTerm, Vt2: vTerm] : (visNV(Vt1) | (vreduce(vPlus(Vt1, Vt2)) = vnoTerm) | visSomeTerm(vreduce(Vt1)))) | visSomeTerm(vreduce(vt1)) | visNV(vt1) | (vreduce(vPlus(vt1, vt2)) = vnoTerm)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (vreduce(vPlus(vt1, vt2)) = vnoTerm),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[31, 25, 12, 11])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (vnoTerm = vreduce(vPlus(vt1, vt2))),
% 0.19/0.42 inference(symmetry,[status(thm)],[32])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 (vnoTerm = vsomeTerm(Vtres!62)),
% 0.19/0.42 inference(transitivity,[status(thm)],[33, 10])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (^[VTerm0: vTerm] : refl((~(vnoTerm = vsomeTerm(VTerm0))) <=> (~(vnoTerm = vsomeTerm(VTerm0))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(38,axiom,(![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-noTerm-someTerm'')).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.42 tff(40,plain,(
% 0.19/0.42 ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[39])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 ((~![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))) | (~(vnoTerm = vsomeTerm(Vtres!62)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (~(vnoTerm = vsomeTerm(Vtres!62))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[43, 34])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------