%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM213_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n017.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 06:23:00 PM UTC 2026
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM213_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:45:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(vPred_type, type, (
% 0.21/0.43 vPred: vTerm > vTerm)).
% 0.21/0.43 tff(vt1_type, type, (
% 0.21/0.43 vt1: vTerm)).
% 0.21/0.43 tff(vSucc_type, type, (
% 0.21/0.43 vSucc: vTerm > vTerm)).
% 0.21/0.43 tff(tptp_fun_Vnv0_9_type, type, (
% 0.21/0.43 tptp_fun_Vnv0_9: vTerm > vTerm)).
% 0.21/0.43 tff(vZero_type, type, (
% 0.21/0.43 vZero: vTerm)).
% 0.21/0.43 tff(visNV_type, type, (
% 0.21/0.43 visNV: vTerm > $o)).
% 0.21/0.43 tff(vptchecksimple_type, type, (
% 0.21/0.43 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.21/0.43 tff(vNat_type, type, (
% 0.21/0.43 vNat: vTy)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 ((vPred(vt1) = vZero) <=> (vZero = vPred(vt1))),
% 0.21/0.43 inference(commutativity,[status(thm)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 ((vZero = vPred(vt1)) <=> (vPred(vt1) = vZero)),
% 0.21/0.43 inference(symmetry,[status(thm)],[1])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 ((~(vZero = vPred(vt1))) <=> (~(vPred(vt1) = vZero))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[2])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (^[VTerm0: vTerm] : refl((~(vZero = vPred(VTerm0))) <=> (~(vZero = vPred(VTerm0))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (![VTerm0: vTerm] : (~(vZero = vPred(VTerm0))) <=> ![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (![VTerm0: vTerm] : (~(vZero = vPred(VTerm0))) <=> ![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(7,axiom,(![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''DIFF-Zero-Pred'')).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.43 tff(9,plain,(
% 0.21/0.43 ![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[8])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 ((~![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))) | (~(vZero = vPred(vt1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (~(vZero = vPred(vt1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (~(vPred(vt1) = vZero)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (visNV(vPred(vt1)) <=> visNV(vPred(vt1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 ((~(visNV(vPred(vt1)) => vptchecksimple(vPred(vt1), vNat))) <=> (~((~visNV(vPred(vt1))) | vptchecksimple(vPred(vt1), vNat)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(16,axiom,(~(visNV(vPred(vt1)) => vptchecksimple(vPred(vt1), vNat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''isNVisNat-Pred'')).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (~((~visNV(vPred(vt1))) | vptchecksimple(vPred(vt1), vNat))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (visNV(vPred(vt1))),
% 0.21/0.43 inference(or_elim,[status(thm)],[17])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (visNV(vPred(vt1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (^[VwildcardName0: vTerm] : refl(((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0)))) <=> ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0)))) <=> ![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (^[VwildcardName0: vTerm] : rewrite(((~visNV(VwildcardName0)) | ((VwildcardName0 = vZero) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) <=> ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | ((VwildcardName0 = vZero) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) <=> ![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))))) <=> ![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (^[VwildcardName0: vTerm] : trans(monotonicity(rewrite(((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) <=> ((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))), ((((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) => (~visNV(VwildcardName0))) <=> (((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) => (~visNV(VwildcardName0))))), rewrite((((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) => (~visNV(VwildcardName0))) <=> ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))), ((((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) => (~visNV(VwildcardName0))) <=> ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (![VwildcardName0: vTerm] : (((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) => (~visNV(VwildcardName0))) <=> ![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.43 tff(27,axiom,(![VwildcardName0: vTerm] : (((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) => (~visNV(VwildcardName0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''isNV-2'')).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.43 tff(30,plain,(
% 0.21/0.43 ![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | ((VwildcardName0 = vZero) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[29])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | ((~visNV(vPred(vt1))) | (vPred(vt1) = vZero) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1)))))) <=> ((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | (~visNV(vPred(vt1))) | (vPred(vt1) = vZero) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (((vPred(vt1) = vZero) | (~visNV(vPred(vt1))) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1))))) <=> ((~visNV(vPred(vt1))) | (vPred(vt1) = vZero) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | ((vPred(vt1) = vZero) | (~visNV(vPred(vt1))) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1)))))) <=> ((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | ((~visNV(vPred(vt1))) | (vPred(vt1) = vZero) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | ((vPred(vt1) = vZero) | (~visNV(vPred(vt1))) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1)))))) <=> ((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | (~visNV(vPred(vt1))) | (vPred(vt1) = vZero) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1)))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[35, 33])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 ((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | ((vPred(vt1) = vZero) | (~visNV(vPred(vt1))) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 ((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | (~visNV(vPred(vt1))) | (vPred(vt1) = vZero) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 ((vPred(vt1) = vZero) | (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[38, 32, 19])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (vPred(vt1) = vSucc(tptp_fun_Vnv0_9(vPred(vt1)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[39, 13])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (vSucc(tptp_fun_Vnv0_9(vPred(vt1))) = vPred(vt1)),
% 0.21/0.44 inference(symmetry,[status(thm)],[40])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (^[VTerm0: vTerm, VTerm1: vTerm] : refl((~(vSucc(VTerm0) = vPred(VTerm1))) <=> (~(vSucc(VTerm0) = vPred(VTerm1))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1))) <=> ![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1))) <=> ![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(45,axiom,(![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''DIFF-Succ-Pred'')).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.44 tff(47,plain,(
% 0.21/0.44 ![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[46])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 ((~![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))) | (~(vSucc(tptp_fun_Vnv0_9(vPred(vt1))) = vPred(vt1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[49, 48, 41])).
% 0.21/0.44 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------