%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM212_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM212_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n010.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:45:37 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 tff(vSucc_type, type, (
% 0.18/0.42 vSucc: vTerm > vTerm)).
% 0.18/0.42 tff(tptp_fun_Vnv0_9_type, type, (
% 0.18/0.42 tptp_fun_Vnv0_9: vTerm > vTerm)).
% 0.18/0.42 tff(vFalse_type, type, (
% 0.18/0.42 vFalse: vTerm)).
% 0.18/0.42 tff(visNV_type, type, (
% 0.18/0.42 visNV: vTerm > $o)).
% 0.18/0.42 tff(vptchecksimple_type, type, (
% 0.18/0.42 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.18/0.42 tff(vNat_type, type, (
% 0.18/0.42 vNat: vTy)).
% 0.18/0.42 tff(vZero_type, type, (
% 0.18/0.42 vZero: vTerm)).
% 0.18/0.42 tff(1,plain,
% 0.18/0.42 (visNV(vFalse) <=> visNV(vFalse)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(2,plain,
% 0.18/0.42 ((~(visNV(vFalse) => vptchecksimple(vFalse, vNat))) <=> (~((~visNV(vFalse)) | vptchecksimple(vFalse, vNat)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(3,axiom,(~(visNV(vFalse) => vptchecksimple(vFalse, vNat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''isNVisNat-False'')).
% 0.18/0.42 tff(4,plain,
% 0.18/0.42 (~((~visNV(vFalse)) | vptchecksimple(vFalse, vNat))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.42 tff(5,plain,
% 0.18/0.42 (visNV(vFalse)),
% 0.18/0.42 inference(or_elim,[status(thm)],[4])).
% 0.18/0.42 tff(6,plain,
% 0.18/0.42 (visNV(vFalse)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.18/0.42 tff(7,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(8,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.18/0.42 tff(9,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(10,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.18/0.42 tff(11,plain,
% 0.18/0.42 (![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))))) <=> ![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(12,plain,
% 0.18/0.42 (^[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))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(13,plain,
% 0.18/0.42 (![VwildcardName0: vTerm] : (((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) => (~visNV(VwildcardName0))) <=> ![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.42 tff(14,axiom,(![VwildcardName0: vTerm] : (((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0)))) => (~visNV(VwildcardName0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''isNV-2'')).
% 0.18/0.42 tff(15,plain,
% 0.18/0.42 (![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.42 tff(16,plain,
% 0.18/0.42 (![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | (~((~(VwildcardName0 = vZero)) & ![Vnv0: vTerm] : (~(VwildcardName0 = vSucc(Vnv0))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.18/0.42 tff(17,plain,(
% 0.18/0.42 ![VwildcardName0: vTerm] : ((~visNV(VwildcardName0)) | ((VwildcardName0 = vZero) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0)))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[16])).
% 0.18/0.42 tff(18,plain,
% 0.18/0.42 (![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.18/0.42 tff(19,plain,
% 0.18/0.42 (![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.18/0.42 tff(20,plain,
% 0.18/0.42 ((~(vFalse = vZero)) <=> (~(vFalse = vZero))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(21,axiom,(~(vFalse = vZero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-False-Zero'')).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 (~(vFalse = vZero)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 (((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | ((vFalse = vZero) | (~visNV(vFalse)) | (vFalse = vSucc(tptp_fun_Vnv0_9(vFalse))))) <=> ((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | (vFalse = vZero) | (~visNV(vFalse)) | (vFalse = vSucc(tptp_fun_Vnv0_9(vFalse))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(24,plain,
% 0.18/0.42 ((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | ((vFalse = vZero) | (~visNV(vFalse)) | (vFalse = vSucc(tptp_fun_Vnv0_9(vFalse))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 ((~![VwildcardName0: vTerm] : ((VwildcardName0 = vZero) | (~visNV(VwildcardName0)) | (VwildcardName0 = vSucc(tptp_fun_Vnv0_9(VwildcardName0))))) | (vFalse = vZero) | (~visNV(vFalse)) | (vFalse = vSucc(tptp_fun_Vnv0_9(vFalse)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 (vFalse = vSucc(tptp_fun_Vnv0_9(vFalse))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[25, 22, 19, 6])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (^[VTerm0: vTerm] : refl((~(vFalse = vSucc(VTerm0))) <=> (~(vFalse = vSucc(VTerm0))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(28,plain,
% 0.18/0.42 (![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0))) <=> ![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.42 tff(29,plain,
% 0.18/0.42 (![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0))) <=> ![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(30,axiom,(![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-False-Succ'')).
% 0.18/0.42 tff(31,plain,
% 0.18/0.42 (![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.42 tff(32,plain,(
% 0.18/0.42 ![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[31])).
% 0.18/0.42 tff(33,plain,
% 0.18/0.42 (![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.18/0.42 tff(34,plain,
% 0.18/0.42 ((~![VTerm0: vTerm] : (~(vFalse = vSucc(VTerm0)))) | (~(vFalse = vSucc(tptp_fun_Vnv0_9(vFalse))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(35,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[34, 33, 26])).
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43 % E exiting
%------------------------------------------------------------------------------