%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM244_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 06:23:03 PM UTC 2026
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : COM244_1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.16/0.35 % Computer : n015.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Mon May 4 19:33:48 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(vTrue_type, type, (
% 0.21/0.44 vTrue: vTerm)).
% 0.21/0.44 tff(vZero_type, type, (
% 0.21/0.44 vZero: vTerm)).
% 0.21/0.44 tff(vFalse_type, type, (
% 0.21/0.44 vFalse: vTerm)).
% 0.21/0.44 tff(visNV_type, type, (
% 0.21/0.44 visNV: vTerm > $o)).
% 0.21/0.44 tff(visValue_type, type, (
% 0.21/0.44 visValue: vTerm > $o)).
% 0.21/0.44 tff(vptchecksimple_type, type, (
% 0.21/0.44 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.21/0.44 tff(tptp_fun_VT_62_type, type, (
% 0.21/0.44 tptp_fun_VT_62: vTy)).
% 0.21/0.44 tff(vnoTerm_type, type, (
% 0.21/0.44 vnoTerm: vOptTerm)).
% 0.21/0.44 tff(vreduce_type, type, (
% 0.21/0.44 vreduce: vTerm > vOptTerm)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 (visNV(vZero) <=> visNV(vZero)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(2,axiom,(visNV(vZero)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''isNV-0'')).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (visNV(vZero)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 ((visNV(vZero) | (vZero = vFalse) | (vZero = vTrue)) | (~visNV(vZero))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (visNV(vZero) | (vZero = vFalse) | (vZero = vTrue)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 ((~![VT: vTy] : ((~(vreduce(vZero) = vnoTerm)) | (~(vptchecksimple(vZero, VT) & (~visValue(vZero)))))) <=> (~![VT: vTy] : ((~(vreduce(vZero) = vnoTerm)) | (~(vptchecksimple(vZero, VT) & (~visValue(vZero))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 ((~![VT: vTy] : ((vptchecksimple(vZero, VT) & (~visValue(vZero))) => (~(vreduce(vZero) = vnoTerm)))) <=> (~![VT: vTy] : ((~(vreduce(vZero) = vnoTerm)) | (~(vptchecksimple(vZero, VT) & (~visValue(vZero))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(8,axiom,(~![VT: vTy] : ((vptchecksimple(vZero, VT) & (~visValue(vZero))) => (~(vreduce(vZero) = vnoTerm)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Progress-Zero'')).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (~![VT: vTy] : ((~(vreduce(vZero) = vnoTerm)) | (~(vptchecksimple(vZero, VT) & (~visValue(vZero)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (~![VT: vTy] : ((~(vreduce(vZero) = vnoTerm)) | (~(vptchecksimple(vZero, VT) & (~visValue(vZero)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (~![VT: vTy] : ((~(vreduce(vZero) = vnoTerm)) | (~(vptchecksimple(vZero, VT) & (~visValue(vZero)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (~![VT: vTy] : ((~(vreduce(vZero) = vnoTerm)) | (~(vptchecksimple(vZero, VT) & (~visValue(vZero)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.21/0.44 tff(13,plain,(
% 0.21/0.44 ~((~(vreduce(vZero) = vnoTerm)) | (~(vptchecksimple(vZero, VT!62) & (~visValue(vZero)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[12])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (vptchecksimple(vZero, VT!62) & (~visValue(vZero))),
% 0.21/0.44 inference(or_elim,[status(thm)],[13])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (~visValue(vZero)),
% 0.21/0.44 inference(and_elim,[status(thm)],[14])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 (^[VTerm0: vTerm] : refl((visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0)))) <=> (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 (![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0)))) <=> ![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (^[VTerm0: vTerm] : rewrite((visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse)))) <=> (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (![VTerm0: vTerm] : (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse)))) <=> ![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (![VTerm0: vTerm] : (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse)))) <=> ![VTerm0: vTerm] : (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (^[VTerm0: vTerm] : trans(monotonicity(trans(quant_intro(proof_bind(^[Vt1: vTerm] : trans(monotonicity(rewrite((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) <=> ((~(Vt1 = vTrue)) & (~(Vt1 = vFalse)) & (VTerm0 = Vt1))), (((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) & (~visNV(Vt1))) <=> (((~(Vt1 = vTrue)) & (~(Vt1 = vFalse)) & (VTerm0 = Vt1)) & (~visNV(Vt1))))), rewrite((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse)) & (VTerm0 = Vt1)) & (~visNV(Vt1))) <=> ((~(Vt1 = vTrue)) & (~(Vt1 = vFalse)) & (VTerm0 = Vt1) & (~visNV(Vt1)))), (((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) & (~visNV(Vt1))) <=> ((~(Vt1 = vTrue)) & (~(Vt1 = vFalse)) & (VTerm0 = Vt1) & (~visNV(Vt1)))))), (?[Vt1: vTerm] : ((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) & (~visNV(Vt1))) <=> ?[Vt1: vTerm] : ((~(Vt1 = vTrue)) & (~(Vt1 = vFalse)) & (VTerm0 = Vt1) & (~visNV(Vt1))))), trans(der(?[Vt1: vTerm] : ((~(Vt1 = vTrue)) & (~(Vt1 = vFalse)) & (VTerm0 = Vt1) & (~visNV(Vt1))) <=> ?[Vt1: vTerm] : ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse)))), elim_unused(?[Vt1: vTerm] : ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))) <=> ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse)))), (?[Vt1: vTerm] : ((~(Vt1 = vTrue)) & (~(Vt1 = vFalse)) & (VTerm0 = Vt1) & (~visNV(Vt1))) <=> ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))), (?[Vt1: vTerm] : ((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) & (~visNV(Vt1))) <=> ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))), (((~visValue(VTerm0)) => ?[Vt1: vTerm] : ((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) & (~visNV(Vt1)))) <=> ((~visValue(VTerm0)) => ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse)))))), rewrite(((~visValue(VTerm0)) => ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse)))) <=> (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))), (((~visValue(VTerm0)) => ?[Vt1: vTerm] : ((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) & (~visNV(Vt1)))) <=> (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 (![VTerm0: vTerm] : ((~visValue(VTerm0)) => ?[Vt1: vTerm] : ((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) & (~visNV(Vt1)))) <=> ![VTerm0: vTerm] : (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.44 tff(23,axiom,(![VTerm0: vTerm] : ((~visValue(VTerm0)) => ?[Vt1: vTerm] : ((((~(Vt1 = vTrue)) & (~(Vt1 = vFalse))) & (VTerm0 = Vt1)) & (~visNV(Vt1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''isValue-false-INV'')).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (![VTerm0: vTerm] : (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (![VTerm0: vTerm] : (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.44 tff(26,plain,(
% 0.21/0.44 ![VTerm0: vTerm] : (visValue(VTerm0) | ((~visNV(VTerm0)) & (~(VTerm0 = vTrue)) & (~(VTerm0 = vFalse))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[25])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (((~![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))) | (visValue(vZero) | (~(visNV(vZero) | (vZero = vFalse) | (vZero = vTrue))))) <=> ((~![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))) | visValue(vZero) | (~(visNV(vZero) | (vZero = vFalse) | (vZero = vTrue))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 ((visValue(vZero) | (~((vZero = vFalse) | (vZero = vTrue) | visNV(vZero)))) <=> (visValue(vZero) | (~(visNV(vZero) | (vZero = vFalse) | (vZero = vTrue))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (((~![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))) | (visValue(vZero) | (~((vZero = vFalse) | (vZero = vTrue) | visNV(vZero))))) <=> ((~![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))) | (visValue(vZero) | (~(visNV(vZero) | (vZero = vFalse) | (vZero = vTrue)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[30])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (((~![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))) | (visValue(vZero) | (~((vZero = vFalse) | (vZero = vTrue) | visNV(vZero))))) <=> ((~![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))) | visValue(vZero) | (~(visNV(vZero) | (vZero = vFalse) | (vZero = vTrue))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[31, 29])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 ((~![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))) | (visValue(vZero) | (~((vZero = vFalse) | (vZero = vTrue) | visNV(vZero))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 ((~![VTerm0: vTerm] : (visValue(VTerm0) | (~((VTerm0 = vFalse) | (VTerm0 = vTrue) | visNV(VTerm0))))) | visValue(vZero) | (~(visNV(vZero) | (vZero = vFalse) | (vZero = vTrue)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[34, 28, 15, 5])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------