%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM215_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n028.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 26.81s 27.05s
% Output : Proof 26.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : COM215_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.08 % Command : run_E %s %d THM
% 0.08/0.27 % Computer : n028.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon May 4 18:52:47 EDT 2026
% 0.08/0.27 % CPUTime :
% 26.81/27.05 % SZS status Theorem
% 26.81/27.05 % SZS output start Proof
% 26.81/27.05 tff(vptchecksimple_type, type, (
% 26.81/27.05 vptchecksimple: ( vTerm * vTy ) > $o)).
% 26.81/27.05 tff(vNat_type, type, (
% 26.81/27.05 vNat: vTy)).
% 26.81/27.05 tff(vplusop_type, type, (
% 26.81/27.05 vplusop: ( vTerm * vTerm ) > vTerm)).
% 26.81/27.05 tff(vPred_type, type, (
% 26.81/27.05 vPred: vTerm > vTerm)).
% 26.81/27.05 tff(vt2_type, type, (
% 26.81/27.05 vt2: vTerm)).
% 26.81/27.05 tff(tptp_fun_Vt_62_type, type, (
% 26.81/27.05 tptp_fun_Vt_62: vTerm)).
% 26.81/27.05 tff(vSucc_type, type, (
% 26.81/27.05 vSucc: vTerm > vTerm)).
% 26.81/27.05 tff(tptp_fun_Vt30_13_type, type, (
% 26.81/27.05 tptp_fun_Vt30_13: vTerm > vTerm)).
% 26.81/27.05 tff(vZero_type, type, (
% 26.81/27.05 vZero: vTerm)).
% 26.81/27.05 tff(1,plain,
% 26.81/27.05 ((vSucc(tptp_fun_Vt30_13(vPred(vt2))) = vPred(vt2)) <=> (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2))))),
% 26.81/27.05 inference(commutativity,[status(thm)],[])).
% 26.81/27.05 tff(2,plain,
% 26.81/27.05 ((~(vSucc(tptp_fun_Vt30_13(vPred(vt2))) = vPred(vt2))) <=> (~(vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2)))))),
% 26.81/27.05 inference(monotonicity,[status(thm)],[1])).
% 26.81/27.05 tff(3,assumption,(vSucc(tptp_fun_Vt30_13(vPred(vt2))) = vPred(vt2)), introduced(assumption)).
% 26.81/27.05 tff(4,plain,
% 26.81/27.05 (^[VTerm0: vTerm, VTerm1: vTerm] : refl((~(vSucc(VTerm0) = vPred(VTerm1))) <=> (~(vSucc(VTerm0) = vPred(VTerm1))))),
% 26.81/27.05 inference(bind,[status(th)],[])).
% 26.81/27.05 tff(5,plain,
% 26.81/27.05 (![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1))) <=> ![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 26.81/27.05 inference(quant_intro,[status(thm)],[4])).
% 26.81/27.05 tff(6,plain,
% 26.81/27.05 (![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1))) <=> ![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 26.81/27.05 inference(rewrite,[status(thm)],[])).
% 26.81/27.05 tff(7,axiom,(![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-Succ-Pred'')).
% 26.81/27.05 tff(8,plain,
% 26.81/27.05 (![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 26.81/27.05 inference(modus_ponens,[status(thm)],[7, 6])).
% 26.81/27.05 tff(9,plain,(
% 26.81/27.05 ![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 26.81/27.05 inference(skolemize,[status(sab)],[8])).
% 26.81/27.05 tff(10,plain,
% 26.81/27.05 (![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))),
% 26.81/27.05 inference(modus_ponens,[status(thm)],[9, 5])).
% 26.81/27.05 tff(11,plain,
% 26.81/27.05 ((~![VTerm0: vTerm, VTerm1: vTerm] : (~(vSucc(VTerm0) = vPred(VTerm1)))) | (~(vSucc(tptp_fun_Vt30_13(vPred(vt2))) = vPred(vt2)))),
% 26.81/27.05 inference(quant_inst,[status(thm)],[])).
% 26.81/27.05 tff(12,plain,
% 26.81/27.05 ($false),
% 26.81/27.05 inference(unit_resolution,[status(thm)],[11, 10, 3])).
% 26.81/27.05 tff(13,plain,(~(vSucc(tptp_fun_Vt30_13(vPred(vt2))) = vPred(vt2))), inference(lemma,lemma(discharge,[]))).
% 26.81/27.05 tff(14,plain,
% 26.81/27.05 (~(vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2))))),
% 26.81/27.05 inference(modus_ponens,[status(thm)],[13, 2])).
% 26.81/27.05 tff(15,plain,
% 26.81/27.05 ((vPred(vt2) = vZero) <=> (vZero = vPred(vt2))),
% 26.81/27.05 inference(commutativity,[status(thm)],[])).
% 26.81/27.05 tff(16,plain,
% 26.81/27.05 ((vZero = vPred(vt2)) <=> (vPred(vt2) = vZero)),
% 26.81/27.05 inference(symmetry,[status(thm)],[15])).
% 26.81/27.05 tff(17,plain,
% 26.81/27.05 ((~(vZero = vPred(vt2))) <=> (~(vPred(vt2) = vZero))),
% 26.81/27.05 inference(monotonicity,[status(thm)],[16])).
% 26.81/27.05 tff(18,plain,
% 26.81/27.05 (^[VTerm0: vTerm] : refl((~(vZero = vPred(VTerm0))) <=> (~(vZero = vPred(VTerm0))))),
% 26.81/27.05 inference(bind,[status(th)],[])).
% 26.81/27.05 tff(19,plain,
% 26.81/27.05 (![VTerm0: vTerm] : (~(vZero = vPred(VTerm0))) <=> ![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 26.81/27.05 inference(quant_intro,[status(thm)],[18])).
% 26.81/27.05 tff(20,plain,
% 26.81/27.05 (![VTerm0: vTerm] : (~(vZero = vPred(VTerm0))) <=> ![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 26.81/27.05 inference(rewrite,[status(thm)],[])).
% 26.81/27.05 tff(21,axiom,(![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-Zero-Pred'')).
% 26.81/27.05 tff(22,plain,
% 26.81/27.05 (![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 26.81/27.05 inference(modus_ponens,[status(thm)],[21, 20])).
% 26.81/27.05 tff(23,plain,(
% 26.81/27.05 ![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 26.81/27.05 inference(skolemize,[status(sab)],[22])).
% 26.81/27.05 tff(24,plain,
% 26.81/27.05 (![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))),
% 26.81/27.05 inference(modus_ponens,[status(thm)],[23, 19])).
% 26.81/27.05 tff(25,plain,
% 26.81/27.05 ((~![VTerm0: vTerm] : (~(vZero = vPred(VTerm0)))) | (~(vZero = vPred(vt2)))),
% 26.81/27.05 inference(quant_inst,[status(thm)],[])).
% 26.81/27.06 tff(26,plain,
% 26.81/27.06 (~(vZero = vPred(vt2))),
% 26.81/27.06 inference(unit_resolution,[status(thm)],[25, 24])).
% 26.81/27.06 tff(27,plain,
% 26.81/27.06 (~(vPred(vt2) = vZero)),
% 26.81/27.06 inference(modus_ponens,[status(thm)],[26, 17])).
% 26.81/27.06 tff(28,plain,
% 26.81/27.06 (^[Vt3: vTerm, Vt2: vTerm] : refl(((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3)))) <=> ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3)))))),
% 26.81/27.06 inference(bind,[status(th)],[])).
% 26.81/27.06 tff(29,plain,
% 26.81/27.06 (![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3)))) <=> ![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))),
% 26.81/27.06 inference(quant_intro,[status(thm)],[28])).
% 26.81/27.06 tff(30,plain,
% 26.81/27.06 (^[Vt3: vTerm, Vt2: vTerm] : rewrite((((Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3)))) | (vplusop(Vt2, Vt3) = Vt3)) <=> ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3)))))),
% 26.81/27.06 inference(bind,[status(th)],[])).
% 26.81/27.06 tff(31,plain,
% 26.81/27.06 (![Vt3: vTerm, Vt2: vTerm] : (((Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3)))) | (vplusop(Vt2, Vt3) = Vt3)) <=> ![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))),
% 26.81/27.06 inference(quant_intro,[status(thm)],[30])).
% 26.81/27.06 tff(32,plain,
% 26.81/27.06 (![Vt3: vTerm, Vt2: vTerm] : ((~((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30))))) | (vplusop(Vt2, Vt3) = Vt3)) <=> ![Vt3: vTerm, Vt2: vTerm] : ((~((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30))))) | (vplusop(Vt2, Vt3) = Vt3))),
% 26.81/27.06 inference(rewrite,[status(thm)],[])).
% 26.81/27.06 tff(33,plain,
% 26.81/27.06 (^[Vt3: vTerm, Vt2: vTerm] : trans(monotonicity(rewrite(((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30)))) <=> ((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30))))), ((((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30)))) => (vplusop(Vt2, Vt3) = Vt3)) <=> (((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30)))) => (vplusop(Vt2, Vt3) = Vt3)))), rewrite((((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30)))) => (vplusop(Vt2, Vt3) = Vt3)) <=> ((~((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30))))) | (vplusop(Vt2, Vt3) = Vt3))), ((((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30)))) => (vplusop(Vt2, Vt3) = Vt3)) <=> ((~((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30))))) | (vplusop(Vt2, Vt3) = Vt3))))),
% 26.81/27.06 inference(bind,[status(th)],[])).
% 26.81/27.06 tff(34,plain,
% 26.81/27.06 (![Vt3: vTerm, Vt2: vTerm] : (((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30)))) => (vplusop(Vt2, Vt3) = Vt3)) <=> ![Vt3: vTerm, Vt2: vTerm] : ((~((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30))))) | (vplusop(Vt2, Vt3) = Vt3))),
% 26.81/27.06 inference(quant_intro,[status(thm)],[33])).
% 26.81/27.06 tff(35,axiom,(![Vt3: vTerm, Vt2: vTerm] : (((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30)))) => (vplusop(Vt2, Vt3) = Vt3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''plusop-2'')).
% 26.81/27.06 tff(36,plain,
% 26.81/27.06 (![Vt3: vTerm, Vt2: vTerm] : ((~((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30))))) | (vplusop(Vt2, Vt3) = Vt3))),
% 26.81/27.06 inference(modus_ponens,[status(thm)],[35, 34])).
% 26.81/27.06 tff(37,plain,
% 26.81/27.06 (![Vt3: vTerm, Vt2: vTerm] : ((~((~(Vt3 = vZero)) & ![Vt30: vTerm] : (~(Vt3 = vSucc(Vt30))))) | (vplusop(Vt2, Vt3) = Vt3))),
% 26.81/27.06 inference(modus_ponens,[status(thm)],[36, 32])).
% 26.81/27.06 tff(38,plain,(
% 26.81/27.06 ![Vt3: vTerm, Vt2: vTerm] : (((Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3)))) | (vplusop(Vt2, Vt3) = Vt3))),
% 26.81/27.06 inference(skolemize,[status(sab)],[37])).
% 26.81/27.06 tff(39,plain,
% 26.81/27.06 (![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))),
% 26.81/27.06 inference(modus_ponens,[status(thm)],[38, 31])).
% 26.81/27.06 tff(40,plain,
% 26.81/27.06 (![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))),
% 26.81/27.06 inference(modus_ponens,[status(thm)],[39, 29])).
% 26.81/27.06 tff(41,plain,
% 26.81/27.06 (((~![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))) | ((vPred(vt2) = vZero) | (vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2)))))) <=> ((~![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))) | (vPred(vt2) = vZero) | (vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2)))))),
% 26.81/27.06 inference(rewrite,[status(thm)],[])).
% 26.81/27.06 tff(42,plain,
% 26.81/27.06 (((vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vZero) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2))))) <=> ((vPred(vt2) = vZero) | (vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2)))))),
% 26.81/27.06 inference(rewrite,[status(thm)],[])).
% 26.81/27.06 tff(43,plain,
% 26.81/27.06 (((~![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))) | ((vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vZero) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2)))))) <=> ((~![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))) | ((vPred(vt2) = vZero) | (vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2))))))),
% 26.81/27.06 inference(monotonicity,[status(thm)],[42])).
% 26.81/27.06 tff(44,plain,
% 26.81/27.06 (((~![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))) | ((vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vZero) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2)))))) <=> ((~![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))) | (vPred(vt2) = vZero) | (vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2)))))),
% 26.81/27.06 inference(transitivity,[status(thm)],[43, 41])).
% 26.81/27.06 tff(45,plain,
% 26.81/27.06 ((~![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))) | ((vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vZero) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2)))))),
% 26.81/27.06 inference(quant_inst,[status(thm)],[])).
% 26.81/27.06 tff(46,plain,
% 26.81/27.06 ((~![Vt3: vTerm, Vt2: vTerm] : ((vplusop(Vt2, Vt3) = Vt3) | (Vt3 = vZero) | (Vt3 = vSucc(tptp_fun_Vt30_13(Vt3))))) | (vPred(vt2) = vZero) | (vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2))))),
% 26.81/27.06 inference(modus_ponens,[status(thm)],[45, 44])).
% 26.81/27.06 tff(47,plain,
% 26.81/27.06 ((vPred(vt2) = vZero) | (vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2))))),
% 26.81/27.06 inference(unit_resolution,[status(thm)],[46, 40])).
% 26.81/27.06 tff(48,plain,
% 26.81/27.06 ((vplusop(Vt!62, vPred(vt2)) = vPred(vt2)) | (vPred(vt2) = vSucc(tptp_fun_Vt30_13(vPred(vt2))))),
% 26.81/27.06 inference(unit_resolution,[status(thm)],[47, 27])).
% 26.81/27.06 tff(49,plain,
% 26.81/27.06 (vplusop(Vt!62, vPred(vt2)) = vPred(vt2)),
% 26.81/27.06 inference(unit_resolution,[status(thm)],[48, 14])).
% 26.81/27.06 tff(50,plain,
% 26.81/27.06 (vptchecksimple(vplusop(Vt!62, vPred(vt2)), vNat) <=> vptchecksimple(vPred(vt2), vNat)),
% 26.81/27.06 inference(monotonicity,[status(thm)],[49])).
% 26.81/27.06 tff(51,plain,
% 26.81/27.06 (vptchecksimple(vPred(vt2), vNat) <=> vptchecksimple(vplusop(Vt!62, vPred(vt2)), vNat)),
% 26.81/27.06 inference(symmetry,[status(thm)],[50])).
% 26.81/27.06 tff(52,plain,
% 26.81/27.06 ((~![Vt: vTerm] : ((~(vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat))) | vptchecksimple(vplusop(Vt, vPred(vt2)), vNat))) <=> (~![Vt: vTerm] : ((~(vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat))) | vptchecksimple(vplusop(Vt, vPred(vt2)), vNat)))),
% 26.81/27.06 inference(rewrite,[status(thm)],[])).
% 26.81/27.06 tff(53,plain,
% 26.81/27.06 ((~![Vt: vTerm] : ((vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat)) => vptchecksimple(vplusop(Vt, vPred(vt2)), vNat))) <=> (~![Vt: vTerm] : ((~(vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat))) | vptchecksimple(vplusop(Vt, vPred(vt2)), vNat)))),
% 26.81/27.06 inference(rewrite,[status(thm)],[])).
% 26.81/27.06 tff(54,axiom,(~![Vt: vTerm] : ((vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat)) => vptchecksimple(vplusop(Vt, vPred(vt2)), vNat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''PlusPreservation-Pred'')).
% 26.81/27.07 tff(55,plain,
% 26.81/27.07 (~![Vt: vTerm] : ((~(vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat))) | vptchecksimple(vplusop(Vt, vPred(vt2)), vNat))),
% 26.81/27.07 inference(modus_ponens,[status(thm)],[54, 53])).
% 26.81/27.07 tff(56,plain,
% 26.81/27.07 (~![Vt: vTerm] : ((~(vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat))) | vptchecksimple(vplusop(Vt, vPred(vt2)), vNat))),
% 26.81/27.07 inference(modus_ponens,[status(thm)],[55, 52])).
% 26.81/27.07 tff(57,plain,
% 26.81/27.07 (~![Vt: vTerm] : ((~(vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat))) | vptchecksimple(vplusop(Vt, vPred(vt2)), vNat))),
% 26.81/27.07 inference(modus_ponens,[status(thm)],[56, 52])).
% 26.81/27.07 tff(58,plain,
% 26.81/27.07 (~![Vt: vTerm] : ((~(vptchecksimple(Vt, vNat) & vptchecksimple(vPred(vt2), vNat))) | vptchecksimple(vplusop(Vt, vPred(vt2)), vNat))),
% 26.81/27.07 inference(modus_ponens,[status(thm)],[57, 52])).
% 26.81/27.07 tff(59,plain,(
% 26.81/27.07 ~((~(vptchecksimple(Vt!62, vNat) & vptchecksimple(vPred(vt2), vNat))) | vptchecksimple(vplusop(Vt!62, vPred(vt2)), vNat))),
% 26.81/27.07 inference(skolemize,[status(sab)],[58])).
% 26.81/27.07 tff(60,plain,
% 26.81/27.07 (vptchecksimple(Vt!62, vNat) & vptchecksimple(vPred(vt2), vNat)),
% 26.81/27.07 inference(or_elim,[status(thm)],[59])).
% 26.81/27.07 tff(61,plain,
% 26.81/27.07 (vptchecksimple(vPred(vt2), vNat)),
% 26.81/27.07 inference(and_elim,[status(thm)],[60])).
% 26.81/27.07 tff(62,plain,
% 26.81/27.07 (vptchecksimple(vplusop(Vt!62, vPred(vt2)), vNat)),
% 26.81/27.07 inference(modus_ponens,[status(thm)],[61, 51])).
% 26.81/27.07 tff(63,plain,
% 26.81/27.07 (~vptchecksimple(vplusop(Vt!62, vPred(vt2)), vNat)),
% 26.81/27.07 inference(or_elim,[status(thm)],[59])).
% 26.81/27.07 tff(64,plain,
% 26.81/27.07 ($false),
% 26.81/27.07 inference(unit_resolution,[status(thm)],[63, 62])).
% 26.81/27.07 % SZS output end Proof
% 26.81/27.08 % E exiting
%------------------------------------------------------------------------------