%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN023^2 : TPTP v9.2.0. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 : Fri Oct 3 07:57:44 PM UTC 2025 % Result : Theorem 122.17s 122.43s % Output : Proof 122.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUN023^2 : TPTP v9.2.0. Released v6.4.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n013.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 11:41:23 EDT 2025 % 0.13/0.35 % CPUTime : % 122.17/122.43 SZS status Theorem for theBenchmark.p % 122.17/122.43 SZS output start Proof for theBenchmark.p % 122.17/122.43 Clause #0 (by assumption #[]): Eq % 122.17/122.43 (Not % 122.17/122.43 (And % 122.17/122.43 (And (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U) % 122.17/122.43 (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V)) % 122.17/122.43 (∀ (X : Iota), Eq (h X) (ite (Eq X zero) (s zero) zero)) → % 122.17/122.43 Exists fun H => And (Eq (H zero) (s zero)) (Eq (H (s zero)) zero))) % 122.17/122.43 True % 122.17/122.43 Clause #1 (by clausification #[0]): Eq % 122.17/122.43 (And % 122.17/122.43 (And (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U) % 122.17/122.43 (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V)) % 122.17/122.43 (∀ (X : Iota), Eq (h X) (ite (Eq X zero) (s zero) zero)) → % 122.17/122.43 Exists fun H => And (Eq (H zero) (s zero)) (Eq (H (s zero)) zero)) % 122.17/122.43 False % 122.17/122.43 Clause #2 (by clausification #[1]): Eq % 122.17/122.43 (And % 122.17/122.43 (And (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U) % 122.17/122.43 (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V)) % 122.17/122.43 (∀ (X : Iota), Eq (h X) (ite (Eq X zero) (s zero) zero))) % 122.17/122.43 True % 122.17/122.43 Clause #3 (by clausification #[1]): Eq (Exists fun H => And (Eq (H zero) (s zero)) (Eq (H (s zero)) zero)) False % 122.17/122.43 Clause #4 (by clausification #[2]): Eq (∀ (X : Iota), Eq (h X) (ite (Eq X zero) (s zero) zero)) True % 122.17/122.43 Clause #5 (by clausification #[2]): Eq % 122.17/122.43 (And (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U) % 122.17/122.43 (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V)) % 122.17/122.43 True % 122.17/122.43 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (h a) (ite (Eq a zero) (s zero) zero)) True % 122.17/122.43 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (h a) (ite (Eq a zero) (s zero) zero) % 122.17/122.43 Clause #8 (by identity loobHoist #[7]): ∀ (a : Iota), Or (Eq (h a) (ite True (s zero) zero)) (Eq (Eq a zero) False) % 122.17/122.43 Clause #9 (by identity boolHoist #[7]): ∀ (a : Iota), Or (Eq (h a) (ite False (s zero) zero)) (Eq (Eq a zero) True) % 122.17/122.43 Clause #10 (by clausification #[8]): ∀ (a : Iota), Or (Eq (h a) (ite True (s zero) zero)) (Ne a zero) % 122.17/122.43 Clause #11 (by destructive equality resolution #[10]): Eq (h zero) (ite True (s zero) zero) % 122.17/122.43 Clause #12 (by clausification #[9]): ∀ (a : Iota), Or (Eq (h a) (ite False (s zero) zero)) (Eq a zero) % 122.17/122.43 Clause #13 (by superposition #[12, 12]): ∀ (a a_1 : Iota), Or (Eq a zero) (Or (Eq (h a_1) (h a)) (Eq a_1 zero)) % 122.17/122.43 Clause #48 (by clausification #[3]): ∀ (a : Iota → Iota), Eq (And (Eq (a zero) (s zero)) (Eq (a (s zero)) zero)) False % 122.17/122.43 Clause #49 (by clausification #[48]): ∀ (a : Iota → Iota), Or (Eq (Eq (a zero) (s zero)) False) (Eq (Eq (a (s zero)) zero) False) % 122.17/122.43 Clause #50 (by clausification #[49]): ∀ (a : Iota → Iota), Or (Eq (Eq (a (s zero)) zero) False) (Ne (a zero) (s zero)) % 122.17/122.43 Clause #51 (by clausification #[50]): ∀ (a : Iota → Iota), Or (Ne (a zero) (s zero)) (Ne (a (s zero)) zero) % 122.17/122.43 Clause #52 (by equality resolution #[51]): Ne ((fun x => s zero) (s zero)) zero % 122.17/122.43 Clause #61 (by betaEtaReduce #[52]): Ne (s zero) zero % 122.17/122.43 Clause #63 (by superposition #[61, 13]): ∀ (a : Iota), Or (Eq a zero) (Or (Eq (h (s zero)) (h a)) (Ne zero zero)) % 122.17/122.43 Clause #79 (by clausification #[5]): Eq (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V) True % 122.17/122.43 Clause #80 (by clausification #[5]): Eq (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U) True % 122.17/122.43 Clause #81 (by clausification #[79]): ∀ (a : Prop), Eq (∀ (U V : Iota), Not a → Eq (ite a U V) V) True % 122.17/122.43 Clause #82 (by clausification #[81]): ∀ (a : Prop) (a_1 : Iota), Eq (∀ (V : Iota), Not a → Eq (ite a a_1 V) V) True % 122.17/122.43 Clause #83 (by clausification #[82]): ∀ (a : Prop) (a_1 a_2 : Iota), Eq (Not a → Eq (ite a a_1 a_2) a_2) True % 122.17/122.43 Clause #84 (by clausification #[83]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq (Not a) False) (Eq (Eq (ite a a_1 a_2) a_2) True) % 122.17/122.43 Clause #85 (by clausification #[84]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq (Eq (ite a a_1 a_2) a_2) True) (Eq a True) % 122.17/122.43 Clause #86 (by clausification #[85]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Eq (ite a a_1 a_2) a_2) % 122.17/122.43 Clause #88 (by identity boolHoist #[86]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Or (Eq (ite False a_1 a_2) a_2) (Eq a True)) % 122.58/122.79 Clause #89 (by eliminate duplicate literals #[88]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Eq (ite False a_1 a_2) a_2) % 122.58/122.79 Clause #91 (by falseElim #[89]): ∀ (a a_1 : Iota), Eq (ite False a a_1) a_1 % 122.58/122.79 Clause #92 (by backward demodulation #[91, 12]): ∀ (a : Iota), Or (Eq (h a) zero) (Eq a zero) % 122.58/122.79 Clause #243 (by eliminate resolved literals #[63]): ∀ (a : Iota), Or (Eq a zero) (Eq (h (s zero)) (h a)) % 122.58/122.79 Clause #274 (by superposition #[243, 92]): ∀ (a : Iota), Or (Eq a zero) (Or (Eq (h (s zero)) zero) (Eq a zero)) % 122.58/122.79 Clause #291 (by eliminate duplicate literals #[274]): ∀ (a : Iota), Or (Eq a zero) (Eq (h (s zero)) zero) % 122.58/122.79 Clause #331 (by equality factoring #[291]): Or (Ne zero zero) (Eq (h (s zero)) zero) % 122.58/122.79 Clause #333 (by eliminate resolved literals #[331]): Eq (h (s zero)) zero % 122.58/122.79 Clause #4342 (by clausification #[80]): ∀ (a : Prop), Eq (∀ (U V : Iota), a → Eq (ite a U V) U) True % 122.58/122.79 Clause #4343 (by clausification #[4342]): ∀ (a : Prop) (a_1 : Iota), Eq (∀ (V : Iota), a → Eq (ite a a_1 V) a_1) True % 122.58/122.79 Clause #4344 (by clausification #[4343]): ∀ (a : Prop) (a_1 a_2 : Iota), Eq (a → Eq (ite a a_1 a_2) a_1) True % 122.58/122.79 Clause #4345 (by clausification #[4344]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a False) (Eq (Eq (ite a a_1 a_2) a_1) True) % 122.58/122.79 Clause #4346 (by clausification #[4345]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a False) (Eq (ite a a_1 a_2) a_1) % 122.58/122.79 Clause #4347 (by identity loobHoist #[4346]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a False) (Or (Eq (ite True a_1 a_2) a_1) (Eq a False)) % 122.58/122.79 Clause #4349 (by eliminate duplicate literals #[4347]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a False) (Eq (ite True a_1 a_2) a_1) % 122.58/122.79 Clause #4350 (by falseElim #[4349]): ∀ (a a_1 : Iota), Eq (ite True a a_1) a % 122.58/122.79 Clause #4351 (by superposition #[4350, 11]): Eq (h zero) (s zero) % 122.58/122.79 Clause #4355 (by backward demodulation #[4351, 51]): ∀ (a : Iota → Iota), Or (Ne (a zero) (h zero)) (Ne (a (s zero)) zero) % 122.58/122.79 Clause #4356 (by backward demodulation #[4351, 61]): Ne (h zero) zero % 122.58/122.79 Clause #4358 (by backward demodulation #[4351, 333]): Eq (h (h zero)) zero % 122.58/122.79 Clause #5246 (by forward demodulation #[4355, 4351]): ∀ (a : Iota → Iota), Or (Ne (a zero) (h zero)) (Ne (a (h zero)) zero) % 122.58/122.79 Clause #5250 (by superposition #[5246, 92]): ∀ (a : Iota) (a_1 : Iota → Iota), Or (Eq (h a) zero) (Or (Ne (a_1 zero) (h a)) (Ne (a_1 (h zero)) a)) % 122.58/122.79 Clause #29957 (by equality resolution #[5250]): ∀ (a : Iota → Iota), Or (Eq (h (a zero)) zero) (Ne ((fun x => h (a x)) (h zero)) (a zero)) % 122.58/122.79 Clause #44655 (by betaEtaReduce #[29957]): ∀ (a : Iota → Iota), Or (Eq (h (a zero)) zero) (Ne (h (a (h zero))) (a zero)) % 122.58/122.79 Clause #44661 (by superposition #[44655, 4358]): Or (Eq (h zero) zero) (Ne zero zero) % 122.58/122.79 Clause #45354 (by eliminate resolved literals #[44661]): Eq (h zero) zero % 122.58/122.79 Clause #45355 (by forward contextual literal cutting #[45354, 4356]): False % 122.58/122.79 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------