%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV282^5 : TPTP v9.2.0. Bugfixed v6.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:03:01 PM UTC 2025 % Result : Theorem 8.65s 8.82s % Output : Proof 8.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEV282^5 : TPTP v9.2.0. Bugfixed v6.2.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n014.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 01:01:23 EDT 2025 % 0.14/0.34 % CPUTime : % 8.65/8.82 SZS status Theorem for theBenchmark.p % 8.65/8.82 SZS output start Proof for theBenchmark.p % 8.65/8.82 Clause #2 (by assumption #[]): Eq % 8.65/8.82 (Eq cNAT fun Xn => % 8.65/8.82 ∀ (Xp : ((Iota → Prop) → Prop) → Prop), % 8.65/8.82 And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp Xn) % 8.65/8.82 True % 8.65/8.82 Clause #3 (by assumption #[]): Eq (Not (cNAT cZERO)) True % 8.65/8.82 Clause #4 (by clausification #[3]): Eq (cNAT cZERO) False % 8.65/8.82 Clause #5 (by clausification #[2]): Eq cNAT fun Xn => % 8.65/8.82 ∀ (Xp : ((Iota → Prop) → Prop) → Prop), And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp Xn % 8.65/8.82 Clause #6 (by argument congruence #[5]): ∀ (a : (Iota → Prop) → Prop), % 8.65/8.82 Eq (cNAT a) % 8.65/8.82 ((fun Xn => % 8.65/8.82 ∀ (Xp : ((Iota → Prop) → Prop) → Prop), % 8.65/8.82 And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp Xn) % 8.65/8.82 a) % 8.65/8.82 Clause #7 (by betaEtaReduce #[6]): ∀ (a : (Iota → Prop) → Prop), % 8.65/8.82 Eq (cNAT a) % 8.65/8.82 (∀ (Xp : ((Iota → Prop) → Prop) → Prop), % 8.65/8.82 And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp a) % 8.65/8.82 Clause #8 (by clausify Prop equality #[7]): ∀ (a : (Iota → Prop) → Prop), % 8.65/8.82 Or (Eq (cNAT a) True) % 8.65/8.82 (Eq % 8.65/8.82 (∀ (Xp : ((Iota → Prop) → Prop) → Prop), % 8.65/8.82 And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp a) % 8.65/8.82 False) % 8.65/8.82 Clause #19 (by clausification #[8]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop), % 8.65/8.82 Or (Eq (cNAT a) True) % 8.65/8.82 (Eq % 8.65/8.82 (Not % 8.65/8.82 (And (skS.0 1 a a_1 cZERO) (∀ (Xx : (Iota → Prop) → Prop), skS.0 1 a a_1 Xx → skS.0 1 a a_1 (cSUCC Xx)) → % 8.65/8.82 skS.0 1 a a_1 a)) % 8.65/8.82 True) % 8.65/8.82 Clause #20 (by clausification #[19]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop), % 8.65/8.82 Or (Eq (cNAT a) True) % 8.65/8.82 (Eq % 8.65/8.82 (And (skS.0 1 a a_1 cZERO) (∀ (Xx : (Iota → Prop) → Prop), skS.0 1 a a_1 Xx → skS.0 1 a a_1 (cSUCC Xx)) → % 8.65/8.82 skS.0 1 a a_1 a) % 8.65/8.82 False) % 8.65/8.82 Clause #21 (by clausification #[20]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop), % 8.65/8.82 Or (Eq (cNAT a) True) % 8.65/8.82 (Eq (And (skS.0 1 a a_1 cZERO) (∀ (Xx : (Iota → Prop) → Prop), skS.0 1 a a_1 Xx → skS.0 1 a a_1 (cSUCC Xx))) True) % 8.65/8.82 Clause #22 (by clausification #[20]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop), Or (Eq (cNAT a) True) (Eq (skS.0 1 a a_1 a) False) % 8.65/8.82 Clause #24 (by clausification #[21]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop), % 8.65/8.82 Or (Eq (cNAT a) True) (Eq (skS.0 1 a a_1 cZERO) True) % 8.65/8.82 Clause #293 (by superposition #[24, 22]): Or (Eq (cNAT fun x => cZERO x) True) (Or (Eq (cNAT cZERO) True) (Eq True False)) % 8.65/8.82 Clause #1531 (by betaEtaReduce #[293]): Or (Eq (cNAT cZERO) True) (Or (Eq (cNAT cZERO) True) (Eq True False)) % 8.65/8.82 Clause #1532 (by clausification #[1531]): Or (Eq (cNAT cZERO) True) (Eq (cNAT cZERO) True) % 8.65/8.82 Clause #1533 (by eliminate duplicate literals #[1532]): Eq (cNAT cZERO) True % 8.65/8.82 Clause #1534 (by superposition #[1533, 4]): Eq True False % 8.65/8.82 Clause #1558 (by clausification #[1534]): False % 8.65/8.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------