%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM636^3 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 07:56:53 PM UTC 2025 % Result : Theorem 17.72s 17.94s % Output : Proof 17.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : NUM636^3 : TPTP v9.2.0. Released v3.7.0. % 0.00/0.12 % Command : duper %s % 0.12/0.31 % Computer : n012.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Fri Oct 3 08:53:38 EDT 2025 % 0.12/0.32 % CPUTime : % 17.72/17.94 SZS status Theorem for theBenchmark.p % 17.72/17.94 SZS output start Proof for theBenchmark.p % 17.72/17.94 Clause #2 (by assumption #[]): Eq (∀ (M : Iota → Prop), And (M one) (∀ (X : Iota), M X → M (succ X)) → ∀ (Y : Iota), M Y) True % 17.72/17.94 Clause #4 (by assumption #[]): Eq (m one) True % 17.72/17.94 Clause #5 (by assumption #[]): Eq (∀ (X : Iota), m X → m (succ X)) True % 17.72/17.94 Clause #6 (by assumption #[]): Eq (Not (∀ (X : Iota), m X)) True % 17.72/17.94 Clause #7 (by clausification #[6]): Eq (∀ (X : Iota), m X) False % 17.72/17.94 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (m (skS.0 0 a))) True % 17.72/17.94 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (m (skS.0 0 a)) False % 17.72/17.94 Clause #10 (by clausification #[5]): ∀ (a : Iota), Eq (m a → m (succ a)) True % 17.72/17.94 Clause #11 (by clausification #[10]): ∀ (a : Iota), Or (Eq (m a) False) (Eq (m (succ a)) True) % 17.72/17.94 Clause #15 (by clausification #[2]): ∀ (a : Iota → Prop), Eq (And (a one) (∀ (X : Iota), a X → a (succ X)) → ∀ (Y : Iota), a Y) True % 17.72/17.94 Clause #16 (by clausification #[15]): ∀ (a : Iota → Prop), Or (Eq (And (a one) (∀ (X : Iota), a X → a (succ X))) False) (Eq (∀ (Y : Iota), a Y) True) % 17.72/17.94 Clause #17 (by clausification #[16]): ∀ (a : Iota → Prop), % 17.72/17.94 Or (Eq (∀ (Y : Iota), a Y) True) (Or (Eq (a one) False) (Eq (∀ (X : Iota), a X → a (succ X)) False)) % 17.72/17.94 Clause #18 (by clausification #[17]): ∀ (a : Iota → Prop) (a_1 : Iota), % 17.72/17.94 Or (Eq (a one) False) (Or (Eq (∀ (X : Iota), a X → a (succ X)) False) (Eq (a a_1) True)) % 17.72/17.94 Clause #19 (by clausification #[18]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 17.72/17.94 Or (Eq (a one) False) (Or (Eq (a a_1) True) (Eq (Not (a (skS.0 1 a a_2) → a (succ (skS.0 1 a a_2)))) True)) % 17.72/17.94 Clause #20 (by clausification #[19]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 17.72/17.94 Or (Eq (a one) False) (Or (Eq (a a_1) True) (Eq (a (skS.0 1 a a_2) → a (succ (skS.0 1 a a_2))) False)) % 17.72/17.94 Clause #21 (by clausification #[20]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a one) False) (Or (Eq (a a_1) True) (Eq (a (skS.0 1 a a_2)) True)) % 17.72/17.94 Clause #22 (by clausification #[20]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a one) False) (Or (Eq (a a_1) True) (Eq (a (succ (skS.0 1 a a_2))) False)) % 17.72/17.94 Clause #33 (by superposition #[21, 4]): ∀ (a a_1 : Iota), % 17.72/17.94 Or (Eq ((fun x => m x) a) True) (Or (Eq ((fun x => m x) (skS.0 1 (fun x => m x) a_1)) True) (Eq False True)) % 17.72/17.94 Clause #104 (by fluidLoobHoist #[22]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 17.72/17.94 Or (Eq (a a_1) True) (Or (Eq (a (succ (skS.0 1 a a_2))) False) (Or (Eq True False) (Eq (a one) False))) % 17.72/17.94 Clause #461 (by betaEtaReduce #[33]): ∀ (a a_1 : Iota), Or (Eq (m a) True) (Or (Eq (m (skS.0 1 m a_1)) True) (Eq False True)) % 17.72/17.94 Clause #462 (by clausification #[461]): ∀ (a a_1 : Iota), Or (Eq (m a) True) (Eq (m (skS.0 1 m a_1)) True) % 17.72/17.94 Clause #463 (by superposition #[462, 9]): ∀ (a : Iota), Or (Eq (m (skS.0 1 m a)) True) (Eq True False) % 17.72/17.94 Clause #495 (by clausification #[463]): ∀ (a : Iota), Eq (m (skS.0 1 m a)) True % 17.72/17.94 Clause #496 (by superposition #[495, 11]): ∀ (a : Iota), Or (Eq True False) (Eq (m (succ (skS.0 1 m a))) True) % 17.72/17.94 Clause #505 (by clausification #[496]): ∀ (a : Iota), Eq (m (succ (skS.0 1 m a))) True % 17.72/17.94 Clause #1559 (by clausification #[104]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a a_1) True) (Or (Eq (a (succ (skS.0 1 a a_2))) False) (Eq (a one) False)) % 17.72/17.94 Clause #1575 (by superposition #[1559, 505]): ∀ (a : Iota), Or (Eq ((fun x => m x) a) True) (Or (Eq ((fun x => m x) one) False) (Eq False True)) % 17.72/17.94 Clause #1677 (by betaEtaReduce #[1575]): ∀ (a : Iota), Or (Eq (m a) True) (Or (Eq (m one) False) (Eq False True)) % 17.72/17.94 Clause #1678 (by clausification #[1677]): ∀ (a : Iota), Or (Eq (m a) True) (Eq (m one) False) % 17.72/17.94 Clause #1679 (by superposition #[1678, 4]): ∀ (a : Iota), Or (Eq (m a) True) (Eq False True) % 17.72/17.94 Clause #1695 (by clausification #[1679]): ∀ (a : Iota), Eq (m a) True % 17.72/17.94 Clause #1707 (by superposition #[1695, 9]): Eq True False % 17.72/17.94 Clause #1724 (by clausification #[1707]): False % 17.72/17.94 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------