%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN998^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:08:24 PM UTC 2025 % Result : Theorem 4.03s 4.18s % Output : Proof 4.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYN998^1 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n016.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 : Thu Oct 2 15:39:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.03/4.18 SZS status Theorem for theBenchmark.p % 4.03/4.18 SZS output start Proof for theBenchmark.p % 4.03/4.18 Clause #0 (by assumption #[]): Eq (Eq leibeq fun X Y => ∀ (P : Iota → Prop), P X → P Y) True % 4.03/4.18 Clause #1 (by assumption #[]): Eq (Not (∀ (X : Iota), leibeq X X)) True % 4.03/4.18 Clause #2 (by clausification #[1]): Eq (∀ (X : Iota), leibeq X X) False % 4.03/4.18 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (leibeq (skS.0 0 a) (skS.0 0 a))) True % 4.03/4.18 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (leibeq (skS.0 0 a) (skS.0 0 a)) False % 4.03/4.18 Clause #5 (by clausification #[0]): Eq leibeq fun X Y => ∀ (P : Iota → Prop), P X → P Y % 4.03/4.18 Clause #6 (by argument congruence #[5]): ∀ (a : Iota), Eq (leibeq a) ((fun X Y => ∀ (P : Iota → Prop), P X → P Y) a) % 4.03/4.18 Clause #8 (by betaEtaReduce #[6]): ∀ (a : Iota), Eq (leibeq a) fun Y => ∀ (P : Iota → Prop), P a → P Y % 4.03/4.18 Clause #9 (by argument congruence #[8]): ∀ (a a_1 : Iota), Eq (leibeq a a_1) ((fun Y => ∀ (P : Iota → Prop), P a → P Y) a_1) % 4.03/4.18 Clause #12 (by betaEtaReduce #[9]): ∀ (a a_1 : Iota), Eq (leibeq a a_1) (∀ (P : Iota → Prop), P a → P a_1) % 4.03/4.18 Clause #13 (by clausify Prop equality #[12]): ∀ (a a_1 : Iota), Or (Eq (leibeq a a_1) True) (Eq (∀ (P : Iota → Prop), P a → P a_1) False) % 4.03/4.18 Clause #23 (by clausification #[13]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.03/4.18 Or (Eq (leibeq a a_1) True) (Eq (Not (skS.0 1 a a_1 a_2 a → skS.0 1 a a_1 a_2 a_1)) True) % 4.03/4.18 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.03/4.18 Or (Eq (leibeq a a_1) True) (Eq (skS.0 1 a a_1 a_2 a → skS.0 1 a a_1 a_2 a_1) False) % 4.03/4.18 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (leibeq a a_1) True) (Eq (skS.0 1 a a_1 a_2 a) True) % 4.03/4.18 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (leibeq a a_1) True) (Eq (skS.0 1 a a_1 a_2 a_1) False) % 4.03/4.18 Clause #29 (by superposition #[26, 25]): ∀ (a : Iota), Or (Eq (leibeq a a) True) (Or (Eq (leibeq a a) True) (Eq False True)) % 4.03/4.18 Clause #40 (by clausification #[29]): ∀ (a : Iota), Or (Eq (leibeq a a) True) (Eq (leibeq a a) True) % 4.03/4.18 Clause #41 (by eliminate duplicate literals #[40]): ∀ (a : Iota), Eq (leibeq a a) True % 4.03/4.18 Clause #42 (by superposition #[41, 4]): Eq True False % 4.03/4.18 Clause #49 (by clausification #[42]): False % 4.03/4.18 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------