%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO301^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:08:52 PM UTC 2025 % Result : Theorem 3.61s 3.78s % Output : Proof 3.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYO301^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n011.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 14:18:38 EDT 2025 % 0.14/0.36 % CPUTime : % 3.61/3.78 SZS status Theorem for theBenchmark.p % 3.61/3.78 SZS output start Proof for theBenchmark.p % 3.61/3.78 Clause #0 (by assumption #[]): Eq (Not (cP (f b) → Exists fun Xs => Exists fun A => And (∀ (Xx : Iota), A Xx → cP Xx) (A (f Xs)))) True % 3.61/3.78 Clause #1 (by clausification #[0]): Eq (cP (f b) → Exists fun Xs => Exists fun A => And (∀ (Xx : Iota), A Xx → cP Xx) (A (f Xs))) False % 3.61/3.78 Clause #2 (by clausification #[1]): Eq (cP (f b)) True % 3.61/3.78 Clause #3 (by clausification #[1]): Eq (Exists fun Xs => Exists fun A => And (∀ (Xx : Iota), A Xx → cP Xx) (A (f Xs))) False % 3.61/3.78 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (Exists fun A => And (∀ (Xx : Iota), A Xx → cP Xx) (A (f a))) False % 3.61/3.78 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (And (∀ (Xx : Iota), a Xx → cP Xx) (a (f a_1))) False % 3.61/3.78 Clause #6 (by clausification #[5]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (∀ (Xx : Iota), a Xx → cP Xx) False) (Eq (a (f a_1)) False) % 3.61/3.78 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a (f a_1)) False) (Eq (Not (a (skS.0 0 a a_2) → cP (skS.0 0 a a_2))) True) % 3.61/3.78 Clause #8 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a (f a_1)) False) (Eq (a (skS.0 0 a a_2) → cP (skS.0 0 a a_2)) False) % 3.61/3.78 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a (f a_1)) False) (Eq (a (skS.0 0 a a_2)) True) % 3.61/3.78 Clause #10 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a (f a_1)) False) (Eq (cP (skS.0 0 a a_2)) False) % 3.61/3.78 Clause #11 (by superposition #[9, 2]): ∀ (a : Iota), Or (Eq ((fun x => cP x) (skS.0 0 (fun x => cP x) a)) True) (Eq False True) % 3.61/3.78 Clause #21 (by superposition #[10, 2]): ∀ (a : Iota), Or (Eq (cP (skS.0 0 (fun x => cP x) a)) False) (Eq False True) % 3.61/3.78 Clause #33 (by betaEtaReduce #[21]): ∀ (a : Iota), Or (Eq (cP (skS.0 0 cP a)) False) (Eq False True) % 3.61/3.78 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (cP (skS.0 0 cP a)) False % 3.61/3.78 Clause #46 (by betaEtaReduce #[11]): ∀ (a : Iota), Or (Eq (cP (skS.0 0 cP a)) True) (Eq False True) % 3.61/3.78 Clause #47 (by clausification #[46]): ∀ (a : Iota), Eq (cP (skS.0 0 cP a)) True % 3.61/3.78 Clause #48 (by superposition #[47, 34]): Eq True False % 3.61/3.78 Clause #54 (by clausification #[48]): False % 3.61/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------