%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO255^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:08:48 PM UTC 2025 % Result : Theorem 4.31s 4.48s % Output : Proof 4.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO255^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n015.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 14:30:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.31/4.48 SZS status Theorem for theBenchmark.p % 4.31/4.48 SZS output start Proof for theBenchmark.p % 4.31/4.48 Clause #0 (by assumption #[]): Eq (Not (cP a → Exists fun A => And (∀ (Xx : Iota), A Xx → cP Xx) (Exists fun Xy => A Xy))) True % 4.31/4.48 Clause #1 (by betaEtaReduce #[0]): Eq (Not (cP a → Exists fun A => And (∀ (Xx : Iota), A Xx → cP Xx) (Exists A))) True % 4.31/4.48 Clause #2 (by clausification #[1]): Eq (cP a → Exists fun A => And (∀ (Xx : Iota), A Xx → cP Xx) (Exists A)) False % 4.31/4.48 Clause #3 (by clausification #[2]): Eq (cP a) True % 4.31/4.48 Clause #4 (by clausification #[2]): Eq (Exists fun A => And (∀ (Xx : Iota), A Xx → cP Xx) (Exists A)) False % 4.31/4.48 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop), Eq (And (∀ (Xx : Iota), a Xx → cP Xx) (Exists a)) False % 4.31/4.48 Clause #6 (by clausification #[5]): ∀ (a : Iota → Prop), Or (Eq (∀ (Xx : Iota), a Xx → cP Xx) False) (Eq (Exists a) False) % 4.31/4.48 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (Exists a) False) (Eq (Not (a (skS.0 0 a a_1) → cP (skS.0 0 a a_1))) True) % 4.31/4.48 Clause #8 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (Not (a (skS.0 0 a a_1) → cP (skS.0 0 a a_1))) True) (Eq (a a_2) False) % 4.31/4.48 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a a_1) False) (Eq (a (skS.0 0 a a_2) → cP (skS.0 0 a a_2)) False) % 4.31/4.48 Clause #10 (by clausification #[9]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a a_1) False) (Eq (a (skS.0 0 a a_2)) True) % 4.31/4.48 Clause #11 (by clausification #[9]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a a_1) False) (Eq (cP (skS.0 0 a a_2)) False) % 4.31/4.48 Clause #21 (by superposition #[10, 3]): ∀ (a : Iota), Or (Eq ((fun x => cP x) (skS.0 0 (fun x => cP x) a)) True) (Eq False True) % 4.31/4.48 Clause #33 (by superposition #[11, 3]): ∀ (a : Iota), Or (Eq (cP (skS.0 0 (fun x => cP x) a)) False) (Eq False True) % 4.31/4.48 Clause #34 (by betaEtaReduce #[33]): ∀ (a : Iota), Or (Eq (cP (skS.0 0 cP a)) False) (Eq False True) % 4.31/4.48 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (cP (skS.0 0 cP a)) False % 4.31/4.48 Clause #106 (by betaEtaReduce #[21]): ∀ (a : Iota), Or (Eq (cP (skS.0 0 cP a)) True) (Eq False True) % 4.31/4.48 Clause #107 (by clausification #[106]): ∀ (a : Iota), Eq (cP (skS.0 0 cP a)) True % 4.31/4.48 Clause #108 (by superposition #[107, 35]): Eq True False % 4.31/4.48 Clause #121 (by clausification #[108]): False % 4.31/4.48 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------