%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PHI045^6 : TPTP v9.2.0. Released v9.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:57:58 PM UTC 2025 % Result : Theorem 3.70s 3.92s % Output : Proof 3.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.11 % Problem : PHI045^6 : TPTP v9.2.0. Released v9.0.0. % 0.05/0.12 % Command : duper %s % 0.11/0.33 % Computer : n024.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Fri Oct 3 09:06:38 EDT 2025 % 0.11/0.33 % CPUTime : % 3.70/3.92 SZS status Theorem for theBenchmark.p % 3.70/3.92 SZS output start Proof for theBenchmark.p % 3.70/3.92 Clause #0 (by assumption #[]): Eq (Not (positive_property fun X => Ne X X)) True % 3.70/3.92 Clause #1 (by assumption #[]): Eq (∀ (P1 P2 : entity → Prop), And (positive_property P1) (∀ (Y : entity), P1 Y → P2 Y) → positive_property P2) True % 3.70/3.92 Clause #2 (by assumption #[]): Eq (positive_property god_like) True % 3.70/3.92 Clause #3 (by assumption #[]): Eq (Not (Exists fun X => god_like X)) True % 3.70/3.92 Clause #4 (by clausification #[1]): ∀ (a : entity → Prop), % 3.70/3.92 Eq (∀ (P2 : entity → Prop), And (positive_property a) (∀ (Y : entity), a Y → P2 Y) → positive_property P2) True % 3.70/3.92 Clause #5 (by clausification #[4]): ∀ (a a_1 : entity → Prop), Eq (And (positive_property a) (∀ (Y : entity), a Y → a_1 Y) → positive_property a_1) True % 3.70/3.92 Clause #6 (by clausification #[5]): ∀ (a a_1 : entity → Prop), % 3.70/3.92 Or (Eq (And (positive_property a) (∀ (Y : entity), a Y → a_1 Y)) False) (Eq (positive_property a_1) True) % 3.70/3.92 Clause #7 (by clausification #[6]): ∀ (a a_1 : entity → Prop), % 3.70/3.92 Or (Eq (positive_property a) True) (Or (Eq (positive_property a_1) False) (Eq (∀ (Y : entity), a_1 Y → a Y) False)) % 3.70/3.92 Clause #8 (by clausification #[7]): ∀ (a a_1 : entity → Prop) (a_2 : entity), % 3.70/3.92 Or (Eq (positive_property a) True) % 3.70/3.92 (Or (Eq (positive_property a_1) False) (Eq (Not (a_1 (skS.0 0 a_1 a a_2) → a (skS.0 0 a_1 a a_2))) True)) % 3.70/3.92 Clause #9 (by clausification #[8]): ∀ (a a_1 : entity → Prop) (a_2 : entity), % 3.70/3.92 Or (Eq (positive_property a) True) % 3.70/3.92 (Or (Eq (positive_property a_1) False) (Eq (a_1 (skS.0 0 a_1 a a_2) → a (skS.0 0 a_1 a a_2)) False)) % 3.70/3.92 Clause #10 (by clausification #[9]): ∀ (a a_1 : entity → Prop) (a_2 : entity), % 3.70/3.92 Or (Eq (positive_property a) True) (Or (Eq (positive_property a_1) False) (Eq (a_1 (skS.0 0 a_1 a a_2)) True)) % 3.70/3.92 Clause #12 (by superposition #[10, 2]): ∀ (a : entity → Prop) (a_1 : entity), % 3.70/3.92 Or (Eq (positive_property a) True) % 3.70/3.92 (Or (Eq ((fun x => god_like x) (skS.0 0 (fun x => god_like x) a a_1)) True) (Eq False True)) % 3.70/3.92 Clause #14 (by betaEtaReduce #[3]): Eq (Not (Exists god_like)) True % 3.70/3.92 Clause #15 (by clausification #[14]): Eq (Exists god_like) False % 3.70/3.92 Clause #16 (by clausification #[15]): ∀ (a : entity), Eq (god_like a) False % 3.70/3.92 Clause #17 (by clausification #[0]): Eq (positive_property fun X => Ne X X) False % 3.70/3.92 Clause #20 (by betaEtaReduce #[12]): ∀ (a : entity → Prop) (a_1 : entity), % 3.70/3.92 Or (Eq (positive_property a) True) (Or (Eq (god_like (skS.0 0 god_like a a_1)) True) (Eq False True)) % 3.70/3.92 Clause #21 (by clausification #[20]): ∀ (a : entity → Prop) (a_1 : entity), Or (Eq (positive_property a) True) (Eq (god_like (skS.0 0 god_like a a_1)) True) % 3.70/3.92 Clause #22 (by superposition #[21, 16]): ∀ (a : entity → Prop), Or (Eq (positive_property a) True) (Eq True False) % 3.70/3.92 Clause #25 (by clausification #[22]): ∀ (a : entity → Prop), Eq (positive_property a) True % 3.70/3.92 Clause #27 (by superposition #[25, 17]): Eq True False % 3.70/3.92 Clause #28 (by clausification #[27]): False % 3.70/3.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------