%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV427^1 : TPTP v9.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:03:10 PM UTC 2025 % Result : Theorem 3.75s 3.98s % Output : Proof 3.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEV427^1 : TPTP v9.2.0. Released v5.2.0. % 0.06/0.14 % Command : duper %s % 0.14/0.35 % Computer : n004.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 01:02:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.75/3.98 SZS status Theorem for theBenchmark.p % 3.75/3.98 SZS output start Proof for theBenchmark.p % 3.75/3.98 Clause #0 (by assumption #[]): Eq (∀ (P : Iota → Prop), (Exists fun X => P X) → P (eps P)) True % 3.75/3.98 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Or (p X) (q X)) True % 3.75/3.98 Clause #2 (by assumption #[]): Eq (Not (Or (p (eps p)) (q (eps q)))) True % 3.75/3.98 Clause #3 (by betaEtaReduce #[0]): Eq (∀ (P : Iota → Prop), Exists P → P (eps P)) True % 3.75/3.98 Clause #4 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (Exists a → a (eps a)) True % 3.75/3.98 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop), Or (Eq (Exists a) False) (Eq (a (eps a)) True) % 3.75/3.98 Clause #6 (by clausification #[5]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a (eps a)) True) (Eq (a a_1) False) % 3.75/3.98 Clause #15 (by clausification #[1]): ∀ (a : Iota), Eq (Or (p a) (q a)) True % 3.75/3.98 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (p a) True) (Eq (q a) True) % 3.75/3.98 Clause #21 (by clausification #[2]): Eq (Or (p (eps p)) (q (eps q))) False % 3.75/3.98 Clause #22 (by clausification #[21]): Eq (q (eps q)) False % 3.75/3.98 Clause #23 (by clausification #[21]): Eq (p (eps p)) False % 3.75/3.98 Clause #27 (by superposition #[23, 16]): Or (Eq False True) (Eq (q (eps p)) True) % 3.75/3.98 Clause #32 (by clausification #[27]): Eq (q (eps p)) True % 3.75/3.98 Clause #34 (by fluidSup #[32, 6]): ∀ (a : Iota → Prop) (a_1 : Prop → Iota), Or (Eq (a (eps a)) True) (Eq (a (a_1 True)) False) % 3.75/3.98 Clause #71 (by superposition #[34, 32]): Or (Eq ((fun x => q x) (eps fun x => q x)) True) (Eq False True) % 3.75/3.98 Clause #74 (by betaEtaReduce #[71]): Or (Eq (q (eps q)) True) (Eq False True) % 3.75/3.98 Clause #75 (by clausification #[74]): Eq (q (eps q)) True % 3.75/3.98 Clause #76 (by superposition #[75, 22]): Eq True False % 3.75/3.98 Clause #98 (by clausification #[76]): False % 3.75/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------