%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN991^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:08:23 PM UTC 2025 % Result : Unsatisfiable 6.21s 6.45s % Output : Proof 6.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN991^1 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 15:22:23 EDT 2025 % 0.13/0.35 % CPUTime : % 6.21/6.45 SZS status Theorem for theBenchmark.p % 6.21/6.45 SZS output start Proof for theBenchmark.p % 6.21/6.45 Clause #0 (by assumption #[]): Eq (Eq refl fun R => ∀ (X : Iota), R X X) True % 6.21/6.45 Clause #1 (by assumption #[]): Eq (∀ (R : Iota → Iota → Prop), refl R) True % 6.21/6.45 Clause #2 (by clausification #[1]): ∀ (a : Iota → Iota → Prop), Eq (refl a) True % 6.21/6.45 Clause #3 (by clausification #[0]): Eq refl fun R => ∀ (X : Iota), R X X % 6.21/6.45 Clause #4 (by argument congruence #[3]): ∀ (a : Iota → Iota → Prop), Eq (refl a) ((fun R => ∀ (X : Iota), R X X) a) % 6.21/6.45 Clause #5 (by betaEtaReduce #[4]): ∀ (a : Iota → Iota → Prop), Eq (refl a) (∀ (X : Iota), a X X) % 6.21/6.45 Clause #6 (by forward demodulation #[5, 2]): ∀ (a : Iota → Iota → Prop), Eq True (∀ (X : Iota), a X X) % 6.21/6.45 Clause #7 (by clausification #[6]): ∀ (a : Iota → Iota → Prop) (a_1 : Iota), Eq (a a_1 a_1) True % 6.21/6.45 Clause #8 (by eqHoist #[7]): ∀ (a : Iota → Iota → Sort _abstMVar.0) (a_1 : Iota) (a_2 a_3 : (x x_1 : Iota) → a x x_1), % 6.21/6.45 Or (Eq False True) (Eq (a_2 a_1 a_1) (a_3 a_1 a_1)) % 6.21/6.45 Clause #19 (by clausification #[8]): ∀ (a : Iota → Iota → Sort _abstMVar.0) (a_1 : Iota) (a_2 a_3 : (x x_1 : Iota) → a x x_1), Eq (a_2 a_1 a_1) (a_3 a_1 a_1) % 6.21/6.45 Clause #23 (by neHoist #[19]): ∀ (a : Iota) (a_1 : (x x_1 : Iota) → (fun x x => Prop) x x_1) (a_2 : Iota → Iota → Sort _abstMVar.0) % 6.21/6.45 (a_3 a_4 : (x x_1 : Iota) → a_2 x x_1), Or (Eq True (a_1 a a)) (Eq (a_3 a a) (a_4 a a)) % 6.21/6.45 Clause #546 (by betaEtaReduce #[23]): ∀ (a : (x x_1 : Iota) → (fun x x => Prop) x x_1) (a_1 : Iota) (a_2 : Iota → Iota → Sort _abstMVar.0) % 6.21/6.45 (a_3 a_4 : (x x_1 : Iota) → a_2 x x_1), Or (Eq True (a a_1 a_1)) (Eq (a_3 a_1 a_1) (a_4 a_1 a_1)) % 6.21/6.45 Clause #549 (by superposition #[546, 2]): ∀ (a : (x x_1 : Iota) → (fun x x => Prop) x x_1) (a_1 : Iota) (a_2 : (x x_1 : Iota) → (fun x x => Prop) x x_1), % 6.21/6.45 Or (Eq True (a a_1 a_1)) (Eq (a_2 a_1 a_1) True) % 6.21/6.45 Clause #726 (by equality factoring #[549]): ∀ (a : Prop) (a_1 : Iota), Or (Ne True True) (Eq True ((fun x x => a) a_1 a_1)) % 6.21/6.45 Clause #889 (by betaEtaReduce #[726]): ∀ (a : Prop), Or (Ne True True) (Eq True a) % 6.21/6.45 Clause #890 (by clausification #[889]): ∀ (a : Prop), Or (Eq True a) (Or (Eq True False) (Eq True False)) % 6.21/6.45 Clause #892 (by clausification #[890]): ∀ (a : Prop), Or (Eq True a) (Eq True False) % 6.21/6.45 Clause #893 (by clausification #[892]): ∀ (a : Prop), Eq True a % 6.21/6.45 Clause #896 (by falseElim #[893]): False % 6.21/6.45 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------