%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO357^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:08:56 PM UTC 2025 % Result : Theorem 4.44s 4.62s % Output : Proof 4.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO357^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 13:30:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.44/4.62 SZS status Theorem for theBenchmark.p % 4.44/4.62 SZS output start Proof for theBenchmark.p % 4.44/4.62 Clause #0 (by assumption #[]): Eq % 4.44/4.62 (Not % 4.44/4.62 ((∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v)) → ∀ (Xq : atype → Prop), Xq u → Xq v)) % 4.44/4.62 True % 4.44/4.62 Clause #1 (by clausification #[0]): Eq ((∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v)) → ∀ (Xq : atype → Prop), Xq u → Xq v) % 4.44/4.62 False % 4.44/4.62 Clause #2 (by clausification #[1]): Eq (∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v)) True % 4.44/4.62 Clause #3 (by clausification #[1]): Eq (∀ (Xq : atype → Prop), Xq u → Xq v) False % 4.44/4.62 Clause #4 (by clausification #[2]): ∀ (a_1 : atype → Prop), Eq (And (Or a (Not a)) (a_1 u) → And (Or b (Not b)) (a_1 v)) True % 4.44/4.62 Clause #5 (by clausification #[4]): ∀ (a_1 : atype → Prop), Or (Eq (And (Or a (Not a)) (a_1 u)) False) (Eq (And (Or b (Not b)) (a_1 v)) True) % 4.44/4.62 Clause #6 (by clausification #[5]): ∀ (a_1 : atype → Prop), Or (Eq (And (Or b (Not b)) (a_1 v)) True) (Or (Eq (Or a (Not a)) False) (Eq (a_1 u) False)) % 4.44/4.62 Clause #7 (by clausification #[6]): ∀ (a_1 : atype → Prop), Or (Eq (Or a (Not a)) False) (Or (Eq (a_1 u) False) (Eq (a_1 v) True)) % 4.44/4.62 Clause #9 (by clausification #[7]): ∀ (a_1 : atype → Prop), Or (Eq (a_1 u) False) (Or (Eq (a_1 v) True) (Eq (Not a) False)) % 4.44/4.62 Clause #10 (by clausification #[7]): ∀ (a_1 : atype → Prop), Or (Eq (a_1 u) False) (Or (Eq (a_1 v) True) (Eq a False)) % 4.44/4.62 Clause #11 (by clausification #[9]): ∀ (a_1 : atype → Prop), Or (Eq (a_1 u) False) (Or (Eq (a_1 v) True) (Eq a True)) % 4.44/4.62 Clause #13 (by neHoist #[11]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x), % 4.44/4.62 Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) v) True) (Or (Eq a True) (Or (Eq True False) (Eq (a_2 u) (a_3 u)))) % 4.44/4.62 Clause #19 (by clausification #[3]): ∀ (a : atype → Prop), Eq (Not (skS.0 0 a u → skS.0 0 a v)) True % 4.44/4.62 Clause #20 (by clausification #[19]): ∀ (a : atype → Prop), Eq (skS.0 0 a u → skS.0 0 a v) False % 4.44/4.62 Clause #21 (by clausification #[20]): ∀ (a : atype → Prop), Eq (skS.0 0 a u) True % 4.44/4.62 Clause #22 (by clausification #[20]): ∀ (a : atype → Prop), Eq (skS.0 0 a v) False % 4.44/4.62 Clause #28 (by neHoist #[10]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x), % 4.44/4.62 Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) v) True) (Or (Eq a False) (Or (Eq True False) (Eq (a_2 u) (a_3 u)))) % 4.44/4.62 Clause #65 (by betaEtaReduce #[13]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x), % 4.44/4.62 Or (Eq (Ne (a_2 v) (a_3 v)) True) (Or (Eq a True) (Or (Eq True False) (Eq (a_2 u) (a_3 u)))) % 4.44/4.62 Clause #66 (by clausification #[65]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x), % 4.44/4.62 Or (Eq a True) (Or (Eq True False) (Or (Eq (a_2 u) (a_3 u)) (Ne (a_2 v) (a_3 v)))) % 4.44/4.62 Clause #67 (by clausification #[66]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x), % 4.44/4.62 Or (Eq a True) (Or (Eq (a_2 u) (a_3 u)) (Ne (a_2 v) (a_3 v))) % 4.44/4.62 Clause #68 (by equality resolution #[67]): Or (Eq a True) (Eq ((fun x => x) u) ((fun x => v) u)) % 4.44/4.62 Clause #78 (by betaEtaReduce #[68]): Or (Eq a True) (Eq u v) % 4.44/4.62 Clause #324 (by betaEtaReduce #[28]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x), % 4.44/4.62 Or (Eq (Ne (a_2 v) (a_3 v)) True) (Or (Eq a False) (Or (Eq True False) (Eq (a_2 u) (a_3 u)))) % 4.44/4.62 Clause #325 (by clausification #[324]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x), % 4.44/4.62 Or (Eq a False) (Or (Eq True False) (Or (Eq (a_2 u) (a_3 u)) (Ne (a_2 v) (a_3 v)))) % 4.44/4.62 Clause #326 (by clausification #[325]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x), % 4.44/4.62 Or (Eq a False) (Or (Eq (a_2 u) (a_3 u)) (Ne (a_2 v) (a_3 v))) % 4.44/4.62 Clause #327 (by superposition #[326, 78]): ∀ (a : atype → Sort _abstMVar.0) (a_1 a_2 : (x : atype) → a x), % 4.44/4.62 Or (Eq (a_1 u) (a_2 u)) (Or (Ne (a_1 v) (a_2 v)) (Or (Eq False True) (Eq u v))) % 4.44/4.62 Clause #348 (by clausification #[327]): ∀ (a : atype → Sort _abstMVar.0) (a_1 a_2 : (x : atype) → a x), % 4.44/4.62 Or (Eq (a_1 u) (a_2 u)) (Or (Ne (a_1 v) (a_2 v)) (Eq u v)) % 4.44/4.62 Clause #349 (by equality resolution #[348]): Or (Eq ((fun x => x) u) ((fun x => v) u)) (Eq u v) % 4.44/4.64 Clause #365 (by betaEtaReduce #[349]): Or (Eq u v) (Eq u v) % 4.44/4.64 Clause #366 (by eliminate duplicate literals #[365]): Eq u v % 4.44/4.64 Clause #369 (by backward demodulation #[366, 22]): ∀ (a : atype → Prop), Eq (skS.0 0 a u) False % 4.44/4.64 Clause #393 (by superposition #[369, 21]): Eq False True % 4.44/4.64 Clause #399 (by clausification #[393]): False % 4.44/4.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------