%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO227^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:08:46 PM UTC 2025 % Result : Theorem 190.23s 190.45s % Output : Proof 191.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO227^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n006.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 12:59:23 EDT 2025 % 0.14/0.34 % CPUTime : % 190.23/190.45 SZS status Theorem for theBenchmark.p % 190.23/190.45 SZS output start Proof for theBenchmark.p % 190.23/190.45 Clause #0 (by assumption #[]): Eq % 190.23/190.45 (Not % 190.23/190.45 ((∀ (Xx Xy : Iota), c_less_ Xx Xy → Ne Xx Xy) → % 190.23/190.45 And (c_less_ a b) (c_less_ b c) → Exists fun A => And (And (Not (A a)) (A b)) (Not (A c)))) % 190.23/190.45 True % 190.23/190.45 Clause #1 (by clausification #[0]): Eq % 190.23/190.45 ((∀ (Xx Xy : Iota), c_less_ Xx Xy → Ne Xx Xy) → % 190.23/190.45 And (c_less_ a b) (c_less_ b c) → Exists fun A => And (And (Not (A a)) (A b)) (Not (A c))) % 190.23/190.45 False % 190.23/190.45 Clause #2 (by clausification #[1]): Eq (∀ (Xx Xy : Iota), c_less_ Xx Xy → Ne Xx Xy) True % 190.23/190.45 Clause #3 (by clausification #[1]): Eq (And (c_less_ a b) (c_less_ b c) → Exists fun A => And (And (Not (A a)) (A b)) (Not (A c))) False % 190.23/190.45 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Xy : Iota), c_less_ a Xy → Ne a Xy) True % 190.23/190.45 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (c_less_ a a_1 → Ne a a_1) True % 190.23/190.45 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (c_less_ a a_1) False) (Eq (Ne a a_1) True) % 190.23/190.45 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (c_less_ a a_1) False) (Ne a a_1) % 190.23/190.45 Clause #8 (by destructive equality resolution #[7]): ∀ (a : Iota), Eq (c_less_ a a) False % 190.23/190.45 Clause #9 (by clausification #[3]): Eq (And (c_less_ a b) (c_less_ b c)) True % 190.23/190.45 Clause #10 (by clausification #[3]): Eq (Exists fun A => And (And (Not (A a)) (A b)) (Not (A c))) False % 190.23/190.45 Clause #11 (by clausification #[9]): Eq (c_less_ b c) True % 190.23/190.45 Clause #12 (by clausification #[9]): Eq (c_less_ a b) True % 190.23/190.45 Clause #13 (by clausification #[10]): ∀ (a_1 : Iota → Prop), Eq (And (And (Not (a_1 a)) (a_1 b)) (Not (a_1 c))) False % 190.23/190.45 Clause #14 (by clausification #[13]): ∀ (a_1 : Iota → Prop), Or (Eq (And (Not (a_1 a)) (a_1 b)) False) (Eq (Not (a_1 c)) False) % 190.23/190.45 Clause #15 (by clausification #[14]): ∀ (a_1 : Iota → Prop), Or (Eq (Not (a_1 c)) False) (Or (Eq (Not (a_1 a)) False) (Eq (a_1 b) False)) % 190.23/190.45 Clause #16 (by clausification #[15]): ∀ (a_1 : Iota → Prop), Or (Eq (Not (a_1 a)) False) (Or (Eq (a_1 b) False) (Eq (a_1 c) True)) % 190.23/190.45 Clause #17 (by clausification #[16]): ∀ (a_1 : Iota → Prop), Or (Eq (a_1 b) False) (Or (Eq (a_1 c) True) (Eq (a_1 a) True)) % 190.23/190.45 Clause #21 (by neHoist #[17]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 190.23/190.45 Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) c) True) % 190.23/190.45 (Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) a) True) (Or (Eq True False) (Eq (a_2 b) (a_3 b)))) % 190.23/190.45 Clause #73 (by betaEtaReduce #[21]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 190.23/190.45 Or (Eq (Ne (a_2 c) (a_3 c)) True) (Or (Eq (Ne (a_2 a) (a_3 a)) True) (Or (Eq True False) (Eq (a_2 b) (a_3 b)))) % 190.23/190.45 Clause #74 (by clausification #[73]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 190.23/190.45 Or (Eq (Ne (a_2 a) (a_3 a)) True) (Or (Eq True False) (Or (Eq (a_2 b) (a_3 b)) (Ne (a_2 c) (a_3 c)))) % 190.23/190.45 Clause #75 (by clausification #[74]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 190.23/190.45 Or (Eq True False) (Or (Eq (a_2 b) (a_3 b)) (Or (Ne (a_2 c) (a_3 c)) (Ne (a_2 a) (a_3 a)))) % 190.23/190.45 Clause #76 (by clausification #[75]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 190.23/190.45 Or (Eq (a_2 b) (a_3 b)) (Or (Ne (a_2 c) (a_3 c)) (Ne (a_2 a) (a_3 a))) % 190.23/190.45 Clause #92 (by fluidSup #[76, 12]): ∀ (a_1 : Sort _abstMVar.0) (a_2 : (x : Iota) → (fun x => a_1) x) (a_3 : a_1), % 190.23/190.45 Or (Eq (a_2 b) ((fun x => a_3) b)) (Or (Ne (a_2 c) ((fun _ => a_3) True)) (Ne (a_2 a) ((fun x => a_3) a))) % 190.23/190.45 Clause #175 (by betaEtaReduce #[92]): ∀ (a_1 : Sort _abstMVar.0) (a_2 : (x : Iota) → (fun x => a_1) x) (a_3 : a_1), % 190.23/190.45 Or (Eq (a_2 b) a_3) (Or (Ne (a_2 c) a_3) (Ne (a_2 a) a_3)) % 190.23/190.45 Clause #176 (by equality resolution #[175]): ∀ (a_1 : Sort _abstMVar.0) (a_2 : (x : Iota) → (fun x => a_1) x), Or (Eq (a_2 b) (a_2 c)) (Ne (a_2 a) (a_2 c)) % 190.23/190.45 Clause #186 (by fluidBoolHoist #[176]): ∀ (a_1 : (x : Iota) → (fun x => Prop) x), Or (Eq (a_1 b) (a_1 c)) (Or (Ne False (a_1 c)) (Eq (a_1 a) True)) % 190.23/190.45 Clause #236 (by clausification #[186]): ∀ (a_1 : (x : Iota) → (fun x => Prop) x), % 190.23/190.45 Or (Eq (a_1 b) (a_1 c)) (Or (Eq (a_1 a) True) (Or (Eq False True) (Eq (a_1 c) True))) % 191.20/191.41 Clause #270 (by clausification #[236]): ∀ (a_1 : (x : Iota) → (fun x => Prop) x), Or (Eq (a_1 b) (a_1 c)) (Or (Eq (a_1 a) True) (Eq (a_1 c) True)) % 191.20/191.41 Clause #291 (by eqHoist #[270]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 191.20/191.41 Or (Eq ((fun x => Eq (a_2 x) (a_3 x)) a) True) % 191.20/191.41 (Or (Eq ((fun x => Eq (a_2 x) (a_3 x)) c) True) % 191.20/191.41 (Or (Eq ((fun x => Eq (a_2 x) (a_3 x)) b) False) (Eq (a_2 c) (a_3 c)))) % 191.20/191.41 Clause #17336 (by betaEtaReduce #[291]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 191.20/191.41 Or (Eq (Eq (a_2 a) (a_3 a)) True) % 191.20/191.41 (Or (Eq (Eq (a_2 c) (a_3 c)) True) (Or (Eq (Eq (a_2 b) (a_3 b)) False) (Eq (a_2 c) (a_3 c)))) % 191.20/191.41 Clause #17337 (by clausification #[17336]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 191.20/191.41 Or (Eq (Eq (a_2 c) (a_3 c)) True) (Or (Eq (Eq (a_2 b) (a_3 b)) False) (Or (Eq (a_2 c) (a_3 c)) (Eq (a_2 a) (a_3 a)))) % 191.20/191.41 Clause #17338 (by clausification #[17337]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 191.20/191.41 Or (Eq (Eq (a_2 b) (a_3 b)) False) (Or (Eq (a_2 c) (a_3 c)) (Or (Eq (a_2 a) (a_3 a)) (Eq (a_2 c) (a_3 c)))) % 191.20/191.41 Clause #17339 (by clausification #[17338]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 191.20/191.41 Or (Eq (a_2 c) (a_3 c)) (Or (Eq (a_2 a) (a_3 a)) (Or (Eq (a_2 c) (a_3 c)) (Ne (a_2 b) (a_3 b)))) % 191.20/191.41 Clause #17340 (by eliminate duplicate literals #[17339]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 191.20/191.41 Or (Eq (a_2 c) (a_3 c)) (Or (Eq (a_2 a) (a_3 a)) (Ne (a_2 b) (a_3 b))) % 191.20/191.41 Clause #17341 (by equality resolution #[17340]): Or (Eq ((fun x => x) c) ((fun x => b) c)) (Eq ((fun x => x) a) ((fun x => b) a)) % 191.20/191.41 Clause #17446 (by betaEtaReduce #[17341]): Or (Eq c b) (Eq a b) % 191.20/191.41 Clause #17447 (by superposition #[17446, 11]): Or (Eq a b) (Eq (c_less_ b b) True) % 191.20/191.41 Clause #19427 (by superposition #[17447, 8]): Or (Eq a b) (Eq True False) % 191.20/191.41 Clause #19625 (by clausification #[19427]): Eq a b % 191.20/191.41 Clause #19626 (by backward demodulation #[19625, 12]): Eq (c_less_ b b) True % 191.20/191.41 Clause #19896 (by superposition #[19626, 8]): Eq True False % 191.20/191.41 Clause #19913 (by clausification #[19896]): False % 191.20/191.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------