%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO103^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:08:35 PM UTC 2025 % Result : Theorem 4.13s 4.29s % Output : Proof 4.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYO103^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.14 % Command : duper %s % 0.15/0.35 % Computer : n013.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 14:34:23 EDT 2025 % 0.15/0.35 % CPUTime : % 4.13/4.29 SZS status Theorem for theBenchmark.p % 4.13/4.29 SZS output start Proof for theBenchmark.p % 4.13/4.29 Clause #0 (by assumption #[]): Eq % 4.13/4.29 (Not % 4.13/4.29 (Not % 4.13/4.29 (And % 4.13/4.29 (And % 4.13/4.29 (And % 4.13/4.29 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 4.13/4.29 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) % 4.13/4.29 (Exists fun Xa => Not (cT (imp Xa Xa)))))) % 4.13/4.29 True % 4.13/4.29 Clause #1 (by clausification #[0]): Eq % 4.13/4.29 (Not % 4.13/4.29 (And % 4.13/4.29 (And % 4.13/4.29 (And % 4.13/4.29 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 4.13/4.29 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) % 4.13/4.29 (Exists fun Xa => Not (cT (imp Xa Xa))))) % 4.13/4.29 False % 4.13/4.29 Clause #2 (by clausification #[1]): Eq % 4.13/4.29 (And % 4.13/4.29 (And % 4.13/4.29 (And % 4.13/4.29 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 4.13/4.29 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) % 4.13/4.29 (Exists fun Xa => Not (cT (imp Xa Xa)))) % 4.13/4.29 True % 4.13/4.29 Clause #3 (by clausification #[2]): Eq (Exists fun Xa => Not (cT (imp Xa Xa))) True % 4.13/4.29 Clause #4 (by clausification #[2]): Eq % 4.13/4.29 (And % 4.13/4.29 (And % 4.13/4.29 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 4.13/4.29 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) % 4.13/4.29 True % 4.13/4.29 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (Not (cT (imp (skS.0 0 a) (skS.0 0 a)))) True % 4.13/4.29 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (cT (imp (skS.0 0 a) (skS.0 0 a))) False % 4.13/4.29 Clause #8 (by clausification #[4]): Eq % 4.13/4.29 (And % 4.13/4.29 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 4.13/4.29 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 4.13/4.29 True % 4.13/4.29 Clause #11 (by clausification #[8]): Eq (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) True % 4.13/4.29 Clause #12 (by clausification #[8]): Eq % 4.13/4.29 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 4.13/4.29 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 4.13/4.29 True % 4.13/4.29 Clause #13 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Xq Xr : Iota), cT (imp (imp a (imp Xq Xr)) (imp (imp a Xq) (imp a Xr)))) True % 4.13/4.29 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (∀ (Xr : Iota), cT (imp (imp a (imp a_1 Xr)) (imp (imp a a_1) (imp a Xr)))) True % 4.13/4.29 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp a (imp a_1 a_2)) (imp (imp a a_1) (imp a a_2)))) True % 4.13/4.29 Clause #16 (by clausification #[12]): Eq (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp))) True % 4.13/4.29 Clause #17 (by clausification #[12]): Eq (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) True % 4.13/4.29 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Xq : Iota), cT (imp a (imp Xq a))) True % 4.13/4.29 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (cT (imp a (imp a_1 a))) True % 4.13/4.29 Clause #20 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Xq : Iota), Or (Or (Not (cT (imp a Xq))) (Not (cT a))) (cT Xq)) True % 4.13/4.29 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (cT (imp a a_1))) (Not (cT a))) (cT a_1)) True % 4.13/4.29 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Or (Not (cT (imp a a_1))) (Not (cT a))) True) (Eq (cT a_1) True) % 4.13/4.29 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (cT a) True) (Or (Eq (Not (cT (imp a_1 a))) True) (Eq (Not (cT a_1)) True)) % 4.13/4.29 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (cT a) True) (Or (Eq (Not (cT a_1)) True) (Eq (cT (imp a_1 a)) False)) % 4.13/4.30 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (cT a) True) (Or (Eq (cT (imp a_1 a)) False) (Eq (cT a_1) False)) % 4.13/4.30 Clause #27 (by superposition #[25, 15]): ∀ (a a_1 a_2 : Iota), % 4.13/4.30 Or (Eq (cT (imp (imp a a_1) (imp a a_2))) True) (Or (Eq (cT (imp a (imp a_1 a_2))) False) (Eq False True)) % 4.13/4.30 Clause #42 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp (imp a a_1) (imp a a_2))) True) (Eq (cT (imp a (imp a_1 a_2))) False) % 4.13/4.30 Clause #45 (by superposition #[42, 19]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp a a_1) (imp a a))) True) (Eq False True) % 4.13/4.30 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (cT (imp (imp a a_1) (imp a a))) True % 4.13/4.30 Clause #49 (by superposition #[48, 25]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a)) True) (Or (Eq True False) (Eq (cT (imp a a_1)) False)) % 4.13/4.30 Clause #52 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a)) True) (Eq (cT (imp a a_1)) False) % 4.13/4.30 Clause #55 (by superposition #[52, 19]): ∀ (a : Iota), Or (Eq (cT (imp a a)) True) (Eq False True) % 4.13/4.30 Clause #57 (by clausification #[55]): ∀ (a : Iota), Eq (cT (imp a a)) True % 4.13/4.30 Clause #58 (by superposition #[57, 6]): Eq True False % 4.13/4.30 Clause #63 (by clausification #[58]): False % 4.13/4.30 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------