%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN413+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:07:37 PM UTC 2025 % Result : Theorem 3.50s 3.68s % Output : Proof 3.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN413+1 : TPTP v9.2.0. Released v2.0.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n005.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 : Thu Oct 2 15:18:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.50/3.68 SZS status Theorem for theBenchmark.p % 3.50/3.68 SZS output start Proof for theBenchmark.p % 3.50/3.68 Clause #0 (by assumption #[]): Eq % 3.50/3.68 (Not % 3.50/3.68 ((∀ (Z : Iota), Exists fun Y => ∀ (X : Iota), Iff (f X Y) (And (f X Z) (Not (f X X)))) → % 3.50/3.68 Not (Exists fun V => ∀ (U : Iota), f U V))) % 3.50/3.68 True % 3.50/3.68 Clause #1 (by clausification #[0]): Eq % 3.50/3.68 ((∀ (Z : Iota), Exists fun Y => ∀ (X : Iota), Iff (f X Y) (And (f X Z) (Not (f X X)))) → % 3.50/3.68 Not (Exists fun V => ∀ (U : Iota), f U V)) % 3.50/3.68 False % 3.50/3.68 Clause #2 (by clausification #[1]): Eq (∀ (Z : Iota), Exists fun Y => ∀ (X : Iota), Iff (f X Y) (And (f X Z) (Not (f X X)))) True % 3.50/3.68 Clause #3 (by clausification #[1]): Eq (Not (Exists fun V => ∀ (U : Iota), f U V)) False % 3.50/3.68 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (Exists fun Y => ∀ (X : Iota), Iff (f X Y) (And (f X a) (Not (f X X)))) True % 3.50/3.68 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (∀ (X : Iota), Iff (f X (skS.0 0 a a_1)) (And (f X a) (Not (f X X)))) True % 3.50/3.68 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (Iff (f a (skS.0 0 a_1 a_2)) (And (f a a_1) (Not (f a a)))) True % 3.50/3.68 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a (skS.0 0 a_1 a_2)) True) (Eq (And (f a a_1) (Not (f a a))) False) % 3.50/3.68 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a (skS.0 0 a_1 a_2)) False) (Eq (And (f a a_1) (Not (f a a))) True) % 3.50/3.68 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a (skS.0 0 a_1 a_2)) True) (Or (Eq (f a a_1) False) (Eq (Not (f a a)) False)) % 3.50/3.68 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a (skS.0 0 a_1 a_2)) True) (Or (Eq (f a a_1) False) (Eq (f a a) True)) % 3.50/3.68 Clause #11 (by clausification #[3]): Eq (Exists fun V => ∀ (U : Iota), f U V) True % 3.50/3.68 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (U : Iota), f U (skS.0 1 a)) True % 3.50/3.68 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (f a (skS.0 1 a_1)) True % 3.50/3.68 Clause #14 (by superposition #[13, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a (skS.0 0 (skS.0 1 a_1) a_2)) True) (Or (Eq True False) (Eq (f a a) True)) % 3.50/3.68 Clause #15 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a (skS.0 0 a_1 a_2)) False) (Eq (Not (f a a)) True) % 3.50/3.68 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a (skS.0 0 a_1 a_2)) False) (Eq (f a a) False) % 3.50/3.68 Clause #18 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a (skS.0 0 (skS.0 1 a_1) a_2)) True) (Eq (f a a) True) % 3.50/3.68 Clause #22 (by superposition #[18, 17]): ∀ (a a_1 a_2 a_3 : Iota), % 3.50/3.68 Or (Eq (f (skS.0 0 a a_1) (skS.0 0 (skS.0 1 a_2) a_3)) True) (Or (Eq True False) (Eq True False)) % 3.50/3.68 Clause #27 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (f (skS.0 0 a a_1) (skS.0 0 (skS.0 1 a_2) a_3)) True) (Eq True False) % 3.50/3.68 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota), Eq (f (skS.0 0 a a_1) (skS.0 0 (skS.0 1 a_2) a_3)) True % 3.50/3.68 Clause #29 (by superposition #[28, 17]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (f (skS.0 0 a a_1) (skS.0 0 a a_1)) False) % 3.50/3.68 Clause #33 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (f (skS.0 0 a a_1) (skS.0 0 a a_1)) False % 3.50/3.68 Clause #34 (by superposition #[33, 28]): Eq False True % 3.50/3.68 Clause #36 (by clausification #[34]): False % 3.50/3.68 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------