%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN057+1 : TPTP v9.2.0. Released v2.0.0. % 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 08:07:04 PM UTC 2025 % Result : Theorem 3.57s 3.78s % Output : Proof 3.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN057+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n013.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 : Thu Oct 2 15:34:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.57/3.78 SZS status Theorem for theBenchmark.p % 3.57/3.78 SZS output start Proof for theBenchmark.p % 3.57/3.78 Clause #0 (by assumption #[]): Eq (Exists fun X => And (big_f X) (Not (big_g X))) True % 3.57/3.78 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), big_f X → big_h X) True % 3.57/3.78 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), And (big_j X) (big_i X) → big_f X) True % 3.57/3.78 Clause #3 (by assumption #[]): Eq ((Exists fun X => And (big_h X) (Not (big_g X))) → ∀ (X1 : Iota), big_i X1 → Not (big_h X1)) True % 3.57/3.78 Clause #4 (by assumption #[]): Eq (Not (∀ (X : Iota), big_j X → Not (big_i X))) True % 3.57/3.78 Clause #5 (by clausification #[2]): ∀ (a : Iota), Eq (And (big_j a) (big_i a) → big_f a) True % 3.57/3.78 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (And (big_j a) (big_i a)) False) (Eq (big_f a) True) % 3.57/3.78 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (big_f a) True) (Or (Eq (big_j a) False) (Eq (big_i a) False)) % 3.57/3.78 Clause #8 (by clausification #[1]): ∀ (a : Iota), Eq (big_f a → big_h a) True % 3.57/3.78 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (big_h a) True) % 3.57/3.78 Clause #10 (by clausification #[3]): Or (Eq (Exists fun X => And (big_h X) (Not (big_g X))) False) (Eq (∀ (X1 : Iota), big_i X1 → Not (big_h X1)) True) % 3.57/3.78 Clause #11 (by clausification #[10]): ∀ (a : Iota), Or (Eq (∀ (X1 : Iota), big_i X1 → Not (big_h X1)) True) (Eq (And (big_h a) (Not (big_g a))) False) % 3.57/3.78 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (And (big_h a) (Not (big_g a))) False) (Eq (big_i a_1 → Not (big_h a_1)) True) % 3.57/3.78 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_i a → Not (big_h a)) True) (Or (Eq (big_h a_1) False) (Eq (Not (big_g a_1)) False)) % 3.57/3.78 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 3.57/3.78 Or (Eq (big_h a) False) (Or (Eq (Not (big_g a)) False) (Or (Eq (big_i a_1) False) (Eq (Not (big_h a_1)) True))) % 3.57/3.78 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), % 3.57/3.78 Or (Eq (big_h a) False) (Or (Eq (big_i a_1) False) (Or (Eq (Not (big_h a_1)) True) (Eq (big_g a) True))) % 3.57/3.78 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (big_h a) False) (Or (Eq (big_i a_1) False) (Or (Eq (big_g a) True) (Eq (big_h a_1) False))) % 3.57/3.78 Clause #17 (by clausification #[4]): Eq (∀ (X : Iota), big_j X → Not (big_i X)) False % 3.57/3.78 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (Not (big_j (skS.0 0 a) → Not (big_i (skS.0 0 a)))) True % 3.57/3.78 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (big_j (skS.0 0 a) → Not (big_i (skS.0 0 a))) False % 3.57/3.78 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (big_j (skS.0 0 a)) True % 3.57/3.78 Clause #21 (by clausification #[19]): ∀ (a : Iota), Eq (Not (big_i (skS.0 0 a))) False % 3.57/3.78 Clause #22 (by superposition #[20, 7]): ∀ (a : Iota), Or (Eq (big_f (skS.0 0 a)) True) (Or (Eq True False) (Eq (big_i (skS.0 0 a)) False)) % 3.57/3.78 Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (big_i (skS.0 0 a)) True % 3.57/3.78 Clause #24 (by clausification #[0]): ∀ (a : Iota), Eq (And (big_f (skS.0 1 a)) (Not (big_g (skS.0 1 a)))) True % 3.57/3.78 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (Not (big_g (skS.0 1 a))) True % 3.57/3.78 Clause #26 (by clausification #[24]): ∀ (a : Iota), Eq (big_f (skS.0 1 a)) True % 3.57/3.78 Clause #27 (by clausification #[25]): ∀ (a : Iota), Eq (big_g (skS.0 1 a)) False % 3.57/3.78 Clause #28 (by superposition #[26, 9]): ∀ (a : Iota), Or (Eq True False) (Eq (big_h (skS.0 1 a)) True) % 3.57/3.78 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (big_h (skS.0 1 a)) True % 3.57/3.78 Clause #30 (by superposition #[29, 16]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_i a) False) (Or (Eq (big_g (skS.0 1 a_1)) True) (Eq (big_h a) False))) % 3.57/3.78 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (big_i a) False) (Or (Eq (big_g (skS.0 1 a_1)) True) (Eq (big_h a) False)) % 3.57/3.78 Clause #32 (by superposition #[31, 23]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 1 a)) True) (Or (Eq (big_h (skS.0 0 a_1)) False) (Eq False True)) % 3.57/3.78 Clause #33 (by clausification #[22]): ∀ (a : Iota), Or (Eq (big_f (skS.0 0 a)) True) (Eq (big_i (skS.0 0 a)) False) % 3.57/3.78 Clause #34 (by forward demodulation #[33, 23]): ∀ (a : Iota), Or (Eq (big_f (skS.0 0 a)) True) (Eq True False) % 3.57/3.78 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (big_f (skS.0 0 a)) True % 3.57/3.78 Clause #36 (by superposition #[35, 9]): ∀ (a : Iota), Or (Eq True False) (Eq (big_h (skS.0 0 a)) True) % 3.57/3.78 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (big_h (skS.0 0 a)) True % 3.57/3.78 Clause #39 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 1 a)) True) (Eq (big_h (skS.0 0 a_1)) False) % 3.57/3.78 Clause #40 (by superposition #[39, 37]): ∀ (a : Iota), Or (Eq (big_g (skS.0 1 a)) True) (Eq False True) % 3.57/3.78 Clause #41 (by clausification #[40]): ∀ (a : Iota), Eq (big_g (skS.0 1 a)) True % 3.57/3.78 Clause #42 (by superposition #[41, 27]): Eq True False % 3.57/3.78 Clause #43 (by clausification #[42]): False % 3.57/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------