%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN321+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:07:23 PM UTC 2025 % Result : Theorem 5.74s 5.94s % Output : Proof 5.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYN321+1 : TPTP v9.2.0. Released v2.0.0. % 0.03/0.12 % Command : duper %s % 0.12/0.32 % Computer : n031.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Thu Oct 2 15:08:23 EDT 2025 % 0.12/0.32 % CPUTime : % 5.74/5.94 SZS status Theorem for theBenchmark.p % 5.74/5.94 SZS output start Proof for theBenchmark.p % 5.74/5.94 Clause #0 (by assumption #[]): Eq % 5.74/5.94 (Not % 5.74/5.94 (Exists fun X => % 5.74/5.94 Exists fun Y => % 5.74/5.94 ((Exists fun Z => big_f X Z) → ∀ (Z : Iota), big_g X Z) → % 5.74/5.94 (∀ (Z : Iota), big_g Z Z → big_f Z Y) → Iff (big_f X Y) (∀ (Z : Iota), big_g X Z))) % 5.74/5.94 True % 5.74/5.94 Clause #1 (by betaEtaReduce #[0]): Eq % 5.74/5.94 (Not % 5.74/5.94 (Exists fun X => % 5.74/5.94 Exists fun Y => % 5.74/5.94 (Exists (big_f X) → ∀ (Z : Iota), big_g X Z) → % 5.74/5.94 (∀ (Z : Iota), big_g Z Z → big_f Z Y) → Iff (big_f X Y) (∀ (Z : Iota), big_g X Z))) % 5.74/5.94 True % 5.74/5.94 Clause #2 (by clausification #[1]): Eq % 5.74/5.94 (Exists fun X => % 5.74/5.94 Exists fun Y => % 5.74/5.94 (Exists (big_f X) → ∀ (Z : Iota), big_g X Z) → % 5.74/5.94 (∀ (Z : Iota), big_g Z Z → big_f Z Y) → Iff (big_f X Y) (∀ (Z : Iota), big_g X Z)) % 5.74/5.94 False % 5.74/5.94 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 5.74/5.94 Eq % 5.74/5.94 (Exists fun Y => % 5.74/5.94 (Exists (big_f a) → ∀ (Z : Iota), big_g a Z) → % 5.74/5.94 (∀ (Z : Iota), big_g Z Z → big_f Z Y) → Iff (big_f a Y) (∀ (Z : Iota), big_g a Z)) % 5.74/5.94 False % 5.74/5.94 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 5.74/5.94 Eq % 5.74/5.94 ((Exists (big_f a) → ∀ (Z : Iota), big_g a Z) → % 5.74/5.94 (∀ (Z : Iota), big_g Z Z → big_f Z a_1) → Iff (big_f a a_1) (∀ (Z : Iota), big_g a Z)) % 5.74/5.94 False % 5.74/5.94 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Exists (big_f a) → ∀ (Z : Iota), big_g a Z) True % 5.74/5.94 Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota), Eq ((∀ (Z : Iota), big_g Z Z → big_f Z a) → Iff (big_f a_1 a) (∀ (Z : Iota), big_g a_1 Z)) False % 5.74/5.94 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Exists (big_f a)) False) (Eq (∀ (Z : Iota), big_g a Z) True) % 5.74/5.94 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (∀ (Z : Iota), big_g a Z) True) (Eq (big_f a a_1) False) % 5.74/5.94 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_g a a_2) True) % 5.74/5.94 Clause #10 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Z : Iota), big_g Z Z → big_f Z a) True % 5.74/5.94 Clause #11 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Iff (big_f a a_1) (∀ (Z : Iota), big_g a Z)) False % 5.74/5.94 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (big_g a a → big_f a a_1) True % 5.74/5.94 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_g a a) False) (Eq (big_f a a_1) True) % 5.74/5.94 Clause #14 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) False) (Eq (∀ (Z : Iota), big_g a Z) False) % 5.74/5.94 Clause #15 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (∀ (Z : Iota), big_g a Z) True) % 5.74/5.94 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (Not (big_g a (skS.0 0 a a_2))) True) % 5.74/5.94 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_g a (skS.0 0 a a_2)) False) % 5.74/5.94 Clause #18 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_g a a_2) True) % 5.74/5.94 Clause #19 (by superposition #[18, 9]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) True) (Or (Eq True False) (Eq (big_g a a_2) True)) % 5.74/5.94 Clause #26 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) True) (Eq (big_g a a_2) True) % 5.74/5.94 Clause #28 (by equality factoring #[26]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (big_g a a_1) True) % 5.74/5.94 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Or (Eq True False) (Eq True False)) % 5.74/5.94 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq True False) % 5.74/5.94 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (big_g a a_1) True % 5.74/5.94 Clause #33 (by superposition #[32, 13]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_f a a_1) True) % 5.74/5.94 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True % 5.74/5.94 Clause #35 (by superposition #[34, 17]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_g a (skS.0 0 a a_1)) False) % 5.74/5.94 Clause #41 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (big_g a (skS.0 0 a a_1)) False % 5.74/5.94 Clause #42 (by superposition #[41, 32]): Eq False True % 5.74/5.94 Clause #43 (by clausification #[42]): False % 5.74/5.94 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------