%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN331+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 08:07:25 PM UTC 2025 % Result : Theorem 3.29s 3.52s % Output : Proof 3.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.07 % Problem : SYN331+1 : TPTP v9.2.0. Released v2.0.0. % 0.04/0.08 % Command : duper %s % 0.07/0.26 % Computer : n012.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Thu Oct 2 15:31:08 EDT 2025 % 0.07/0.26 % CPUTime : % 3.29/3.52 SZS status Theorem for theBenchmark.p % 3.29/3.52 SZS output start Proof for theBenchmark.p % 3.29/3.52 Clause #0 (by assumption #[]): Eq % 3.29/3.52 (Not % 3.29/3.52 (Exists fun X => % 3.29/3.52 Exists fun Y => % 3.29/3.52 ∀ (Z : Iota), % 3.29/3.52 big_f X Z → % 3.29/3.52 big_f Y Z → Iff (big_f X Y) (big_f Z Z) → Or (big_f Y X) (big_f Z Z) → Or (big_f Z X) (big_f Z Y))) % 3.29/3.52 True % 3.29/3.52 Clause #1 (by clausification #[0]): Eq % 3.29/3.52 (Exists fun X => % 3.29/3.52 Exists fun Y => % 3.29/3.52 ∀ (Z : Iota), % 3.29/3.52 big_f X Z → big_f Y Z → Iff (big_f X Y) (big_f Z Z) → Or (big_f Y X) (big_f Z Z) → Or (big_f Z X) (big_f Z Y)) % 3.29/3.52 False % 3.29/3.52 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.29/3.52 Eq % 3.29/3.52 (Exists fun Y => % 3.29/3.52 ∀ (Z : Iota), % 3.29/3.52 big_f a Z → big_f Y Z → Iff (big_f a Y) (big_f Z Z) → Or (big_f Y a) (big_f Z Z) → Or (big_f Z a) (big_f Z Y)) % 3.29/3.52 False % 3.29/3.52 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 3.29/3.52 Eq % 3.29/3.52 (∀ (Z : Iota), % 3.29/3.52 big_f a Z → % 3.29/3.52 big_f a_1 Z → Iff (big_f a a_1) (big_f Z Z) → Or (big_f a_1 a) (big_f Z Z) → Or (big_f Z a) (big_f Z a_1)) % 3.29/3.52 False % 3.29/3.52 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota), % 3.29/3.52 Eq % 3.29/3.52 (Not % 3.29/3.52 (big_f a (skS.0 0 a a_1 a_2) → % 3.29/3.52 big_f a_1 (skS.0 0 a a_1 a_2) → % 3.29/3.52 Iff (big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.29/3.52 Or (big_f a_1 a) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.29/3.52 Or (big_f (skS.0 0 a a_1 a_2) a) (big_f (skS.0 0 a a_1 a_2) a_1))) % 3.29/3.52 True % 3.29/3.52 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 3.29/3.52 Eq % 3.29/3.52 (big_f a (skS.0 0 a a_1 a_2) → % 3.29/3.52 big_f a_1 (skS.0 0 a a_1 a_2) → % 3.29/3.52 Iff (big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.29/3.52 Or (big_f a_1 a) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.29/3.52 Or (big_f (skS.0 0 a a_1 a_2) a) (big_f (skS.0 0 a a_1 a_2) a_1)) % 3.29/3.52 False % 3.29/3.52 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.29/3.52 Eq % 3.29/3.52 (big_f a (skS.0 0 a_1 a a_2) → % 3.29/3.52 Iff (big_f a_1 a) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) → % 3.29/3.52 Or (big_f a a_1) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) → % 3.29/3.52 Or (big_f (skS.0 0 a_1 a a_2) a_1) (big_f (skS.0 0 a_1 a a_2) a)) % 3.29/3.52 False % 3.29/3.52 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.29/3.52 Eq % 3.29/3.52 (Iff (big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.29/3.52 Or (big_f a_1 a) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.29/3.52 Or (big_f (skS.0 0 a a_1 a_2) a) (big_f (skS.0 0 a a_1 a_2) a_1)) % 3.29/3.52 False % 3.29/3.52 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) True % 3.29/3.52 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.29/3.52 Eq % 3.29/3.52 (Or (big_f a a_1) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) → % 3.29/3.52 Or (big_f (skS.0 0 a_1 a a_2) a_1) (big_f (skS.0 0 a_1 a a_2) a)) % 3.29/3.52 False % 3.29/3.52 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 3.29/3.52 Clause #16 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (Or (big_f a a_1) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2))) True % 3.29/3.52 Clause #17 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (Or (big_f (skS.0 0 a a_1 a_2) a) (big_f (skS.0 0 a a_1 a_2) a_1)) False % 3.29/3.52 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) True) % 3.29/3.52 Clause #19 (by superposition #[18, 12]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq (big_f a_1 a) True) (Eq True False)) % 3.29/3.52 Clause #24 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True) % 3.29/3.52 Clause #26 (by equality factoring #[24]): ∀ (a : Iota), Or (Ne True True) (Eq (big_f a a) True) % 3.29/3.52 Clause #27 (by clausification #[26]): ∀ (a : Iota), Or (Eq (big_f a a) True) (Or (Eq True False) (Eq True False)) % 3.29/3.52 Clause #29 (by clausification #[27]): ∀ (a : Iota), Or (Eq (big_f a a) True) (Eq True False) % 3.29/3.52 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (big_f a a) True % 3.29/3.52 Clause #31 (by superposition #[30, 12]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq True False) % 3.29/3.52 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True % 3.29/3.52 Clause #35 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a a_1 a_2) a_1) False % 3.29/3.52 Clause #37 (by superposition #[35, 32]): Eq False True % 3.29/3.52 Clause #38 (by clausification #[37]): False % 3.29/3.52 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------