%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN350+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:07:27 PM UTC 2025 % Result : Theorem 3.58s 3.74s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SYN350+1 : TPTP v9.2.0. Released v2.0.0. % 0.13/0.14 % Command : duper %s % 0.13/0.35 % Computer : n009.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 15:21:08 EDT 2025 % 0.13/0.36 % CPUTime : % 3.58/3.74 SZS status Theorem for theBenchmark.p % 3.58/3.74 SZS output start Proof for theBenchmark.p % 3.58/3.74 Clause #0 (by assumption #[]): Eq % 3.58/3.74 (Not % 3.58/3.74 (∀ (X : Iota), % 3.58/3.74 Exists fun Y1 => % 3.58/3.74 Exists fun Y2 => % 3.58/3.74 ∀ (Z : Iota), Iff (big_f X Z) (big_f Z X) → Iff (big_f X Z) (And (big_f Y2 Z) (big_f Y1 Z → big_f Y1 Y2)))) % 3.58/3.74 True % 3.58/3.74 Clause #1 (by clausification #[0]): Eq % 3.58/3.74 (∀ (X : Iota), % 3.58/3.74 Exists fun Y1 => % 3.58/3.74 Exists fun Y2 => % 3.58/3.74 ∀ (Z : Iota), Iff (big_f X Z) (big_f Z X) → Iff (big_f X Z) (And (big_f Y2 Z) (big_f Y1 Z → big_f Y1 Y2))) % 3.58/3.74 False % 3.58/3.74 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.58/3.74 Eq % 3.58/3.74 (Not % 3.58/3.74 (Exists fun Y1 => % 3.58/3.74 Exists fun Y2 => % 3.58/3.74 ∀ (Z : Iota), % 3.58/3.74 Iff (big_f (skS.0 0 a) Z) (big_f Z (skS.0 0 a)) → % 3.58/3.74 Iff (big_f (skS.0 0 a) Z) (And (big_f Y2 Z) (big_f Y1 Z → big_f Y1 Y2)))) % 3.58/3.74 True % 3.58/3.74 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 3.58/3.74 Eq % 3.58/3.74 (Exists fun Y1 => % 3.58/3.74 Exists fun Y2 => % 3.58/3.74 ∀ (Z : Iota), % 3.58/3.74 Iff (big_f (skS.0 0 a) Z) (big_f Z (skS.0 0 a)) → % 3.58/3.74 Iff (big_f (skS.0 0 a) Z) (And (big_f Y2 Z) (big_f Y1 Z → big_f Y1 Y2))) % 3.58/3.74 False % 3.58/3.74 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.58/3.74 Eq % 3.58/3.74 (Exists fun Y2 => % 3.58/3.74 ∀ (Z : Iota), % 3.58/3.74 Iff (big_f (skS.0 0 a) Z) (big_f Z (skS.0 0 a)) → % 3.58/3.74 Iff (big_f (skS.0 0 a) Z) (And (big_f Y2 Z) (big_f a_1 Z → big_f a_1 Y2))) % 3.58/3.74 False % 3.58/3.74 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 3.58/3.74 Eq % 3.58/3.74 (∀ (Z : Iota), % 3.58/3.74 Iff (big_f (skS.0 0 a) Z) (big_f Z (skS.0 0 a)) → % 3.58/3.74 Iff (big_f (skS.0 0 a) Z) (And (big_f a_1 Z) (big_f a_2 Z → big_f a_2 a_1))) % 3.58/3.74 False % 3.58/3.74 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Eq % 3.58/3.74 (Not % 3.58/3.74 (Iff (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a)) → % 3.58/3.74 Iff (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) % 3.58/3.74 (And (big_f a_1 (skS.0 1 a a_1 a_2 a_3)) (big_f a_2 (skS.0 1 a a_1 a_2 a_3) → big_f a_2 a_1)))) % 3.58/3.74 True % 3.58/3.74 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Eq % 3.58/3.74 (Iff (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a)) → % 3.58/3.74 Iff (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) % 3.58/3.74 (And (big_f a_1 (skS.0 1 a a_1 a_2 a_3)) (big_f a_2 (skS.0 1 a a_1 a_2 a_3) → big_f a_2 a_1))) % 3.58/3.74 False % 3.58/3.74 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Eq (Iff (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a))) True % 3.58/3.74 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Eq % 3.58/3.74 (Iff (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) % 3.58/3.74 (And (big_f a_1 (skS.0 1 a a_1 a_2 a_3)) (big_f a_2 (skS.0 1 a a_1 a_2 a_3) → big_f a_2 a_1))) % 3.58/3.74 False % 3.58/3.74 Clause #11 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) False) (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a)) True) % 3.58/3.74 Clause #12 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) False) % 3.58/3.74 (Eq (And (big_f a_1 (skS.0 1 a a_1 a_2 a_3)) (big_f a_2 (skS.0 1 a a_1 a_2 a_3) → big_f a_2 a_1)) False) % 3.58/3.74 Clause #13 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) True) % 3.58/3.74 (Eq (And (big_f a_1 (skS.0 1 a a_1 a_2 a_3)) (big_f a_2 (skS.0 1 a a_1 a_2 a_3) → big_f a_2 a_1)) True) % 3.58/3.74 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) False) % 3.58/3.74 (Or (Eq (big_f a_1 (skS.0 1 a a_1 a_2 a_3)) False) (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3) → big_f a_2 a_1) False)) % 3.58/3.74 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) False) % 3.58/3.74 (Or (Eq (big_f a_1 (skS.0 1 a a_1 a_2 a_3)) False) (Eq (big_f a_2 a_1) False)) % 3.58/3.74 Clause #18 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.74 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1 a_2 a_3)) True) (Eq (big_f a_1 (skS.0 1 a a_1 a_2 a_3)) True) % 3.58/3.74 Clause #24 (by equality factoring #[18]): ∀ (a a_1 a_2 : Iota), Or (Ne True True) (Eq (big_f (skS.0 0 a) (skS.0 1 a (skS.0 0 a) a_1 a_2)) True) % 3.58/3.75 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 3.58/3.75 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a (skS.0 0 a) a_1 a_2)) True) (Or (Eq True False) (Eq True False)) % 3.58/3.75 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a) (skS.0 1 a (skS.0 0 a) a_1 a_2)) True) (Eq True False) % 3.58/3.75 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a (skS.0 0 a) a_1 a_2)) True % 3.58/3.75 Clause #31 (by superposition #[29, 16]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq True False) (Eq (big_f a (skS.0 0 a_1)) False)) % 3.58/3.75 Clause #32 (by superposition #[29, 11]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_f (skS.0 1 a (skS.0 0 a) a_1 a_2) (skS.0 0 a)) True) % 3.58/3.75 Clause #33 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_f a (skS.0 0 a_1)) False) % 3.58/3.75 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (big_f a (skS.0 0 a_1)) False % 3.58/3.75 Clause #42 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 1 a (skS.0 0 a) a_1 a_2) (skS.0 0 a)) True % 3.58/3.75 Clause #43 (by superposition #[42, 34]): Eq True False % 3.58/3.75 Clause #45 (by clausification #[43]): False % 3.58/3.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------