%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN326+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:07:24 PM UTC 2025 % Result : Theorem 4.48s 4.72s % Output : Proof 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.15 % Problem : SYN326+1 : TPTP v9.2.0. Released v2.0.0. % 0.12/0.16 % Command : duper %s % 0.14/0.38 % Computer : n015.cluster.edu % 0.14/0.38 % Model : x86_64 x86_64 % 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.38 % Memory : 8042.1875MB % 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.38 % CPULimit : 300 % 0.14/0.38 % WCLimit : 300 % 0.14/0.38 % DateTime : Thu Oct 2 15:41:53 EDT 2025 % 0.14/0.38 % CPUTime : % 4.48/4.72 SZS status Theorem for theBenchmark.p % 4.48/4.72 SZS output start Proof for theBenchmark.p % 4.48/4.72 Clause #0 (by assumption #[]): Eq % 4.48/4.72 (Not % 4.48/4.72 (Exists fun X => % 4.48/4.72 ∀ (Y Z : Iota), % 4.48/4.72 ((big_f Y Z → big_g Y → big_h X) → big_f X X) → ((big_f Z X → big_g X) → big_h Z) → big_f X Y → big_f Z Z)) % 4.48/4.72 True % 4.48/4.72 Clause #1 (by clausification #[0]): Eq % 4.48/4.72 (Exists fun X => % 4.48/4.72 ∀ (Y Z : Iota), % 4.48/4.72 ((big_f Y Z → big_g Y → big_h X) → big_f X X) → ((big_f Z X → big_g X) → big_h Z) → big_f X Y → big_f Z Z) % 4.48/4.72 False % 4.48/4.72 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 4.48/4.72 Eq % 4.48/4.72 (∀ (Y Z : Iota), % 4.48/4.72 ((big_f Y Z → big_g Y → big_h a) → big_f a a) → ((big_f Z a → big_g a) → big_h Z) → big_f a Y → big_f Z Z) % 4.48/4.72 False % 4.48/4.72 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (Not % 4.48/4.72 (∀ (Z : Iota), % 4.48/4.72 ((big_f (skS.0 0 a a_1) Z → big_g (skS.0 0 a a_1) → big_h a) → big_f a a) → % 4.48/4.72 ((big_f Z a → big_g a) → big_h Z) → big_f a (skS.0 0 a a_1) → big_f Z Z)) % 4.48/4.72 True % 4.48/4.72 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (∀ (Z : Iota), % 4.48/4.72 ((big_f (skS.0 0 a a_1) Z → big_g (skS.0 0 a a_1) → big_h a) → big_f a a) → % 4.48/4.72 ((big_f Z a → big_g a) → big_h Z) → big_f a (skS.0 0 a a_1) → big_f Z Z) % 4.48/4.72 False % 4.48/4.72 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (Not % 4.48/4.72 (((big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2) → big_g (skS.0 0 a a_1) → big_h a) → big_f a a) → % 4.48/4.72 ((big_f (skS.0 1 a a_1 a_2) a → big_g a) → big_h (skS.0 1 a a_1 a_2)) → % 4.48/4.72 big_f a (skS.0 0 a a_1) → big_f (skS.0 1 a a_1 a_2) (skS.0 1 a a_1 a_2))) % 4.48/4.72 True % 4.48/4.72 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (((big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2) → big_g (skS.0 0 a a_1) → big_h a) → big_f a a) → % 4.48/4.72 ((big_f (skS.0 1 a a_1 a_2) a → big_g a) → big_h (skS.0 1 a a_1 a_2)) → % 4.48/4.72 big_f a (skS.0 0 a a_1) → big_f (skS.0 1 a a_1 a_2) (skS.0 1 a a_1 a_2)) % 4.48/4.72 False % 4.48/4.72 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 4.48/4.72 Eq ((big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2) → big_g (skS.0 0 a a_1) → big_h a) → big_f a a) True % 4.48/4.72 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (((big_f (skS.0 1 a a_1 a_2) a → big_g a) → big_h (skS.0 1 a a_1 a_2)) → % 4.48/4.72 big_f a (skS.0 0 a a_1) → big_f (skS.0 1 a a_1 a_2) (skS.0 1 a a_1 a_2)) % 4.48/4.72 False % 4.48/4.72 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 4.48/4.72 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2) → big_g (skS.0 0 a a_1) → big_h a) False) (Eq (big_f a a) True) % 4.48/4.72 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (big_f a a) True) (Eq (big_g (skS.0 0 a a_1) → big_h a) False) % 4.48/4.72 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (big_f a a) True) (Eq (big_g (skS.0 0 a a_1)) True) % 4.48/4.72 Clause #13 (by clausification #[11]): ∀ (a : Iota), Or (Eq (big_f a a) True) (Eq (big_h a) False) % 4.48/4.72 Clause #14 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Eq ((big_f (skS.0 1 a a_1 a_2) a → big_g a) → big_h (skS.0 1 a a_1 a_2)) True % 4.48/4.72 Clause #15 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Eq (big_f a (skS.0 0 a a_1) → big_f (skS.0 1 a a_1 a_2) (skS.0 1 a a_1 a_2)) False % 4.48/4.72 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 1 a a_1 a_2) a → big_g a) False) (Eq (big_h (skS.0 1 a a_1 a_2)) True) % 4.48/4.72 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_h (skS.0 1 a a_1 a_2)) True) (Eq (big_g a) False) % 4.48/4.72 Clause #21 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 1 a a_1 a_2) (skS.0 1 a a_1 a_2)) False % 4.48/4.72 Clause #22 (by superposition #[21, 12]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq False True) (Eq (big_g (skS.0 0 (skS.0 1 a a_1 a_2) a_3)) True) % 4.48/4.72 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_g (skS.0 0 (skS.0 1 a a_1 a_2) a_3)) True % 4.48/4.72 Clause #24 (by superposition #[23, 18]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.48/4.72 Or (Eq (big_h (skS.0 1 (skS.0 0 (skS.0 1 a a_1 a_2) a_3) a_4 a_5)) True) (Eq True False) % 4.48/4.72 Clause #27 (by clausification #[24]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (big_h (skS.0 1 (skS.0 0 (skS.0 1 a a_1 a_2) a_3) a_4 a_5)) True % 4.54/4.72 Clause #28 (by superposition #[27, 13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.54/4.72 Or % 4.54/4.72 (Eq (big_f (skS.0 1 (skS.0 0 (skS.0 1 a a_1 a_2) a_3) a_4 a_5) (skS.0 1 (skS.0 0 (skS.0 1 a a_1 a_2) a_3) a_4 a_5)) % 4.54/4.72 True) % 4.54/4.72 (Eq True False) % 4.54/4.72 Clause #31 (by clausification #[28]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.54/4.72 Eq (big_f (skS.0 1 (skS.0 0 (skS.0 1 a a_1 a_2) a_3) a_4 a_5) (skS.0 1 (skS.0 0 (skS.0 1 a a_1 a_2) a_3) a_4 a_5)) % 4.54/4.72 True % 4.54/4.72 Clause #32 (by superposition #[31, 21]): Eq True False % 4.54/4.72 Clause #33 (by clausification #[32]): False % 4.54/4.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------