%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN334+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 4.75s 4.93s % Output : Proof 4.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN334+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 15:42:08 EDT 2025 % 0.13/0.35 % CPUTime : % 4.75/4.93 SZS status Theorem for theBenchmark.p % 4.75/4.93 SZS output start Proof for theBenchmark.p % 4.75/4.93 Clause #0 (by assumption #[]): Eq % 4.75/4.93 (Not % 4.75/4.93 (Exists fun X => % 4.75/4.93 Exists fun Y => % 4.75/4.93 ∀ (Z : Iota), % 4.75/4.93 (big_f X Y → Iff (big_f X Z) (big_g Y Z)) → % 4.75/4.93 Iff (big_f X Y) (big_f Z Z → big_g Z Z) → Iff (big_g X Y) (big_g Z Z))) % 4.75/4.93 True % 4.75/4.93 Clause #1 (by clausification #[0]): Eq % 4.75/4.93 (Exists fun X => % 4.75/4.93 Exists fun Y => % 4.75/4.93 ∀ (Z : Iota), % 4.75/4.93 (big_f X Y → Iff (big_f X Z) (big_g Y Z)) → % 4.75/4.93 Iff (big_f X Y) (big_f Z Z → big_g Z Z) → Iff (big_g X Y) (big_g Z Z)) % 4.75/4.93 False % 4.75/4.93 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 4.75/4.93 Eq % 4.75/4.93 (Exists fun Y => % 4.75/4.93 ∀ (Z : Iota), % 4.75/4.93 (big_f a Y → Iff (big_f a Z) (big_g Y Z)) → % 4.75/4.93 Iff (big_f a Y) (big_f Z Z → big_g Z Z) → Iff (big_g a Y) (big_g Z Z)) % 4.75/4.93 False % 4.75/4.93 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 4.75/4.93 Eq % 4.75/4.93 (∀ (Z : Iota), % 4.75/4.93 (big_f a a_1 → Iff (big_f a Z) (big_g a_1 Z)) → % 4.75/4.93 Iff (big_f a a_1) (big_f Z Z → big_g Z Z) → Iff (big_g a a_1) (big_g Z Z)) % 4.75/4.93 False % 4.75/4.93 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 Eq % 4.75/4.93 (Not % 4.75/4.93 ((big_f a a_1 → Iff (big_f a (skS.0 0 a a_1 a_2)) (big_g a_1 (skS.0 0 a a_1 a_2))) → % 4.75/4.93 Iff (big_f a a_1) % 4.75/4.93 (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 4.75/4.93 Iff (big_g a a_1) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)))) % 4.75/4.93 True % 4.75/4.93 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 Eq % 4.75/4.93 ((big_f a a_1 → Iff (big_f a (skS.0 0 a a_1 a_2)) (big_g a_1 (skS.0 0 a a_1 a_2))) → % 4.75/4.93 Iff (big_f a a_1) % 4.75/4.93 (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 4.75/4.93 Iff (big_g a a_1) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) % 4.75/4.93 False % 4.75/4.93 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (big_f a a_1 → Iff (big_f a (skS.0 0 a a_1 a_2)) (big_g a_1 (skS.0 0 a a_1 a_2))) True % 4.75/4.93 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 Eq % 4.75/4.93 (Iff (big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 4.75/4.93 Iff (big_g a a_1) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) % 4.75/4.93 False % 4.75/4.93 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 Or (Eq (big_f a a_1) False) (Eq (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_g a_1 (skS.0 0 a a_1 a_2))) True) % 4.75/4.93 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 Or (Eq (big_f a a_1) False) (Or (Eq (big_f a (skS.0 0 a a_1 a_2)) True) (Eq (big_g a_1 (skS.0 0 a a_1 a_2)) False)) % 4.75/4.93 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 Or (Eq (big_f a a_1) False) (Or (Eq (big_f a (skS.0 0 a a_1 a_2)) False) (Eq (big_g a_1 (skS.0 0 a a_1 a_2)) True)) % 4.75/4.93 Clause #11 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 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) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) % 4.75/4.93 True % 4.75/4.93 Clause #12 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_g a a_1) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) False % 4.75/4.93 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 Or (Eq (big_f a a_1) True) % 4.75/4.93 (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 4.75/4.93 Clause #14 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.75/4.93 Or (Eq (big_f a a_1) False) % 4.75/4.93 (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) → big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True) % 4.75/4.93 Clause #15 (by clausification #[13]): ∀ (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)) True) % 4.75/4.93 Clause #16 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 4.75/4.93 Clause #17 (by superposition #[15, 9]): ∀ (a a_1 a_2 a_3 : Iota), % 4.75/4.93 Or (Eq (big_f a a_1) True) % 4.75/4.93 (Or (Eq True False) % 4.75/4.93 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True) % 4.75/4.93 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) False))) % 4.78/4.96 Clause #18 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 4.78/4.96 Clause #19 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) True) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True) % 4.78/4.96 Clause #20 (by superposition #[19, 16]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Or (Eq (big_f a a_1) True) (Eq True False)) % 4.78/4.96 Clause #21 (by superposition #[19, 18]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_g a a_1) True) % 4.78/4.96 (Or (Eq True False) % 4.78/4.96 (Eq % 4.78/4.96 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) % 4.78/4.96 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) % 4.78/4.96 False)) % 4.78/4.96 Clause #22 (by superposition #[10, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq True False) % 4.78/4.96 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) False) % 4.78/4.96 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True))) % 4.78/4.96 Clause #23 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq (big_f a a_1) True) % 4.78/4.96 Clause #26 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) False) % 4.78/4.96 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 4.78/4.96 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True)) % 4.78/4.96 Clause #30 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_g a a_1) True) % 4.78/4.96 (Eq % 4.78/4.96 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) % 4.78/4.96 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) % 4.78/4.96 False) % 4.78/4.96 Clause #33 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True) % 4.78/4.96 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) False)) % 4.78/4.96 Clause #34 (by superposition #[33, 23]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True) % 4.78/4.96 (Or (Eq False True) (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True))) % 4.78/4.96 Clause #39 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) False) % 4.78/4.96 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)) % 4.78/4.96 Clause #40 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True) % 4.78/4.96 (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)) % 4.78/4.96 Clause #41 (by eliminate duplicate literals #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True) % 4.78/4.96 Clause #42 (by superposition #[41, 39]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True))) % 4.78/4.96 Clause #45 (by superposition #[41, 26]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq True False) % 4.78/4.96 (Or % 4.78/4.96 (Eq % 4.78/4.96 (big_f (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.96 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.96 False) % 4.78/4.96 (Eq % 4.78/4.96 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.96 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.96 True))) % 4.78/4.96 Clause #46 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (big_f a a_1) True) % 4.78/4.96 (Or (Eq (big_f a a_1) True) % 4.78/4.96 (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True)) % 4.78/4.98 Clause #47 (by eliminate duplicate literals #[46]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3)) True) % 4.78/4.98 Clause #48 (by superposition #[47, 18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) % 4.78/4.98 (Or (Eq True False) % 4.78/4.98 (Eq % 4.78/4.98 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 False)) % 4.78/4.98 Clause #55 (by clausification #[48]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) % 4.78/4.98 (Eq % 4.78/4.98 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 False) % 4.78/4.98 Clause #57 (by superposition #[55, 23]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) % 4.78/4.98 (Or (Eq False True) % 4.78/4.98 (Eq % 4.78/4.98 (big_f (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 True)) % 4.78/4.98 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) % 4.78/4.98 (Eq % 4.78/4.98 (big_f (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 True) % 4.78/4.98 Clause #70 (by clausification #[45]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) % 4.78/4.98 (Or % 4.78/4.98 (Eq % 4.78/4.98 (big_f (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 False) % 4.78/4.98 (Eq % 4.78/4.98 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 True)) % 4.78/4.98 Clause #72 (by superposition #[70, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) % 4.78/4.98 (Or % 4.78/4.98 (Eq % 4.78/4.98 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 True) % 4.78/4.98 (Or (Eq (big_f a a_1) True) (Eq False True))) % 4.78/4.98 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) % 4.78/4.98 (Or % 4.78/4.98 (Eq % 4.78/4.98 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 True) % 4.78/4.98 (Eq (big_f a a_1) True)) % 4.78/4.98 Clause #74 (by eliminate duplicate literals #[73]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) True) % 4.78/4.98 (Eq % 4.78/4.98 (big_g (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4) % 4.78/4.98 (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2) a_3) a_4)) % 4.78/4.98 True) % 4.78/4.98 Clause #77 (by superposition #[74, 55]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq (big_f a a_1) True) (Eq True False)) % 4.78/4.98 Clause #81 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a a_1) True) % 4.78/4.98 Clause #82 (by eliminate duplicate literals #[81]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True % 4.78/4.98 Clause #83 (by backward demodulation #[82, 26]): ∀ (a a_1 a_2 : Iota), % 4.78/4.98 Or (Eq (big_f a a_1) False) (Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True)) % 4.78/4.98 Clause #108 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True) % 4.78/4.98 Clause #109 (by forward demodulation #[108, 82]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True) % 4.78/4.98 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) True % 4.78/4.98 Clause #111 (by superposition #[110, 30]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq True False) % 4.78/4.98 Clause #113 (by clausification #[111]): ∀ (a a_1 : Iota), Eq (big_g a a_1) True % 4.78/4.98 Clause #114 (by backward demodulation #[113, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 4.78/4.98 Clause #116 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False % 4.78/4.98 Clause #117 (by superposition #[116, 113]): Eq False True % 4.78/4.98 Clause #120 (by clausification #[117]): False % 4.78/4.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------