%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO256^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:08:48 PM UTC 2025 % Result : Theorem 4.46s 4.64s % Output : Proof 4.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO256^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 : Fri Oct 3 12:53:53 EDT 2025 % 0.13/0.34 % CPUTime : % 4.46/4.64 SZS status Theorem for theBenchmark.p % 4.46/4.64 SZS output start Proof for theBenchmark.p % 4.46/4.64 Clause #0 (by assumption #[]): Eq (Not (∀ (Xr : Prop → Prop) (Xp Xq : a → Prop), Exists fun Xh => Iff (Xr Xh) (Xr (∀ (Xx : a), Or (Xp Xx) (Xq Xx))))) % 4.46/4.64 True % 4.46/4.64 Clause #1 (by clausification #[0]): Eq (∀ (Xr : Prop → Prop) (Xp Xq : a → Prop), Exists fun Xh => Iff (Xr Xh) (Xr (∀ (Xx : a), Or (Xp Xx) (Xq Xx)))) False % 4.46/4.64 Clause #2 (by clausification #[1]): ∀ (a_1 : Prop → Prop), % 4.46/4.64 Eq (Not (∀ (Xp Xq : a → Prop), Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (Xp Xx) (Xq Xx))))) % 4.46/4.64 True % 4.46/4.64 Clause #3 (by clausification #[2]): ∀ (a_1 : Prop → Prop), % 4.46/4.64 Eq (∀ (Xp Xq : a → Prop), Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (Xp Xx) (Xq Xx)))) False % 4.46/4.64 Clause #4 (by clausification #[3]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop), % 4.46/4.64 Eq % 4.46/4.64 (Not % 4.46/4.64 (∀ (Xq : a → Prop), % 4.46/4.64 Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (Xq Xx))))) % 4.46/4.64 True % 4.46/4.64 Clause #5 (by clausification #[4]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop), % 4.46/4.64 Eq % 4.46/4.64 (∀ (Xq : a → Prop), % 4.46/4.64 Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (Xq Xx)))) % 4.46/4.64 False % 4.46/4.64 Clause #6 (by clausification #[5]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop), % 4.46/4.64 Eq % 4.46/4.64 (Not % 4.46/4.64 (Exists fun Xh => % 4.46/4.64 Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))))) % 4.46/4.64 True % 4.46/4.64 Clause #7 (by clausification #[6]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop), % 4.46/4.64 Eq % 4.46/4.64 (Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)))) % 4.46/4.64 False % 4.46/4.64 Clause #8 (by clausification #[7]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop), % 4.46/4.64 Eq (Iff (skS.0 0 a_1 a_2) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)))) False % 4.46/4.64 Clause #9 (by clausification #[8]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop), % 4.46/4.64 Or (Eq (skS.0 0 a_1 a_2) False) % 4.46/4.64 (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx))) False) % 4.46/4.64 Clause #10 (by clausification #[8]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop), % 4.46/4.64 Or (Eq (skS.0 0 a_1 a_2) True) (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx))) True) % 4.46/4.64 Clause #11 (by identity loobHoist #[9]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : Prop), % 4.46/4.64 Or (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) False) % 4.46/4.64 (Or (Eq (skS.0 0 a_1 True) False) (Eq a_4 False)) % 4.46/4.64 Clause #12 (by identity boolHoist #[9]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : Prop), % 4.46/4.64 Or (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) False) % 4.46/4.64 (Or (Eq (skS.0 0 a_1 False) False) (Eq a_4 True)) % 4.46/4.64 Clause #13 (by identity loobHoist #[11]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop), % 4.46/4.64 Or (Eq (skS.0 0 a_1 True) False) % 4.46/4.64 (Or (Eq a_2 False) % 4.46/4.64 (Or (Eq (skS.0 0 a_1 True) False) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) False))) % 4.46/4.64 Clause #15 (by clausification #[13]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.46/4.64 Or (Eq (skS.0 0 a_1 True) False) % 4.46/4.64 (Or (Eq a_2 False) % 4.46/4.64 (Or (Eq (skS.0 0 a_1 True) False) % 4.46/4.64 (Eq (Not (Or (skS.0 1 a_1 a_3 (skS.0 3 a_1 a_3 a_4 a_5)) (skS.0 2 a_1 a_3 a_4 (skS.0 3 a_1 a_3 a_4 a_5)))) % 4.46/4.64 True))) % 4.46/4.64 Clause #16 (by clausification #[15]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.46/4.64 Or (Eq (skS.0 0 a_1 True) False) % 4.46/4.64 (Or (Eq a_2 False) % 4.46/4.64 (Or (Eq (skS.0 0 a_1 True) False) % 4.46/4.64 (Eq (Or (skS.0 1 a_1 a_3 (skS.0 3 a_1 a_3 a_4 a_5)) (skS.0 2 a_1 a_3 a_4 (skS.0 3 a_1 a_3 a_4 a_5))) False))) % 4.46/4.64 Clause #17 (by clausification #[16]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.46/4.64 Or (Eq (skS.0 0 a_1 True) False) % 4.46/4.64 (Or (Eq a_2 False) (Or (Eq (skS.0 0 a_1 True) False) (Eq (skS.0 2 a_1 a_3 a_4 (skS.0 3 a_1 a_3 a_4 a_5)) False))) % 4.51/4.67 Clause #18 (by clausification #[16]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) False) % 4.51/4.67 (Or (Eq a_2 False) (Or (Eq (skS.0 0 a_1 True) False) (Eq (skS.0 1 a_1 a_3 (skS.0 3 a_1 a_3 a_4 a_5)) False))) % 4.51/4.67 Clause #19 (by eliminate duplicate literals #[17]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) False) (Or (Eq a_2 False) (Eq (skS.0 2 a_1 a_3 a_4 (skS.0 3 a_1 a_3 a_4 a_5)) False)) % 4.51/4.67 Clause #20 (by identity loobHoist #[10]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : Prop), % 4.51/4.67 Or (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) True) % 4.51/4.67 (Or (Eq (skS.0 0 a_1 True) True) (Eq a_4 False)) % 4.51/4.67 Clause #21 (by identity boolHoist #[10]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : Prop), % 4.51/4.67 Or (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) True) % 4.51/4.67 (Or (Eq (skS.0 0 a_1 False) True) (Eq a_4 True)) % 4.51/4.67 Clause #22 (by identity loobHoist #[20]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.67 (Or (Eq a_2 False) % 4.51/4.67 (Or (Eq (skS.0 0 a_1 True) True) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) False))) % 4.51/4.67 Clause #23 (by identity boolHoist #[20]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.67 (Or (Eq a_2 False) % 4.51/4.67 (Or (Eq (skS.0 0 a_1 False) True) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) True))) % 4.51/4.67 Clause #24 (by clausification #[22]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.67 (Or (Eq a_2 False) % 4.51/4.67 (Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.67 (Eq (Not (Or (skS.0 1 a_1 a_3 (skS.0 4 a_1 a_3 a_4 a_5)) (skS.0 2 a_1 a_3 a_4 (skS.0 4 a_1 a_3 a_4 a_5)))) % 4.51/4.67 True))) % 4.51/4.67 Clause #25 (by clausification #[24]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.67 (Or (Eq a_2 False) % 4.51/4.67 (Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.67 (Eq (Or (skS.0 1 a_1 a_3 (skS.0 4 a_1 a_3 a_4 a_5)) (skS.0 2 a_1 a_3 a_4 (skS.0 4 a_1 a_3 a_4 a_5))) False))) % 4.51/4.67 Clause #26 (by clausification #[25]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.67 (Or (Eq a_2 False) (Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 2 a_1 a_3 a_4 (skS.0 4 a_1 a_3 a_4 a_5)) False))) % 4.51/4.67 Clause #27 (by clausification #[25]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.67 (Or (Eq a_2 False) (Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 1 a_1 a_3 (skS.0 4 a_1 a_3 a_4 a_5)) False))) % 4.51/4.67 Clause #28 (by eliminate duplicate literals #[26]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) (Or (Eq a_2 False) (Eq (skS.0 2 a_1 a_3 a_4 (skS.0 4 a_1 a_3 a_4 a_5)) False)) % 4.51/4.67 Clause #29 (by falseElim #[28]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) False) % 4.51/4.67 Clause #30 (by eliminate duplicate literals #[18]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) False) (Or (Eq a_2 False) (Eq (skS.0 1 a_1 a_3 (skS.0 3 a_1 a_3 a_4 a_5)) False)) % 4.51/4.67 Clause #31 (by eliminate duplicate literals #[27]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) (Or (Eq a_2 False) (Eq (skS.0 1 a_1 a_3 (skS.0 4 a_1 a_3 a_4 a_5)) False)) % 4.51/4.67 Clause #32 (by falseElim #[31]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.67 Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False) % 4.51/4.67 Clause #34 (by identity boolHoist #[12]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop), % 4.51/4.67 Or (Eq (skS.0 0 a_1 False) False) % 4.51/4.67 (Or (Eq a_2 True) % 4.51/4.67 (Or (Eq (skS.0 0 a_1 False) False) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) True))) % 4.51/4.69 Clause #40 (by identity boolHoist #[21]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.69 (Or (Eq a_2 True) % 4.51/4.69 (Or (Eq (skS.0 0 a_1 False) True) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) True))) % 4.51/4.69 Clause #47 (by clausification #[23]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.69 (Or (Eq a_2 False) % 4.51/4.69 (Or (Eq (skS.0 0 a_1 False) True) (Eq (Or (skS.0 1 a_1 a_3 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) True))) % 4.51/4.69 Clause #48 (by clausification #[47]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.69 (Or (Eq a_2 False) % 4.51/4.69 (Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True)))) % 4.51/4.69 Clause #49 (by falseElim #[48]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.69 (Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True))) % 4.51/4.69 Clause #50 (by superposition #[49, 29]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.69 Or (Eq (skS.0 0 (fun x => a_1 x) True) True) % 4.51/4.69 (Or (Eq (skS.0 0 (fun x => a_1 x) False) True) % 4.51/4.69 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 4 a_1 a_2 a_3 a_4)) True) % 4.51/4.69 (Or (Eq (skS.0 0 a_1 True) True) (Eq True False)))) % 4.51/4.69 Clause #52 (by clausification #[34]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) False) % 4.51/4.69 (Or (Eq a_2 True) % 4.51/4.69 (Or (Eq (skS.0 0 a_1 False) False) (Eq (Or (skS.0 1 a_1 a_3 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) True))) % 4.51/4.69 Clause #53 (by clausification #[52]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) False) % 4.51/4.69 (Or (Eq a_2 True) % 4.51/4.69 (Or (Eq (skS.0 0 a_1 False) False) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True)))) % 4.51/4.69 Clause #54 (by eliminate duplicate literals #[53]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) False) % 4.51/4.69 (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True))) % 4.51/4.69 Clause #55 (by clausification #[40]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.69 (Or (Eq a_2 True) (Or (Eq (skS.0 0 a_1 False) True) (Eq (Or (skS.0 1 a_1 a_3 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) True))) % 4.51/4.69 Clause #56 (by clausification #[55]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.69 (Or (Eq a_2 True) % 4.51/4.69 (Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True)))) % 4.51/4.69 Clause #57 (by eliminate duplicate literals #[56]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.69 (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True))) % 4.51/4.69 Clause #71 (by equality factoring #[57]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.69 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Ne True True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True))) % 4.51/4.69 Clause #72 (by clausification #[71]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.69 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Or (Eq True False) (Eq True False)))) % 4.51/4.69 Clause #74 (by clausification #[72]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.69 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Eq True False))) % 4.51/4.69 Clause #75 (by clausification #[74]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.69 Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True)) % 4.51/4.72 Clause #78 (by betaEtaReduce #[50]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.72 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Or (Eq (skS.0 0 a_1 True) True) (Eq True False)))) % 4.51/4.72 Clause #79 (by clausification #[78]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq (skS.0 0 a_1 False) True) % 4.51/4.72 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 True) True))) % 4.51/4.72 Clause #80 (by eliminate duplicate literals #[79]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq (skS.0 0 a_1 False) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True)) % 4.51/4.72 Clause #81 (by superposition #[80, 32]): ∀ (a : Prop → Prop), % 4.51/4.72 Or (Eq (skS.0 0 (fun x => a x) True) True) % 4.51/4.72 (Or (Eq (skS.0 0 (fun x => a x) False) True) (Or (Eq (skS.0 0 a True) True) (Eq True False))) % 4.51/4.72 Clause #82 (by betaEtaReduce #[81]): ∀ (a : Prop → Prop), % 4.51/4.72 Or (Eq (skS.0 0 a True) True) (Or (Eq (skS.0 0 a False) True) (Or (Eq (skS.0 0 a True) True) (Eq True False))) % 4.51/4.72 Clause #83 (by clausification #[82]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Or (Eq (skS.0 0 a False) True) (Eq (skS.0 0 a True) True)) % 4.51/4.72 Clause #84 (by eliminate duplicate literals #[83]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq (skS.0 0 a False) True) % 4.51/4.72 Clause #87 (by superposition #[84, 54]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.72 Or (Eq (skS.0 0 (fun x => a_1 x) True) True) % 4.51/4.72 (Or (Eq True False) (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True)))) % 4.51/4.72 Clause #88 (by betaEtaReduce #[87]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq True False) (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True)))) % 4.51/4.72 Clause #89 (by clausification #[88]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True))) % 4.51/4.72 Clause #101 (by equality factoring #[89]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Ne True True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True))) % 4.51/4.72 Clause #102 (by clausification #[101]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Or (Eq True False) (Eq True False)))) % 4.51/4.72 Clause #104 (by clausification #[102]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Eq True False))) % 4.51/4.72 Clause #105 (by clausification #[104]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True)) % 4.51/4.72 Clause #106 (by superposition #[105, 29]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.72 Or (Eq (skS.0 0 (fun x => a_1 x) True) True) % 4.51/4.72 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 4 a_1 a_2 a_3 a_4)) True) % 4.51/4.72 (Or (Eq (skS.0 0 a_1 True) True) (Eq True False))) % 4.51/4.72 Clause #132 (by betaEtaReduce #[106]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Or (Eq (skS.0 0 a_1 True) True) (Eq True False))) % 4.51/4.72 Clause #133 (by clausification #[132]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.51/4.72 Or (Eq (skS.0 0 a_1 True) True) % 4.51/4.72 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 True) True)) % 4.59/4.74 Clause #134 (by eliminate duplicate literals #[133]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.59/4.74 Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 4.59/4.74 Clause #135 (by superposition #[134, 32]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 (fun x => a x) True) True) (Or (Eq (skS.0 0 a True) True) (Eq True False)) % 4.59/4.74 Clause #136 (by betaEtaReduce #[135]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Or (Eq (skS.0 0 a True) True) (Eq True False)) % 4.59/4.74 Clause #137 (by clausification #[136]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq (skS.0 0 a True) True) % 4.59/4.74 Clause #138 (by eliminate duplicate literals #[137]): ∀ (a : Prop → Prop), Eq (skS.0 0 a True) True % 4.59/4.74 Clause #139 (by backward demodulation #[138, 19]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.59/4.74 Or (Eq True False) (Or (Eq a_1 False) (Eq (skS.0 2 a_2 a_3 a_4 (skS.0 3 a_2 a_3 a_4 a_5)) False)) % 4.59/4.74 Clause #141 (by backward demodulation #[138, 30]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.59/4.74 Or (Eq True False) (Or (Eq a_1 False) (Eq (skS.0 1 a_2 a_3 (skS.0 3 a_2 a_3 a_4 a_5)) False)) % 4.59/4.74 Clause #152 (by clausification #[141]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.59/4.74 Or (Eq a_1 False) (Eq (skS.0 1 a_2 a_3 (skS.0 3 a_2 a_3 a_4 a_5)) False) % 4.59/4.74 Clause #155 (by falseElim #[152]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) False % 4.59/4.74 Clause #159 (by clausification #[139]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 a_4 : a → Prop) (a_5 : a), % 4.59/4.74 Or (Eq a_1 False) (Eq (skS.0 2 a_2 a_3 a_4 (skS.0 3 a_2 a_3 a_4 a_5)) False) % 4.59/4.74 Clause #162 (by falseElim #[159]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False % 4.59/4.74 Clause #163 (by superposition #[162, 75]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.59/4.74 Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq False True)) % 4.59/4.74 Clause #166 (by clausification #[163]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.59/4.74 Or (Eq (skS.0 0 a_1 False) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 4.59/4.74 Clause #167 (by superposition #[166, 155]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 (fun x => a x) False) True) (Eq True False) % 4.59/4.74 Clause #168 (by betaEtaReduce #[167]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a False) True) (Eq True False) % 4.59/4.74 Clause #169 (by clausification #[168]): ∀ (a : Prop → Prop), Eq (skS.0 0 a False) True % 4.59/4.74 Clause #170 (by backward demodulation #[169, 54]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.59/4.74 Or (Eq True False) (Or (Eq a_1 True) (Or (Eq (skS.0 1 a_2 a_3 a_4) True) (Eq (skS.0 2 a_2 a_3 a_5 a_4) True))) % 4.59/4.74 Clause #172 (by clausification #[170]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 4.59/4.74 Or (Eq a_1 True) (Or (Eq (skS.0 1 a_2 a_3 a_4) True) (Eq (skS.0 2 a_2 a_3 a_5 a_4) True)) % 4.59/4.74 Clause #173 (by superposition #[172, 155]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.59/4.74 Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Eq True False)) % 4.59/4.74 Clause #180 (by clausification #[173]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 4.59/4.74 Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) % 4.59/4.74 Clause #181 (by superposition #[180, 162]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.59/4.74 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq True False) % 4.59/4.74 Clause #184 (by betaEtaReduce #[181]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), % 4.59/4.74 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq True False) % 4.59/4.74 Clause #185 (by clausification #[184]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True % 4.59/4.74 Clause #186 (by superposition #[185, 155]): Eq True False % 4.59/4.74 Clause #187 (by clausification #[186]): False % 4.59/4.74 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------