%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU852^5 : TPTP v9.2.0. Released v4.0.0. % 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 08:02:33 PM UTC 2025 % Result : Theorem 10.20s 10.38s % Output : Proof 10.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SEU852^5 : TPTP v9.2.0. Released v4.0.0. % 0.14/0.14 % Command : duper %s % 0.15/0.36 % Computer : n012.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 06:34:08 EDT 2025 % 0.15/0.36 % CPUTime : % 10.20/10.38 SZS status Theorem for theBenchmark.p % 10.20/10.38 SZS output start Proof for theBenchmark.p % 10.20/10.38 Clause #0 (by assumption #[]): Eq % 10.20/10.38 (Not % 10.20/10.38 (∀ (S T U : a → Prop), % 10.20/10.38 And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) → % 10.20/10.38 Iff (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), And (And (S Xx) (U Xx)) (Not (T Xx)) → T Xx))) % 10.20/10.38 True % 10.20/10.38 Clause #1 (by clausification #[0]): Eq % 10.20/10.38 (∀ (S T U : a → Prop), % 10.20/10.38 And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) → % 10.20/10.38 Iff (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), And (And (S Xx) (U Xx)) (Not (T Xx)) → T Xx)) % 10.20/10.38 False % 10.20/10.38 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 10.20/10.38 Eq % 10.20/10.38 (Not % 10.20/10.38 (∀ (T U : a → Prop), % 10.20/10.38 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) → % 10.20/10.38 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (T Xx)) → T Xx))) % 10.20/10.38 True % 10.20/10.38 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 10.20/10.38 Eq % 10.20/10.38 (∀ (T U : a → Prop), % 10.20/10.38 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) → % 10.20/10.38 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (T Xx)) → T Xx)) % 10.20/10.38 False % 10.20/10.38 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 10.20/10.38 Eq % 10.20/10.38 (Not % 10.20/10.38 (∀ (U : a → Prop), % 10.20/10.38 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx) → % 10.20/10.38 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 10.20/10.38 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx))) % 10.20/10.38 True % 10.20/10.38 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 10.20/10.38 Eq % 10.20/10.38 (∀ (U : a → Prop), % 10.20/10.38 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx) → % 10.20/10.38 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 10.20/10.38 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx)) % 10.20/10.38 False % 10.20/10.38 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 10.20/10.38 Eq % 10.20/10.38 (Not % 10.20/10.38 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 10.20/10.38 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 10.20/10.38 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 10.20/10.38 (∀ (Xx : a), % 10.20/10.38 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx))) % 10.20/10.38 True % 10.20/10.38 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 10.20/10.38 Eq % 10.20/10.38 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 10.20/10.38 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 10.20/10.38 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 10.20/10.38 (∀ (Xx : a), % 10.20/10.38 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx)) % 10.20/10.38 False % 10.20/10.38 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 10.20/10.38 Eq % 10.20/10.38 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 10.20/10.38 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 10.20/10.38 True % 10.20/10.38 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 10.20/10.38 Eq % 10.20/10.38 (Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 10.20/10.38 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx)) % 10.20/10.38 False % 10.20/10.38 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) True % 10.20/10.38 Clause #14 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Eq (skS.0 0 a_1 a_2 → skS.0 2 a_1 a_3 a_4 a_2) True % 10.20/10.38 Clause #15 (by clausification #[14]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True) % 10.20/10.38 Clause #16 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop), % 10.20/10.38 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False) % 10.20/10.38 (Eq % 10.20/10.38 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx) % 10.20/10.38 False) % 10.20/10.40 Clause #17 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop), % 10.20/10.40 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True) % 10.20/10.40 (Eq % 10.20/10.40 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx) % 10.20/10.40 True) % 10.20/10.40 Clause #18 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 10.20/10.40 Or % 10.20/10.40 (Eq % 10.20/10.40 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx) % 10.20/10.40 False) % 10.20/10.40 (Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_4))) True) % 10.20/10.40 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.40 Or (Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3))) True) % 10.20/10.40 (Eq % 10.20/10.40 (Not % 10.20/10.40 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5))) % 10.20/10.40 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) → % 10.20/10.40 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) % 10.20/10.40 True) % 10.20/10.40 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 10.20/10.40 Or % 10.20/10.40 (Eq % 10.20/10.40 (Not % 10.20/10.40 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) % 10.20/10.40 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) → % 10.20/10.40 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) % 10.20/10.40 True) % 10.20/10.40 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_5) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_5)) False) % 10.20/10.40 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.40 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) % 10.20/10.40 (Eq % 10.20/10.40 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5))) % 10.20/10.40 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) → % 10.20/10.40 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)) % 10.20/10.40 False) % 10.20/10.40 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 10.20/10.40 Or % 10.20/10.40 (Eq % 10.20/10.41 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) % 10.20/10.41 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) → % 10.20/10.41 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) % 10.20/10.41 False) % 10.20/10.41 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_5)) True) % 10.20/10.41 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 10.20/10.41 Or % 10.20/10.41 (Eq % 10.20/10.41 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) % 10.20/10.41 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) → % 10.20/10.41 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) % 10.20/10.41 False) % 10.20/10.41 (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_5)) False) % 10.20/10.41 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.41 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) % 10.20/10.41 (Eq % 10.20/10.41 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5))) % 10.20/10.41 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)))) % 10.20/10.41 True) % 10.20/10.41 Clause #25 (by clausification #[22]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.41 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)) False) % 10.20/10.41 Clause #27 (by clausification #[24]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.41 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) % 10.20/10.41 (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5))) True) % 10.20/10.41 Clause #28 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 10.20/10.41 Or % 10.20/10.41 (Eq % 10.20/10.41 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx) % 10.20/10.41 True) % 10.20/10.41 (Eq (skS.0 0 a_1 a_4 → skS.0 1 a_1 a_2 a_4) True) % 10.20/10.41 Clause #29 (by clausification #[28]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 10.20/10.41 Or (Eq (skS.0 0 a_1 a_2 → skS.0 1 a_1 a_3 a_2) True) % 10.20/10.41 (Eq (And (And (skS.0 0 a_1 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) (Not (skS.0 1 a_1 a_3 a_4)) → skS.0 1 a_1 a_3 a_4) True) % 10.20/10.43 Clause #30 (by clausification #[29]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop) (a_5 : a), % 10.20/10.43 Or (Eq (And (And (skS.0 0 a_1 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) (Not (skS.0 1 a_1 a_3 a_2)) → skS.0 1 a_1 a_3 a_2) True) % 10.20/10.43 (Or (Eq (skS.0 0 a_1 a_5) False) (Eq (skS.0 1 a_1 a_3 a_5) True)) % 10.20/10.43 Clause #31 (by clausification #[30]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 10.20/10.43 Or (Eq (skS.0 0 a_1 a_2) False) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 10.20/10.43 (Or (Eq (And (And (skS.0 0 a_1 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) (Not (skS.0 1 a_1 a_3 a_4))) False) % 10.20/10.43 (Eq (skS.0 1 a_1 a_3 a_4) True))) % 10.20/10.43 Clause #32 (by clausification #[31]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 10.20/10.43 Or (Eq (skS.0 0 a_1 a_2) False) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_4) True) % 10.20/10.43 (Or (Eq (And (skS.0 0 a_1 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) False) (Eq (Not (skS.0 1 a_1 a_3 a_4)) False)))) % 10.20/10.43 Clause #33 (by clausification #[32]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 10.20/10.43 Or (Eq (skS.0 0 a_1 a_2) False) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_4) True) % 10.20/10.43 (Or (Eq (Not (skS.0 1 a_1 a_3 a_4)) False) % 10.20/10.43 (Or (Eq (skS.0 0 a_1 a_4) False) (Eq (skS.0 2 a_1 a_3 a_5 a_4) False))))) % 10.20/10.43 Clause #34 (by clausification #[33]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 10.20/10.43 Or (Eq (skS.0 0 a_1 a_2) False) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_4) True) % 10.20/10.43 (Or (Eq (skS.0 0 a_1 a_4) False) (Or (Eq (skS.0 2 a_1 a_3 a_5 a_4) False) (Eq (skS.0 1 a_1 a_3 a_4) True))))) % 10.20/10.43 Clause #35 (by eliminate duplicate literals #[34]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 10.20/10.43 Or (Eq (skS.0 0 a_1 a_2) False) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Or (Eq (skS.0 0 a_1 a_4) False) (Eq (skS.0 2 a_1 a_3 a_5 a_4) False)))) % 10.20/10.43 Clause #36 (by clausification #[23]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.43 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) % 10.20/10.43 (Eq % 10.20/10.43 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5))) % 10.20/10.43 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)))) % 10.20/10.43 True) % 10.20/10.43 Clause #37 (by clausification #[23]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.43 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)) False) % 10.20/10.43 Clause #39 (by clausification #[36]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.43 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) % 10.20/10.43 (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5))) True) % 10.20/10.43 Clause #41 (by clausification #[27]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.20/10.43 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) True) % 10.20/10.43 Clause #44 (by superposition #[41, 15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 10.20/10.43 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3 a_4)) True) % 10.20/10.43 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True)) % 10.20/10.43 Clause #45 (by superposition #[41, 35]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop), % 10.20/10.43 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3 a_4)) True) % 10.20/10.43 (Or (Eq True False) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.20/10.43 (Or (Eq (skS.0 1 a_1 a_5 a_7) True) (Or (Eq (skS.0 0 a_1 a_7) False) (Eq (skS.0 2 a_1 a_5 a_8 a_7) False))))) % 10.20/10.43 Clause #52 (by betaEtaReduce #[44]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 10.20/10.43 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.20/10.43 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True)) % 10.20/10.43 Clause #53 (by clausification #[52]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 10.28/10.46 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True) % 10.28/10.46 Clause #57 (by clausification #[39]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 10.28/10.46 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) True) % 10.28/10.46 Clause #64 (by betaEtaReduce #[45]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop), % 10.28/10.46 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.28/10.46 (Or (Eq True False) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 a_7) True) (Or (Eq (skS.0 0 a_1 a_7) False) (Eq (skS.0 2 a_1 a_5 a_8 a_7) False))))) % 10.28/10.46 Clause #65 (by clausification #[64]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop), % 10.28/10.46 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 a_7) True) (Or (Eq (skS.0 0 a_1 a_7) False) (Eq (skS.0 2 a_1 a_5 a_8 a_7) False)))) % 10.28/10.46 Clause #66 (by superposition #[65, 41]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 a_10 : a → Prop) % 10.28/10.46 (a_11 : a), % 10.28/10.46 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3 a_4)) True) % 10.28/10.46 (Or (Eq (skS.0 1 (fun x => a_1 x) a_5 (skS.0 3 (fun x => a_1 x) a_2 a_6)) True) % 10.28/10.46 (Or (Eq (skS.0 1 (fun x => a_1 x) a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.28/10.46 (Or (Eq (skS.0 2 (fun x => a_1 x) a_5 a_9 (skS.0 3 a_1 a_7 a_8)) False) % 10.28/10.46 (Or (Eq False True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_10 a_11)) True))))) % 10.28/10.46 Clause #98 (by betaEtaReduce #[66]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 a_10 : a → Prop) % 10.28/10.46 (a_11 : a), % 10.28/10.46 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.28/10.46 (Or (Eq (skS.0 2 a_1 a_5 a_9 (skS.0 3 a_1 a_7 a_8)) False) % 10.28/10.46 (Or (Eq False True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_10 a_11)) True))))) % 10.28/10.46 Clause #99 (by clausification #[98]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 a_10 : a → Prop) % 10.28/10.46 (a_11 : a), % 10.28/10.46 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.28/10.46 (Or (Eq (skS.0 2 a_1 a_5 a_9 (skS.0 3 a_1 a_7 a_8)) False) % 10.28/10.46 (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_10 a_11)) True)))) % 10.28/10.46 Clause #100 (by superposition #[99, 53]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a) % 10.28/10.46 (a_11 : a → Prop) (a_12 : a), % 10.28/10.46 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3 a_4)) True) % 10.28/10.46 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_5 x) (skS.0 3 (fun x => a_1 x) a_2 a_6)) True) % 10.28/10.46 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_5 x) (skS.0 3 (fun x => a_1 x) (fun x => a_7 x) a_8)) True) % 10.28/10.46 (Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_7 x) a_9 a_10)) True) % 10.28/10.46 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True) (Eq False True))))) % 10.28/10.46 Clause #342 (by betaEtaReduce #[100]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a) % 10.28/10.46 (a_11 : a → Prop) (a_12 : a), % 10.28/10.46 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.28/10.46 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.28/10.46 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) % 10.28/10.46 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True) (Eq False True))))) % 10.28/10.46 Clause #343 (by clausification #[342]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a) % 10.28/10.46 (a_11 : a → Prop) (a_12 : a), % 10.28/10.46 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.32/10.48 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True)))) % 10.32/10.48 Clause #368 (by equality factoring #[343]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.32/10.48 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 (fun x => a_9 x) a_10)) True)))) % 10.32/10.48 Clause #377 (by betaEtaReduce #[368]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.32/10.48 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True)))) % 10.32/10.48 Clause #378 (by clausification #[377]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.32/10.48 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) (Or (Eq True False) (Eq True False))))) % 10.32/10.48 Clause #380 (by clausification #[378]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 10.32/10.48 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) (Eq True False)))) % 10.32/10.48 Clause #381 (by clausification #[380]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True))) % 10.32/10.48 Clause #405 (by equality factoring #[381]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 (fun x => a_2 x) a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 10.32/10.48 (Or (Ne True True) (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 (fun x => a_2 x) a_8)) True))) % 10.32/10.48 Clause #408 (by betaEtaReduce #[405]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 10.32/10.48 (Or (Ne True True) (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True))) % 10.32/10.48 Clause #409 (by clausification #[408]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True) (Or (Eq True False) (Eq True False)))) % 10.32/10.48 Clause #411 (by clausification #[409]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 10.32/10.48 (Or (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True) (Eq True False))) % 10.32/10.48 Clause #412 (by clausification #[411]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a), % 10.32/10.48 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.48 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True)) % 10.32/10.51 Clause #423 (by equality factoring #[412]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.51 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 (fun x => a_5 x) a_6)) True)) % 10.32/10.51 Clause #424 (by betaEtaReduce #[423]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.51 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True)) % 10.32/10.51 Clause #425 (by clausification #[424]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.51 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True) (Or (Eq True False) (Eq True False))) % 10.32/10.51 Clause #427 (by clausification #[425]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.51 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True) (Eq True False)) % 10.32/10.51 Clause #428 (by clausification #[427]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True) % 10.32/10.51 Clause #431 (by superposition #[428, 57]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) a_3 a_4)) True) % 10.32/10.51 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)) % 10.32/10.51 Clause #437 (by betaEtaReduce #[431]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.51 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)) % 10.32/10.51 Clause #438 (by clausification #[437]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 10.32/10.51 Clause #444 (by equality factoring #[438]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 (fun x => a_3 x) a_4)) True) % 10.32/10.51 Clause #445 (by betaEtaReduce #[444]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 10.32/10.51 Clause #446 (by clausification #[445]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 10.32/10.51 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Or (Eq True False) (Eq True False)) % 10.32/10.51 Clause #448 (by clausification #[446]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq True False) % 10.32/10.51 Clause #449 (by clausification #[448]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True % 10.32/10.51 Clause #450 (by superposition #[449, 15]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 10.32/10.51 Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_4 a_5 a_6)) True) % 10.32/10.51 Clause #451 (by superposition #[449, 35]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 a_6 : a) (a_7 : a → Prop), % 10.32/10.51 Or (Eq True False) % 10.32/10.51 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 10.32/10.51 (Or (Eq (skS.0 1 a_1 a_2 a_6) True) (Or (Eq (skS.0 0 a_1 a_6) False) (Eq (skS.0 2 a_1 a_2 a_7 a_6) False)))) % 10.32/10.51 Clause #457 (by clausification #[450]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_4 a_5 a_6)) True % 10.32/10.51 Clause #489 (by clausification #[451]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 a_6 : a) (a_7 : a → Prop), % 10.32/10.51 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 10.32/10.51 (Or (Eq (skS.0 1 a_1 a_2 a_6) True) (Or (Eq (skS.0 0 a_1 a_6) False) (Eq (skS.0 2 a_1 a_2 a_7 a_6) False))) % 10.32/10.51 Clause #490 (by superposition #[489, 449]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop), % 10.32/10.51 Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 4 (fun x => a_1 x) a_3 a_4 a_5)) True) % 10.32/10.51 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True) % 10.32/10.51 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_9 (skS.0 4 a_1 a_6 a_7 a_8)) False) (Eq False True))) % 10.32/10.51 Clause #527 (by betaEtaReduce #[490]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop), % 10.32/10.53 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 10.32/10.53 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True) % 10.32/10.53 (Or (Eq (skS.0 2 a_1 a_2 a_9 (skS.0 4 a_1 a_6 a_7 a_8)) False) (Eq False True))) % 10.32/10.53 Clause #528 (by clausification #[527]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop), % 10.32/10.53 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 10.32/10.53 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True) % 10.32/10.53 (Eq (skS.0 2 a_1 a_2 a_9 (skS.0 4 a_1 a_6 a_7 a_8)) False)) % 10.32/10.53 Clause #529 (by superposition #[528, 457]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a), % 10.32/10.53 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 4 (fun x => a_1 x) a_3 a_4 a_5)) True) % 10.32/10.53 (Or % 10.32/10.53 (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 4 (fun x => a_1 x) (fun x => a_6 x) (fun x => a_7 x) a_8)) % 10.32/10.53 True) % 10.32/10.53 (Eq False True)) % 10.32/10.53 Clause #530 (by betaEtaReduce #[529]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a), % 10.32/10.53 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 10.32/10.53 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True) (Eq False True)) % 10.32/10.53 Clause #531 (by clausification #[530]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a), % 10.32/10.53 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True) % 10.32/10.53 Clause #534 (by equality factoring #[531]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 10.32/10.53 Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 (fun x => a_3 x) (fun x => a_4 x) a_5)) True) % 10.32/10.53 Clause #535 (by betaEtaReduce #[534]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 10.32/10.53 Clause #536 (by clausification #[535]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 10.32/10.53 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Or (Eq True False) (Eq True False)) % 10.32/10.53 Clause #538 (by clausification #[536]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Eq True False) % 10.32/10.53 Clause #539 (by clausification #[538]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True % 10.32/10.53 Clause #540 (by superposition #[539, 25]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) (Eq True False) % 10.32/10.53 Clause #543 (by clausification #[540]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True % 10.32/10.53 Clause #544 (by superposition #[543, 15]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5)) True) % 10.32/10.53 Clause #545 (by superposition #[543, 35]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a) (a_6 : a → Prop), % 10.32/10.53 Or (Eq True False) % 10.32/10.53 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.53 (Or (Eq (skS.0 1 a_1 a_2 a_5) True) (Or (Eq (skS.0 0 a_1 a_5) False) (Eq (skS.0 2 a_1 a_2 a_6 a_5) False)))) % 10.32/10.53 Clause #546 (by clausification #[544]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5)) True % 10.32/10.53 Clause #553 (by clausification #[545]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a) (a_6 : a → Prop), % 10.32/10.53 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.53 (Or (Eq (skS.0 1 a_1 a_2 a_5) True) (Or (Eq (skS.0 0 a_1 a_5) False) (Eq (skS.0 2 a_1 a_2 a_6 a_5) False))) % 10.32/10.53 Clause #555 (by superposition #[553, 543]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop), % 10.32/10.53 Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 (fun x => a_1 x) a_3 a_4)) True) % 10.32/10.53 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_5 a_6)) True) % 10.32/10.53 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_7 (skS.0 3 a_1 a_5 a_6)) False) (Eq False True))) % 10.32/10.53 Clause #556 (by betaEtaReduce #[555]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop), % 10.32/10.53 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.53 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True) % 10.32/10.53 (Or (Eq (skS.0 2 a_1 a_2 a_7 (skS.0 3 a_1 a_5 a_6)) False) (Eq False True))) % 10.32/10.55 Clause #557 (by clausification #[556]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop), % 10.32/10.55 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.55 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True) (Eq (skS.0 2 a_1 a_2 a_7 (skS.0 3 a_1 a_5 a_6)) False)) % 10.32/10.55 Clause #558 (by superposition #[557, 546]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.55 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) a_3 a_4)) True) % 10.32/10.55 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) (fun x => a_5 x) a_6)) True) % 10.32/10.55 (Eq False True)) % 10.32/10.55 Clause #559 (by betaEtaReduce #[558]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.55 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.55 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True) (Eq False True)) % 10.32/10.55 Clause #560 (by clausification #[559]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 10.32/10.55 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True) % 10.32/10.55 Clause #563 (by equality factoring #[560]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 (fun x => a_3 x) a_4)) True) % 10.32/10.55 Clause #564 (by betaEtaReduce #[563]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 10.32/10.55 Clause #565 (by clausification #[564]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 10.32/10.55 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Or (Eq True False) (Eq True False)) % 10.32/10.55 Clause #567 (by clausification #[565]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq True False) % 10.32/10.55 Clause #568 (by clausification #[567]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True % 10.32/10.55 Clause #569 (by superposition #[568, 37]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False) % 10.32/10.55 Clause #570 (by clausification #[569]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False % 10.32/10.55 Clause #571 (by superposition #[570, 539]): Eq False True % 10.32/10.55 Clause #574 (by clausification #[571]): False % 10.32/10.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------