%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU853^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 14.57s 14.76s % Output : Proof 14.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU853^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n018.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 04:54:38 EDT 2025 % 0.14/0.36 % CPUTime : % 14.57/14.76 SZS status Theorem for theBenchmark.p % 14.57/14.76 SZS output start Proof for theBenchmark.p % 14.57/14.76 Clause #0 (by assumption #[]): Eq % 14.57/14.76 (Not % 14.57/14.76 (∀ (S T U : a → Prop), % 14.57/14.76 And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) → % 14.57/14.76 Iff (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), And (And (S Xx) (U Xx)) (Not (T Xx)) → And (U Xx) (Not (S Xx))))) % 14.57/14.76 True % 14.57/14.76 Clause #1 (by clausification #[0]): Eq % 14.57/14.76 (∀ (S T U : a → Prop), % 14.57/14.76 And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) → % 14.57/14.76 Iff (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), And (And (S Xx) (U Xx)) (Not (T Xx)) → And (U Xx) (Not (S Xx)))) % 14.57/14.76 False % 14.57/14.76 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 14.57/14.76 Eq % 14.57/14.76 (Not % 14.57/14.76 (∀ (T U : a → Prop), % 14.57/14.76 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) → % 14.57/14.76 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) % 14.57/14.76 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (T Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx))))) % 14.57/14.76 True % 14.57/14.76 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 14.57/14.76 Eq % 14.57/14.76 (∀ (T U : a → Prop), % 14.57/14.76 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) → % 14.57/14.76 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) % 14.57/14.76 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (T Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx)))) % 14.57/14.76 False % 14.57/14.76 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 14.57/14.76 Eq % 14.57/14.76 (Not % 14.57/14.76 (∀ (U : a → Prop), % 14.57/14.76 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx) → % 14.57/14.76 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 14.57/14.76 (∀ (Xx : a), % 14.57/14.76 And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx))))) % 14.57/14.76 True % 14.57/14.76 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 14.57/14.76 Eq % 14.57/14.76 (∀ (U : a → Prop), % 14.57/14.76 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx) → % 14.57/14.76 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 14.57/14.76 (∀ (Xx : a), % 14.57/14.76 And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx)))) % 14.57/14.76 False % 14.57/14.76 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 14.57/14.76 Eq % 14.57/14.76 (Not % 14.57/14.76 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 14.57/14.76 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 14.57/14.76 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 14.57/14.76 (∀ (Xx : a), % 14.57/14.76 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)) → % 14.57/14.76 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))))) % 14.57/14.76 True % 14.57/14.76 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 14.57/14.76 Eq % 14.57/14.76 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 14.57/14.76 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) → % 14.57/14.76 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 14.57/14.76 (∀ (Xx : a), % 14.57/14.76 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)) → % 14.57/14.76 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))) % 14.57/14.76 False % 14.57/14.76 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 14.57/14.76 Eq % 14.57/14.76 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 14.57/14.76 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 14.57/14.76 True % 14.57/14.76 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 14.57/14.76 Eq % 14.57/14.76 (Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 14.57/14.76 (∀ (Xx : a), % 14.57/14.76 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)) → % 14.57/14.76 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))) % 14.57/14.76 False % 14.57/14.76 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 % 14.57/14.76 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 % 14.57/14.76 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) % 14.57/14.79 Clause #16 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop), % 14.57/14.79 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False) % 14.57/14.79 (Eq % 14.57/14.79 (∀ (Xx : a), % 14.57/14.79 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)) → % 14.57/14.79 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))) % 14.57/14.79 False) % 14.57/14.79 Clause #17 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop), % 14.57/14.79 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True) % 14.57/14.79 (Eq % 14.57/14.79 (∀ (Xx : a), % 14.57/14.79 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)) → % 14.57/14.79 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))) % 14.57/14.79 True) % 14.57/14.79 Clause #18 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 14.57/14.79 Or % 14.57/14.79 (Eq % 14.57/14.79 (∀ (Xx : a), % 14.57/14.79 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)) → % 14.57/14.79 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))) % 14.57/14.79 False) % 14.57/14.79 (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) % 14.57/14.79 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.57/14.79 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) % 14.57/14.79 (Eq % 14.57/14.79 (Not % 14.57/14.79 (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))) % 14.57/14.79 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) → % 14.57/14.79 And (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5))))) % 14.57/14.79 True) % 14.57/14.79 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 14.57/14.79 Or % 14.57/14.79 (Eq % 14.57/14.79 (Not % 14.57/14.79 (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))) % 14.57/14.79 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) → % 14.57/14.79 And (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4))))) % 14.57/14.79 True) % 14.57/14.79 (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) % 14.57/14.79 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.57/14.79 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) % 14.57/14.79 (Eq % 14.57/14.79 (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))) % 14.57/14.79 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) → % 14.57/14.79 And (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)))) % 14.57/14.79 False) % 14.57/14.79 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 14.57/14.79 Or % 14.57/14.79 (Eq % 14.57/14.79 (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))) % 14.57/14.79 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) → % 14.57/14.79 And (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)))) % 14.57/14.79 False) % 14.57/14.79 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_5)) True) % 14.57/14.79 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 14.57/14.79 Or % 14.57/14.79 (Eq % 14.57/14.79 (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))) % 14.57/14.79 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) → % 14.57/14.79 And (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)))) % 14.57/14.79 False) % 14.57/14.79 (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_5)) False) % 14.57/14.79 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.57/14.79 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) % 14.57/14.79 (Eq % 14.57/14.79 (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))) % 14.57/14.79 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)))) % 14.57/14.79 True) % 14.57/14.79 Clause #26 (by clausification #[24]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.57/14.79 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) (Eq (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) True) % 14.57/14.79 Clause #27 (by clausification #[24]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.57/14.82 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) % 14.57/14.82 (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) % 14.57/14.82 Clause #28 (by clausification #[26]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.57/14.82 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) % 14.57/14.82 Clause #29 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 14.57/14.82 Or % 14.57/14.82 (Eq % 14.57/14.82 (∀ (Xx : a), % 14.57/14.82 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)) → % 14.57/14.82 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))) % 14.57/14.82 True) % 14.57/14.82 (Eq (skS.0 0 a_1 a_4 → skS.0 1 a_1 a_2 a_4) True) % 14.57/14.82 Clause #30 (by clausification #[29]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 14.57/14.82 Or (Eq (skS.0 0 a_1 a_2 → skS.0 1 a_1 a_3 a_2) True) % 14.57/14.82 (Eq % 14.57/14.82 (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)) → % 14.57/14.82 And (skS.0 2 a_1 a_3 a_5 a_4) (Not (skS.0 0 a_1 a_4))) % 14.57/14.82 True) % 14.57/14.82 Clause #31 (by clausification #[30]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop) (a_5 : a), % 14.57/14.82 Or % 14.57/14.82 (Eq % 14.57/14.82 (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)) → % 14.57/14.82 And (skS.0 2 a_1 a_3 a_4 a_2) (Not (skS.0 0 a_1 a_2))) % 14.57/14.82 True) % 14.57/14.82 (Or (Eq (skS.0 0 a_1 a_5) False) (Eq (skS.0 1 a_1 a_3 a_5) True)) % 14.57/14.82 Clause #32 (by clausification #[31]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 14.57/14.82 Or (Eq (skS.0 0 a_1 a_2) False) % 14.57/14.82 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 14.57/14.82 (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) % 14.57/14.82 (Eq (And (skS.0 2 a_1 a_3 a_5 a_4) (Not (skS.0 0 a_1 a_4))) True))) % 14.57/14.82 Clause #33 (by clausification #[32]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop) (a_5 : a), % 14.57/14.82 Or (Eq (skS.0 0 a_1 a_2) False) % 14.57/14.82 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 14.57/14.82 (Or (Eq (And (skS.0 2 a_1 a_3 a_4 a_5) (Not (skS.0 0 a_1 a_5))) True) % 14.57/14.82 (Or (Eq (And (skS.0 0 a_1 a_5) (skS.0 2 a_1 a_3 a_4 a_5)) False) (Eq (Not (skS.0 1 a_1 a_3 a_5)) False)))) % 14.57/14.82 Clause #34 (by clausification #[33]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 14.57/14.82 Or (Eq (skS.0 0 a_1 a_2) False) % 14.57/14.82 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 14.57/14.82 (Or (Eq (And (skS.0 0 a_1 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) False) % 14.57/14.82 (Or (Eq (Not (skS.0 1 a_1 a_3 a_4)) False) (Eq (Not (skS.0 0 a_1 a_4)) True)))) % 14.57/14.82 Clause #36 (by clausification #[34]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 14.57/14.82 Or (Eq (skS.0 0 a_1 a_2) False) % 14.57/14.82 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 14.57/14.82 (Or (Eq (Not (skS.0 1 a_1 a_3 a_4)) False) % 14.57/14.82 (Or (Eq (Not (skS.0 0 a_1 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))))) % 14.57/14.82 Clause #37 (by clausification #[36]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 14.57/14.82 Or (Eq (skS.0 0 a_1 a_2) False) % 14.57/14.82 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 14.57/14.82 (Or (Eq (Not (skS.0 0 a_1 a_4)) True) % 14.57/14.82 (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))))) % 14.57/14.82 Clause #38 (by clausification #[37]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 14.57/14.82 Or (Eq (skS.0 0 a_1 a_2) False) % 14.57/14.82 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 14.57/14.82 (Or (Eq (skS.0 0 a_1 a_4) False) % 14.57/14.82 (Or (Eq (skS.0 2 a_1 a_3 a_5 a_4) False) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 0 a_1 a_4) False))))) % 14.57/14.82 Clause #39 (by eliminate duplicate literals #[38]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 14.57/14.82 Or (Eq (skS.0 0 a_1 a_2) False) % 14.57/14.82 (Or (Eq (skS.0 1 a_1 a_3 a_2) True) % 14.57/14.82 (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)))) % 14.57/14.82 Clause #41 (by clausification #[27]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.57/14.82 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) % 14.67/14.86 Clause #44 (by clausification #[23]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.67/14.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) % 14.67/14.86 (Eq % 14.67/14.86 (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))) % 14.67/14.86 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)))) % 14.67/14.86 True) % 14.67/14.86 Clause #46 (by clausification #[44]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.67/14.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) (Eq (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) True) % 14.67/14.86 Clause #47 (by clausification #[44]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.67/14.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) % 14.67/14.86 (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) % 14.67/14.86 Clause #48 (by clausification #[46]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.67/14.86 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) % 14.67/14.86 Clause #49 (by superposition #[41, 15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 14.67/14.86 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) % 14.67/14.86 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True)) % 14.67/14.86 Clause #50 (by superposition #[41, 39]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop), % 14.67/14.86 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) % 14.67/14.86 (Or (Eq True False) % 14.67/14.86 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.86 (Or (Eq (skS.0 0 a_1 a_7) False) (Or (Eq (skS.0 2 a_1 a_5 a_8 a_7) False) (Eq (skS.0 1 a_1 a_5 a_7) True))))) % 14.67/14.86 Clause #57 (by betaEtaReduce #[49]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 14.67/14.86 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.86 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True)) % 14.67/14.86 Clause #58 (by clausification #[57]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 14.67/14.86 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) % 14.67/14.86 Clause #70 (by clausification #[47]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a), % 14.67/14.86 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) % 14.67/14.86 Clause #87 (by betaEtaReduce #[50]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop), % 14.67/14.86 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.86 (Or (Eq True False) % 14.67/14.86 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.86 (Or (Eq (skS.0 0 a_1 a_7) False) (Or (Eq (skS.0 2 a_1 a_5 a_8 a_7) False) (Eq (skS.0 1 a_1 a_5 a_7) True))))) % 14.67/14.86 Clause #88 (by clausification #[87]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop), % 14.67/14.86 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.86 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.86 (Or (Eq (skS.0 0 a_1 a_7) False) (Or (Eq (skS.0 2 a_1 a_5 a_8 a_7) False) (Eq (skS.0 1 a_1 a_5 a_7) True)))) % 14.67/14.86 Clause #89 (by superposition #[88, 41]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 a_8 : a → Prop) (a_9 : a) (a_10 : a → Prop) % 14.67/14.86 (a_11 : a), % 14.67/14.86 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) % 14.67/14.86 (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) % 14.67/14.86 (Or (Eq (skS.0 2 (fun x => a_1 x) a_5 a_7 (skS.0 3 a_1 a_8 a_9)) False) % 14.67/14.86 (Or (Eq (skS.0 1 (fun x => a_1 x) a_5 (skS.0 3 a_1 a_8 a_9)) True) % 14.67/14.86 (Or (Eq False True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_8 a_10 a_11)) True))))) % 14.67/14.86 Clause #105 (by betaEtaReduce #[89]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 a_8 : a → Prop) (a_9 : a) (a_10 : a → Prop) % 14.67/14.86 (a_11 : a), % 14.67/14.86 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.86 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.86 (Or (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 3 a_1 a_8 a_9)) False) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_8 a_9)) True) % 14.67/14.89 (Or (Eq False True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_8 a_10 a_11)) True))))) % 14.67/14.89 Clause #106 (by clausification #[105]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 a_8 : a → Prop) (a_9 : a) (a_10 : a → Prop) % 14.67/14.89 (a_11 : a), % 14.67/14.89 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.89 (Or (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 3 a_1 a_8 a_9)) False) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_8 a_9)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_8 a_10 a_11)) True)))) % 14.67/14.89 Clause #107 (by superposition #[106, 58]): ∀ (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) % 14.67/14.89 (a_11 : a → Prop) (a_12 : a), % 14.67/14.89 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) % 14.67/14.89 (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) % 14.67/14.89 (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) % 14.67/14.89 (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) % 14.67/14.89 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True) (Eq False True))))) % 14.67/14.89 Clause #267 (by betaEtaReduce #[107]): ∀ (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) % 14.67/14.89 (a_11 : a → Prop) (a_12 : a), % 14.67/14.89 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 14.67/14.89 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) % 14.67/14.89 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True) (Eq False True))))) % 14.67/14.89 Clause #268 (by clausification #[267]): ∀ (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) % 14.67/14.89 (a_11 : a → Prop) (a_12 : a), % 14.67/14.89 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 14.67/14.89 (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)))) % 14.67/14.89 Clause #293 (by equality factoring #[268]): ∀ (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), % 14.67/14.89 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 14.67/14.89 (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)))) % 14.67/14.89 Clause #481 (by betaEtaReduce #[293]): ∀ (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), % 14.67/14.89 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 14.67/14.89 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True)))) % 14.67/14.89 Clause #482 (by clausification #[481]): ∀ (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), % 14.67/14.89 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 14.67/14.89 (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))))) % 14.67/14.89 Clause #484 (by clausification #[482]): ∀ (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), % 14.67/14.89 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.67/14.89 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) % 14.67/14.89 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) (Eq True False)))) % 14.73/14.92 Clause #485 (by clausification #[484]): ∀ (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), % 14.73/14.92 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.73/14.92 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True) % 14.73/14.92 (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))) % 14.73/14.92 Clause #509 (by equality factoring #[485]): ∀ (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), % 14.73/14.92 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 (fun x => a_2 x) a_3 a_4)) True) % 14.73/14.92 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 14.73/14.92 (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))) % 14.73/14.92 Clause #510 (by betaEtaReduce #[509]): ∀ (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), % 14.73/14.92 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.73/14.92 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 14.73/14.92 (Or (Ne True True) (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True))) % 14.73/14.92 Clause #511 (by clausification #[510]): ∀ (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), % 14.73/14.92 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.73/14.92 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 14.73/14.92 (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)))) % 14.73/14.92 Clause #513 (by clausification #[511]): ∀ (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), % 14.73/14.92 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.73/14.92 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) % 14.73/14.92 (Or (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True) (Eq True False))) % 14.73/14.92 Clause #514 (by clausification #[513]): ∀ (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), % 14.73/14.92 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.73/14.92 (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)) % 14.73/14.92 Clause #525 (by equality factoring #[514]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.73/14.92 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.73/14.92 (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)) % 14.73/14.92 Clause #526 (by betaEtaReduce #[525]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.73/14.92 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.73/14.92 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True)) % 14.73/14.92 Clause #527 (by clausification #[526]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.73/14.92 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.73/14.92 (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))) % 14.73/14.92 Clause #529 (by clausification #[527]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.73/14.92 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.73/14.92 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True) (Eq True False)) % 14.73/14.92 Clause #530 (by clausification #[529]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.73/14.92 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) % 14.73/14.92 Clause #533 (by superposition #[530, 70]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.73/14.92 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) % 14.73/14.92 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)) % 14.73/14.92 Clause #541 (by betaEtaReduce #[533]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.73/14.92 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 14.73/14.92 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)) % 14.73/14.92 Clause #542 (by clausification #[541]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.73/14.92 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) % 14.73/14.92 Clause #548 (by equality factoring #[542]): ∀ (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) % 14.73/14.95 Clause #549 (by betaEtaReduce #[548]): ∀ (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) % 14.73/14.95 Clause #550 (by clausification #[549]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 14.73/14.95 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)) % 14.73/14.95 Clause #552 (by clausification #[550]): ∀ (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) % 14.73/14.95 Clause #553 (by clausification #[552]): ∀ (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 % 14.73/14.95 Clause #554 (by superposition #[553, 15]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 14.73/14.95 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) % 14.73/14.95 Clause #555 (by superposition #[553, 39]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 a_6 : a) (a_7 : a → Prop), % 14.73/14.95 Or (Eq True False) % 14.73/14.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 14.73/14.95 (Or (Eq (skS.0 0 a_1 a_6) False) (Or (Eq (skS.0 2 a_1 a_2 a_7 a_6) False) (Eq (skS.0 1 a_1 a_2 a_6) True)))) % 14.73/14.95 Clause #559 (by clausification #[554]): ∀ (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 % 14.73/14.95 Clause #574 (by clausification #[555]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 a_6 : a) (a_7 : a → Prop), % 14.73/14.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 14.73/14.95 (Or (Eq (skS.0 0 a_1 a_6) False) (Or (Eq (skS.0 2 a_1 a_2 a_7 a_6) False) (Eq (skS.0 1 a_1 a_2 a_6) True))) % 14.73/14.95 Clause #575 (by superposition #[574, 553]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 a_8 : a → Prop) (a_9 : a), % 14.73/14.95 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) % 14.73/14.95 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_6 (skS.0 4 a_1 a_7 a_8 a_9)) False) % 14.73/14.95 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 4 a_1 a_7 a_8 a_9)) True) (Eq False True))) % 14.73/14.95 Clause #624 (by betaEtaReduce #[575]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 a_8 : a → Prop) (a_9 : a), % 14.73/14.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 14.73/14.95 (Or (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 4 a_1 a_7 a_8 a_9)) False) % 14.73/14.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_7 a_8 a_9)) True) (Eq False True))) % 14.73/14.95 Clause #625 (by clausification #[624]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 a_8 : a → Prop) (a_9 : a), % 14.73/14.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 14.73/14.95 (Or (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 4 a_1 a_7 a_8 a_9)) False) % 14.73/14.95 (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_7 a_8 a_9)) True)) % 14.73/14.95 Clause #626 (by superposition #[625, 559]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a), % 14.73/14.95 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) % 14.73/14.95 (Or % 14.73/14.95 (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)) % 14.73/14.95 True) % 14.73/14.95 (Eq False True)) % 14.73/14.95 Clause #629 (by betaEtaReduce #[626]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a), % 14.73/14.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 14.73/14.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True) (Eq False True)) % 14.73/14.95 Clause #630 (by clausification #[629]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a), % 14.73/14.95 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) % 14.73/14.95 Clause #633 (by equality factoring #[630]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 14.73/14.95 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) % 14.73/14.95 Clause #634 (by betaEtaReduce #[633]): ∀ (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) % 14.73/14.95 Clause #635 (by clausification #[634]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), % 14.73/14.95 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)) % 14.73/14.95 Clause #637 (by clausification #[635]): ∀ (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) % 14.80/14.98 Clause #638 (by clausification #[637]): ∀ (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 % 14.80/14.98 Clause #639 (by superposition #[638, 28]): ∀ (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) % 14.80/14.98 Clause #640 (by clausification #[639]): ∀ (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 % 14.80/14.98 Clause #641 (by superposition #[640, 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) % 14.80/14.98 Clause #642 (by superposition #[640, 39]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a) (a_6 : a → Prop), % 14.80/14.98 Or (Eq True False) % 14.80/14.98 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.80/14.98 (Or (Eq (skS.0 0 a_1 a_5) False) (Or (Eq (skS.0 2 a_1 a_2 a_6 a_5) False) (Eq (skS.0 1 a_1 a_2 a_5) True)))) % 14.80/14.98 Clause #643 (by clausification #[641]): ∀ (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 % 14.80/14.98 Clause #650 (by clausification #[642]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a) (a_6 : a → Prop), % 14.80/14.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.80/14.98 (Or (Eq (skS.0 0 a_1 a_5) False) (Or (Eq (skS.0 2 a_1 a_2 a_6 a_5) False) (Eq (skS.0 1 a_1 a_2 a_5) True))) % 14.80/14.98 Clause #652 (by superposition #[650, 640]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 14.80/14.98 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) % 14.80/14.98 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_5 (skS.0 3 a_1 a_6 a_7)) False) % 14.80/14.98 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_6 a_7)) True) (Eq False True))) % 14.80/14.98 Clause #653 (by betaEtaReduce #[652]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 14.80/14.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.80/14.98 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_6 a_7)) False) % 14.80/14.98 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_6 a_7)) True) (Eq False True))) % 14.80/14.98 Clause #654 (by clausification #[653]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a), % 14.80/14.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.80/14.98 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_6 a_7)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_6 a_7)) True)) % 14.80/14.98 Clause #655 (by superposition #[654, 643]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.80/14.98 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) % 14.80/14.98 (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) % 14.80/14.98 (Eq False True)) % 14.80/14.98 Clause #656 (by betaEtaReduce #[655]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.80/14.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 14.80/14.98 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True) (Eq False True)) % 14.80/14.98 Clause #657 (by clausification #[656]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a), % 14.80/14.98 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) % 14.80/14.98 Clause #660 (by equality factoring #[657]): ∀ (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) % 14.80/14.98 Clause #663 (by betaEtaReduce #[660]): ∀ (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) % 14.80/14.98 Clause #664 (by clausification #[663]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 14.80/14.98 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)) % 14.80/14.98 Clause #666 (by clausification #[664]): ∀ (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) % 14.80/14.98 Clause #667 (by clausification #[666]): ∀ (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 % 14.80/14.98 Clause #668 (by superposition #[667, 48]): ∀ (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) % 14.80/14.98 Clause #669 (by clausification #[668]): ∀ (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 % 14.80/14.99 Clause #670 (by superposition #[669, 638]): Eq False True % 14.80/14.99 Clause #671 (by clausification #[670]): False % 14.80/14.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------