%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET593^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:00:12 PM UTC 2025 % Result : Theorem 5.63s 5.86s % Output : Proof 5.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET593^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 14:49:53 EDT 2025 % 0.13/0.34 % CPUTime : % 5.63/5.86 SZS status Theorem for theBenchmark.p % 5.63/5.86 SZS output start Proof for theBenchmark.p % 5.63/5.86 Clause #0 (by assumption #[]): Eq % 5.63/5.86 (Not % 5.63/5.86 (∀ (X Y Z : a → Prop), % 5.63/5.86 (∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) → % 5.63/5.86 And (∀ (Xx : a), And (X Xx) (Not (Y Xx)) → Z Xx) (∀ (Xx : a), And (X Xx) (Not (Z Xx)) → Y Xx))) % 5.63/5.86 True % 5.63/5.86 Clause #1 (by clausification #[0]): Eq % 5.63/5.86 (∀ (X Y Z : a → Prop), % 5.63/5.86 (∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) → % 5.63/5.86 And (∀ (Xx : a), And (X Xx) (Not (Y Xx)) → Z Xx) (∀ (Xx : a), And (X Xx) (Not (Z Xx)) → Y Xx)) % 5.63/5.86 False % 5.63/5.86 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 5.63/5.86 Eq % 5.63/5.86 (Not % 5.63/5.86 (∀ (Y Z : a → Prop), % 5.63/5.86 (∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx)) → % 5.63/5.86 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Y Xx)) → Z Xx) % 5.63/5.86 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Z Xx)) → Y Xx))) % 5.63/5.86 True % 5.63/5.86 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 5.63/5.86 Eq % 5.63/5.86 (∀ (Y Z : a → Prop), % 5.63/5.86 (∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx)) → % 5.63/5.86 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Y Xx)) → Z Xx) % 5.63/5.86 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Z Xx)) → Y Xx)) % 5.63/5.86 False % 5.63/5.86 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 5.63/5.86 Eq % 5.63/5.86 (Not % 5.63/5.86 (∀ (Z : a → Prop), % 5.63/5.86 (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx)) → % 5.63/5.86 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → Z Xx) % 5.63/5.86 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Z Xx)) → skS.0 1 a_1 a_2 Xx))) % 5.63/5.86 True % 5.63/5.86 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 5.63/5.86 Eq % 5.63/5.86 (∀ (Z : a → Prop), % 5.63/5.86 (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx)) → % 5.63/5.86 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → Z Xx) % 5.63/5.86 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Z Xx)) → skS.0 1 a_1 a_2 Xx)) % 5.63/5.86 False % 5.63/5.86 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 5.63/5.86 Eq % 5.63/5.86 (Not % 5.63/5.86 ((∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) → % 5.63/5.86 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) % 5.63/5.86 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx))) % 5.63/5.86 True % 5.63/5.86 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 5.63/5.86 Eq % 5.63/5.86 ((∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) → % 5.63/5.86 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) % 5.63/5.86 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx)) % 5.63/5.86 False % 5.63/5.86 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) True % 5.63/5.86 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 5.63/5.86 Eq % 5.63/5.86 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) % 5.63/5.86 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx)) % 5.63/5.87 False % 5.63/5.87 Clause #10 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 5.63/5.87 Eq (skS.0 0 a_1 a_2 → Or (skS.0 1 a_1 a_3 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True % 5.63/5.87 Clause #11 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 5.63/5.87 Or (Eq (skS.0 0 a_1 a_2) False) (Eq (Or (skS.0 1 a_1 a_3 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True) % 5.63/5.87 Clause #12 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 5.63/5.87 Or (Eq (skS.0 0 a_1 a_2) False) (Or (Eq (skS.0 1 a_1 a_3 a_2) True) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True)) % 5.63/5.87 Clause #13 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop), % 5.63/5.87 Or (Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) False) % 5.63/5.87 (Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) False) % 5.63/5.87 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 5.63/5.87 Or (Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) False) % 5.72/5.89 (Eq % 5.72/5.89 (Not % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) → % 5.72/5.89 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))) % 5.72/5.89 True) % 5.72/5.89 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or % 5.72/5.89 (Eq % 5.72/5.89 (Not % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) → % 5.72/5.89 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))) % 5.72/5.89 True) % 5.72/5.89 (Eq % 5.72/5.89 (Not % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) → % 5.72/5.89 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5))) % 5.72/5.89 True) % 5.72/5.89 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or % 5.72/5.89 (Eq % 5.72/5.89 (Not % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) → % 5.72/5.89 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) % 5.72/5.89 True) % 5.72/5.89 (Eq % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5))) → % 5.72/5.89 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5)) % 5.72/5.89 False) % 5.72/5.89 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or % 5.72/5.89 (Eq % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) → % 5.72/5.89 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) % 5.72/5.89 False) % 5.72/5.89 (Eq % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) → % 5.72/5.89 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) % 5.72/5.89 False) % 5.72/5.89 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or % 5.72/5.89 (Eq % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) → % 5.72/5.89 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) % 5.72/5.89 False) % 5.72/5.89 (Eq (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)))) True) % 5.72/5.89 Clause #19 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or % 5.72/5.89 (Eq % 5.72/5.89 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) → % 5.72/5.89 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) % 5.72/5.89 False) % 5.72/5.89 (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5)) False) % 5.72/5.89 Clause #20 (by clausification #[18]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or (Eq (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)))) True) % 5.72/5.89 (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)))) True) % 5.72/5.89 Clause #21 (by clausification #[18]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or (Eq (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)))) True) % 5.72/5.89 (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False) % 5.72/5.89 Clause #22 (by clausification #[20]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)))) True) % 5.72/5.89 (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5))) True) % 5.72/5.89 Clause #23 (by clausification #[20]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)))) True) % 5.72/5.89 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True) % 5.72/5.89 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) True) % 5.72/5.89 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) True) % 5.72/5.89 Clause #25 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True) % 5.72/5.89 Clause #26 (by clausification #[24]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.72/5.89 Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) True) % 5.72/5.89 (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) False) % 5.72/5.89 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False) % 5.74/5.92 Clause #28 (by clausification #[25]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) False) % 5.74/5.92 Clause #29 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) % 5.74/5.92 (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)))) True) % 5.74/5.92 Clause #30 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False) % 5.74/5.92 Clause #31 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) % 5.74/5.92 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) True) % 5.74/5.92 Clause #32 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True) % 5.74/5.92 Clause #33 (by clausification #[31]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) % 5.74/5.92 (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False) % 5.74/5.92 Clause #34 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False) (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5))) True) % 5.74/5.92 Clause #35 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True) % 5.74/5.92 Clause #36 (by clausification #[34]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) False) % 5.74/5.92 Clause #37 (by clausification #[23]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) True) % 5.74/5.92 Clause #38 (by clausification #[23]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True) % 5.74/5.92 Clause #39 (by clausification #[37]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.92 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False) % 5.74/5.92 Clause #41 (by superposition #[38, 12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop), % 5.74/5.92 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) a_2 a_3 a_4)) True) % 5.74/5.92 (Or (Eq True False) % 5.74/5.92 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 4 a_1 a_2 a_3 a_6)) True) % 5.74/5.92 (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 4 a_1 a_2 a_3 a_6)) True))) % 5.74/5.92 Clause #48 (by betaEtaReduce #[41]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop), % 5.74/5.92 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.92 (Or (Eq True False) % 5.74/5.92 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 4 a_1 a_2 a_3 a_6)) True) % 5.74/5.92 (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 4 a_1 a_2 a_3 a_6)) True))) % 5.74/5.92 Clause #49 (by clausification #[48]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop), % 5.74/5.92 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.92 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 4 a_1 a_2 a_3 a_6)) True) (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 4 a_1 a_2 a_3 a_6)) True)) % 5.74/5.92 Clause #51 (by superposition #[49, 39]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a), % 5.74/5.92 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True) % 5.74/5.92 (Or % 5.74/5.92 (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_2 x) (fun x => a_3 x) a_5)) % 5.74/5.92 True) % 5.74/5.92 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_6)) True) (Eq True False))) % 5.74/5.92 Clause #52 (by betaEtaReduce #[51]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a), % 5.74/5.94 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.94 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True) % 5.74/5.94 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_6)) True) (Eq True False))) % 5.74/5.94 Clause #53 (by clausification #[52]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a), % 5.74/5.94 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.94 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_6)) True)) % 5.74/5.94 Clause #58 (by equality factoring #[53]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 5.74/5.94 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)) % 5.74/5.94 Clause #59 (by clausification #[58]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 5.74/5.94 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Or (Eq True False) (Eq True False))) % 5.74/5.94 Clause #61 (by clausification #[59]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 5.74/5.94 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq True False)) % 5.74/5.94 Clause #62 (by clausification #[61]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 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 (skS.0 3 a_1 a_2 a_3 a_5)) True) % 5.74/5.94 Clause #64 (by superposition #[62, 35]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True) % 5.74/5.94 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)) % 5.74/5.94 Clause #66 (by betaEtaReduce #[64]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.94 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)) % 5.74/5.94 Clause #67 (by clausification #[66]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True) % 5.74/5.94 Clause #69 (by equality factoring #[67]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.94 Clause #70 (by clausification #[69]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 5.74/5.94 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Or (Eq True False) (Eq True False)) % 5.74/5.94 Clause #72 (by clausification #[70]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq True False) % 5.74/5.94 Clause #73 (by clausification #[72]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True % 5.74/5.94 Clause #74 (by superposition #[73, 12]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop), % 5.74/5.94 Or (Eq True False) % 5.74/5.94 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 3 a_1 a_3 a_4 a_5)) True)) % 5.74/5.94 Clause #80 (by clausification #[74]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop), % 5.74/5.94 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 3 a_1 a_3 a_4 a_5)) True) % 5.74/5.94 Clause #81 (by superposition #[80, 33]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or % 5.74/5.94 (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_2 x) (fun x => a_3 x) a_4)) % 5.74/5.94 True) % 5.74/5.94 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False)) % 5.74/5.94 Clause #82 (by superposition #[80, 32]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or % 5.74/5.94 (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_2 x) (fun x => a_3 x) a_4)) % 5.74/5.94 True) % 5.74/5.94 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True)) % 5.74/5.94 Clause #83 (by superposition #[80, 30]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.94 Or % 5.74/5.94 (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_2 x) (fun x => a_3 x) a_4)) % 5.74/5.94 True) % 5.74/5.94 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False)) % 5.74/5.94 Clause #86 (by betaEtaReduce #[82]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.97 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True)) % 5.74/5.97 Clause #87 (by clausification #[86]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True) % 5.74/5.97 Clause #89 (by superposition #[87, 28]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True) % 5.74/5.97 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq True False)) % 5.74/5.97 Clause #91 (by betaEtaReduce #[89]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) % 5.74/5.97 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq True False)) % 5.74/5.97 Clause #92 (by clausification #[91]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 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_3 a_5)) True) % 5.74/5.97 Clause #94 (by equality factoring #[92]): ∀ (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) % 5.74/5.97 Clause #97 (by clausification #[94]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 5.74/5.97 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)) % 5.74/5.97 Clause #99 (by clausification #[97]): ∀ (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) % 5.74/5.97 Clause #100 (by clausification #[99]): ∀ (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 % 5.74/5.97 Clause #101 (by superposition #[100, 12]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop), % 5.74/5.97 Or (Eq True False) % 5.74/5.97 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 4 a_1 a_3 a_4 a_5)) True)) % 5.74/5.97 Clause #102 (by clausification #[101]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 4 a_1 a_3 a_4 a_5)) True) % 5.74/5.97 Clause #105 (by betaEtaReduce #[83]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.97 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False)) % 5.74/5.97 Clause #106 (by clausification #[105]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False) % 5.74/5.97 Clause #109 (by betaEtaReduce #[81]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.97 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False)) % 5.74/5.97 Clause #110 (by clausification #[109]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False) % 5.74/5.97 Clause #111 (by superposition #[110, 102]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or % 5.74/5.97 (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_2 x) (fun x => a_3 x) a_4)) % 5.74/5.97 True) % 5.74/5.97 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq False True)) % 5.74/5.97 Clause #112 (by betaEtaReduce #[111]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.97 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq False True)) % 5.74/5.97 Clause #113 (by clausification #[112]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True) % 5.74/5.97 Clause #116 (by superposition #[113, 106]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or % 5.74/5.97 (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_2 x) (fun x => a_3 x) a_4)) % 5.74/5.97 True) % 5.74/5.97 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq True False)) % 5.74/5.97 Clause #117 (by betaEtaReduce #[116]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.97 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 5.74/5.98 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq True False)) % 5.74/5.98 Clause #118 (by clausification #[117]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a), % 5.74/5.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) True) % 5.74/5.98 Clause #119 (by equality factoring #[118]): ∀ (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_2 a_3 a_4)) True) % 5.74/5.98 Clause #120 (by clausification #[119]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 5.74/5.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Or (Eq True False) (Eq True False)) % 5.74/5.98 Clause #122 (by clausification #[120]): ∀ (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_2 a_3 a_4)) True) (Eq True False) % 5.74/5.98 Clause #123 (by clausification #[122]): ∀ (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_2 a_3 a_4)) True % 5.74/5.98 Clause #124 (by superposition #[123, 27]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) False) % 5.74/5.98 Clause #127 (by clausification #[124]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) False % 5.74/5.98 Clause #128 (by superposition #[127, 102]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq False True) % 5.74/5.98 Clause #129 (by clausification #[128]): ∀ (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)) True % 5.74/5.98 Clause #130 (by superposition #[129, 36]): ∀ (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 3 a_1 a_2 a_3 a_4)) False) % 5.74/5.98 Clause #131 (by clausification #[130]): ∀ (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_2 a_3 a_4)) False % 5.74/5.98 Clause #132 (by superposition #[131, 123]): Eq False True % 5.74/5.98 Clause #133 (by clausification #[132]): False % 5.74/5.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------