%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV061^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:02:48 PM UTC 2025 % Result : Theorem 3.89s 4.04s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV061^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.14 % Command : duper %s % 0.15/0.35 % Computer : n016.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 01:51:08 EDT 2025 % 0.15/0.35 % CPUTime : % 3.89/4.04 SZS status Theorem for theBenchmark.p % 3.89/4.04 SZS output start Proof for theBenchmark.p % 3.89/4.04 Clause #0 (by assumption #[]): Eq % 3.89/4.04 (Not % 3.89/4.04 (∀ (Xx : b) (Xy : a) (Xs Xk : b → a → Prop), % 3.89/4.04 (∀ (Xx_2 : b) (Xy_47 : a), Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 Xx) (Eq Xy_47 Xy))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 Xx) (Eq Xy_48 Xy))) → Xs Xx_3 Xy_48)) % 3.89/4.04 True % 3.89/4.04 Clause #1 (by clausification #[0]): Eq % 3.89/4.04 (∀ (Xx : b) (Xy : a) (Xs Xk : b → a → Prop), % 3.89/4.04 (∀ (Xx_2 : b) (Xy_47 : a), Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 Xx) (Eq Xy_47 Xy))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 Xx) (Eq Xy_48 Xy))) → Xs Xx_3 Xy_48) % 3.89/4.04 False % 3.89/4.04 Clause #2 (by clausification #[1]): ∀ (a_1 : b), % 3.89/4.04 Eq % 3.89/4.04 (Not % 3.89/4.04 (∀ (Xy : a) (Xs Xk : b → a → Prop), % 3.89/4.04 (∀ (Xx_2 : b) (Xy_47 : a), Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 Xy))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), % 3.89/4.04 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 Xy))) → Xs Xx_3 Xy_48)) % 3.89/4.04 True % 3.89/4.04 Clause #3 (by clausification #[2]): ∀ (a_1 : b), % 3.89/4.04 Eq % 3.89/4.04 (∀ (Xy : a) (Xs Xk : b → a → Prop), % 3.89/4.04 (∀ (Xx_2 : b) (Xy_47 : a), Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 Xy))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 Xy))) → Xs Xx_3 Xy_48) % 3.89/4.04 False % 3.89/4.04 Clause #4 (by clausification #[3]): ∀ (a_1 : b) (a_2 : a), % 3.89/4.04 Eq % 3.89/4.04 (Not % 3.89/4.04 (∀ (Xs Xk : b → a → Prop), % 3.89/4.04 (∀ (Xx_2 : b) (Xy_47 : a), % 3.89/4.04 Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), % 3.89/4.04 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → Xs Xx_3 Xy_48)) % 3.89/4.04 True % 3.89/4.04 Clause #5 (by clausification #[4]): ∀ (a_1 : b) (a_2 : a), % 3.89/4.04 Eq % 3.89/4.04 (∀ (Xs Xk : b → a → Prop), % 3.89/4.04 (∀ (Xx_2 : b) (Xy_47 : a), % 3.89/4.04 Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), % 3.89/4.04 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → Xs Xx_3 Xy_48) % 3.89/4.04 False % 3.89/4.04 Clause #6 (by clausification #[5]): ∀ (a_1 : b) (a_2 : a) (a_3 : b → a → Prop), % 3.89/4.04 Eq % 3.89/4.04 (Not % 3.89/4.04 (∀ (Xk : b → a → Prop), % 3.89/4.04 (∀ (Xx_2 : b) (Xy_47 : a), % 3.89/4.04 Xk Xx_2 Xy_47 → % 3.89/4.04 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), % 3.89/4.04 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → % 3.89/4.04 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48)) % 3.89/4.04 True % 3.89/4.04 Clause #7 (by clausification #[6]): ∀ (a_1 : b) (a_2 : a) (a_3 : b → a → Prop), % 3.89/4.04 Eq % 3.89/4.04 (∀ (Xk : b → a → Prop), % 3.89/4.04 (∀ (Xx_2 : b) (Xy_47 : a), % 3.89/4.04 Xk Xx_2 Xy_47 → % 3.89/4.04 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), % 3.89/4.04 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → % 3.89/4.04 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48) % 3.89/4.04 False % 3.89/4.04 Clause #8 (by clausification #[7]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 3.89/4.04 Eq % 3.89/4.04 (Not % 3.89/4.04 ((∀ (Xx_2 : b) (Xy_47 : a), % 3.89/4.04 skS.0 3 a_1 a_2 a_3 a_4 Xx_2 Xy_47 → % 3.89/4.04 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) → % 3.89/4.04 ∀ (Xx_3 : b) (Xy_48 : a), % 3.89/4.04 And (skS.0 3 a_1 a_2 a_3 a_4 Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → % 3.89/4.04 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48)) % 3.89/4.04 True % 3.89/4.04 Clause #9 (by clausification #[8]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 3.89/4.04 Eq % 3.89/4.04 ((∀ (Xx_2 : b) (Xy_47 : a), % 3.89/4.04 skS.0 3 a_1 a_2 a_3 a_4 Xx_2 Xy_47 → % 3.89/4.04 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) → % 3.91/4.07 ∀ (Xx_3 : b) (Xy_48 : a), % 3.91/4.07 And (skS.0 3 a_1 a_2 a_3 a_4 Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → % 3.91/4.07 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48) % 3.91/4.07 False % 3.91/4.07 Clause #10 (by clausification #[9]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 3.91/4.07 Eq % 3.91/4.07 (∀ (Xx_2 : b) (Xy_47 : a), % 3.91/4.07 skS.0 3 a_1 a_2 a_3 a_4 Xx_2 Xy_47 → % 3.91/4.07 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) % 3.91/4.07 True % 3.91/4.07 Clause #11 (by clausification #[9]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 3.91/4.07 Eq % 3.91/4.07 (∀ (Xx_3 : b) (Xy_48 : a), % 3.91/4.07 And (skS.0 3 a_1 a_2 a_3 a_4 Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → % 3.91/4.07 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48) % 3.91/4.07 False % 3.91/4.07 Clause #12 (by clausification #[10]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 3.91/4.07 Eq % 3.91/4.07 (∀ (Xy_47 : a), % 3.91/4.07 skS.0 3 a_1 a_2 a_3 a_4 a_5 Xy_47 → % 3.91/4.07 Or (skS.0 2 a_1 a_2 a_3 a_5 Xy_47) (And (Eq a_5 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) % 3.91/4.07 True % 3.91/4.07 Clause #13 (by clausification #[12]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.07 Eq % 3.91/4.07 (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6 → % 3.91/4.07 Or (skS.0 2 a_1 a_2 a_3 a_5 a_6) (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2)))) % 3.91/4.07 True % 3.91/4.07 Clause #14 (by clausification #[13]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.07 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 3.91/4.07 (Eq (Or (skS.0 2 a_1 a_2 a_3 a_5 a_6) (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2)))) True) % 3.91/4.07 Clause #15 (by clausification #[14]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.07 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 3.91/4.07 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2))) True)) % 3.91/4.07 Clause #16 (by clausification #[15]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.07 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 3.91/4.07 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (Eq a_6 (skS.0 1 a_1 a_2)) True)) % 3.91/4.07 Clause #17 (by clausification #[15]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.07 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 3.91/4.07 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (Eq a_5 (skS.0 0 a_1)) True)) % 3.91/4.07 Clause #18 (by clausification #[16]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.07 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 3.91/4.07 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq a_6 (skS.0 1 a_1 a_2))) % 3.91/4.07 Clause #19 (by clausification #[11]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 3.91/4.07 Eq % 3.91/4.07 (Not % 3.91/4.07 (∀ (Xy_48 : a), % 3.91/4.07 And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy_48) % 3.91/4.07 (Not (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → % 3.91/4.07 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy_48)) % 3.91/4.07 True % 3.91/4.07 Clause #20 (by clausification #[19]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 3.91/4.07 Eq % 3.91/4.07 (∀ (Xy_48 : a), % 3.91/4.07 And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy_48) % 3.91/4.07 (Not (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → % 3.91/4.07 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy_48) % 3.91/4.07 False % 3.91/4.07 Clause #21 (by clausification #[20]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.07 Eq % 3.91/4.07 (Not % 3.91/4.07 (And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) % 3.91/4.07 (Not % 3.91/4.07 (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) % 3.91/4.07 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)))) → % 3.91/4.07 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))) % 3.91/4.07 True % 3.91/4.07 Clause #22 (by clausification #[21]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.07 Eq % 3.91/4.07 (And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) % 3.91/4.09 (Not % 3.91/4.09 (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) % 3.91/4.09 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)))) → % 3.91/4.09 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) % 3.91/4.09 False % 3.91/4.09 Clause #23 (by clausification #[22]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Eq % 3.91/4.09 (And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) % 3.91/4.09 (Not % 3.91/4.09 (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) % 3.91/4.09 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2))))) % 3.91/4.09 True % 3.91/4.09 Clause #24 (by clausification #[22]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) False % 3.91/4.09 Clause #25 (by clausification #[23]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Eq % 3.91/4.09 (Not % 3.91/4.09 (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)))) % 3.91/4.09 True % 3.91/4.09 Clause #26 (by clausification #[23]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True % 3.91/4.09 Clause #27 (by clausification #[25]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Eq (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2))) % 3.91/4.09 False % 3.91/4.09 Clause #28 (by clausification #[27]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or (Eq (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) False) % 3.91/4.09 (Eq (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) False) % 3.91/4.09 Clause #29 (by clausification #[28]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or (Eq (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) False) % 3.91/4.09 (Ne (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) % 3.91/4.09 Clause #30 (by clausification #[29]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or (Ne (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Ne (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) % 3.91/4.09 Clause #31 (by clausification #[17]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq a_5 (skS.0 0 a_1))) % 3.91/4.09 Clause #32 (by superposition #[26, 18]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or (Eq True False) % 3.91/4.09 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True) % 3.91/4.09 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2))) % 3.91/4.09 Clause #33 (by superposition #[26, 31]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or % 3.91/4.09 (Eq (skS.0 2 a_1 a_2 (fun x x_1 => a_3 x x_1) (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True) % 3.91/4.09 (Or (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq False True)) % 3.91/4.09 Clause #34 (by clausification #[32]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True) % 3.91/4.09 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) % 3.91/4.09 Clause #35 (by superposition #[34, 24]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or (Eq (skS.0 5 a_1 a_2 (fun x x_1 => a_3 x x_1) (fun x x_1 => a_4 x x_1) a_5 a_6) (skS.0 1 a_1 a_2)) (Eq True False) % 3.91/4.09 Clause #36 (by betaEtaReduce #[35]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Or (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) (Eq True False) % 3.91/4.09 Clause #37 (by clausification #[36]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.09 Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2) % 3.91/4.09 Clause #39 (by backward demodulation #[37, 24]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 3.91/4.09 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) False % 3.91/4.10 Clause #42 (by backward contextual literal cutting #[37, 30]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), Ne (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1) % 3.91/4.10 Clause #44 (by betaEtaReduce #[33]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.10 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True) % 3.91/4.10 (Or (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq False True)) % 3.91/4.10 Clause #45 (by clausification #[44]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 3.91/4.10 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True) % 3.91/4.10 (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) % 3.91/4.10 Clause #46 (by forward demodulation #[45, 37]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 3.91/4.10 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) True) % 3.91/4.10 (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) % 3.91/4.10 Clause #47 (by forward contextual literal cutting #[46, 42]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 3.91/4.10 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) True % 3.91/4.10 Clause #48 (by superposition #[47, 39]): Eq True False % 3.91/4.10 Clause #49 (by clausification #[48]): False % 3.91/4.10 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------