%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : DAT056^1 : TPTP v9.2.0. Released v5.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 07:47:08 PM UTC 2025 % Result : Theorem 4.18s 4.33s % Output : Proof 4.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.12 % Problem : DAT056^1 : TPTP v9.2.0. Released v5.4.0. % 0.02/0.13 % Command : duper %s % 0.14/0.34 % Computer : n004.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 21:56:08 EDT 2025 % 0.14/0.34 % CPUTime : % 4.18/4.33 SZS status Theorem for theBenchmark.p % 4.18/4.33 SZS output start Proof for theBenchmark.p % 4.18/4.33 Clause #0 (by assumption #[]): Eq % 4.18/4.33 (∀ (Lst : lst), % 4.18/4.33 (∀ (Ys Zs : lst), Eq (ap nl (ap Ys Zs)) (ap (ap nl Ys) Zs)) → % 4.18/4.33 (∀ (A : a) (Lst2 : lst), % 4.18/4.33 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.33 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) → % 4.18/4.33 ∀ (Ys3 Zs2 : lst), Eq (ap Lst (ap Ys3 Zs2)) (ap (ap Lst Ys3) Zs2)) % 4.18/4.33 True % 4.18/4.33 Clause #1 (by assumption #[]): Eq (∀ (Ys2 Xs : lst) (X : a), Eq (ap (cns X Xs) Ys2) (cns X (ap Xs Ys2))) True % 4.18/4.33 Clause #2 (by assumption #[]): Eq (∀ (Ys2 : lst), Eq (ap nl Ys2) Ys2) True % 4.18/4.33 Clause #3 (by assumption #[]): Eq (Not (∀ (Ys Zs : lst), Eq (ap xs (ap Ys Zs)) (ap (ap xs Ys) Zs))) True % 4.18/4.33 Clause #4 (by clausification #[2]): ∀ (a : lst), Eq (Eq (ap nl a) a) True % 4.18/4.33 Clause #5 (by clausification #[4]): ∀ (a : lst), Eq (ap nl a) a % 4.18/4.33 Clause #6 (by clausification #[3]): Eq (∀ (Ys Zs : lst), Eq (ap xs (ap Ys Zs)) (ap (ap xs Ys) Zs)) False % 4.18/4.33 Clause #7 (by clausification #[6]): ∀ (a : lst), Eq (Not (∀ (Zs : lst), Eq (ap xs (ap (skS.0 0 a) Zs)) (ap (ap xs (skS.0 0 a)) Zs))) True % 4.18/4.33 Clause #8 (by clausification #[7]): ∀ (a : lst), Eq (∀ (Zs : lst), Eq (ap xs (ap (skS.0 0 a) Zs)) (ap (ap xs (skS.0 0 a)) Zs)) False % 4.18/4.33 Clause #9 (by clausification #[8]): ∀ (a a_1 : lst), Eq (Not (Eq (ap xs (ap (skS.0 0 a) (skS.0 1 a a_1))) (ap (ap xs (skS.0 0 a)) (skS.0 1 a a_1)))) True % 4.18/4.33 Clause #10 (by clausification #[9]): ∀ (a a_1 : lst), Eq (Eq (ap xs (ap (skS.0 0 a) (skS.0 1 a a_1))) (ap (ap xs (skS.0 0 a)) (skS.0 1 a a_1))) False % 4.18/4.33 Clause #11 (by clausification #[10]): ∀ (a a_1 : lst), Ne (ap xs (ap (skS.0 0 a) (skS.0 1 a a_1))) (ap (ap xs (skS.0 0 a)) (skS.0 1 a a_1)) % 4.18/4.33 Clause #12 (by clausification #[1]): ∀ (a_1 : lst), Eq (∀ (Xs : lst) (X : a), Eq (ap (cns X Xs) a_1) (cns X (ap Xs a_1))) True % 4.18/4.33 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : lst), Eq (∀ (X : a), Eq (ap (cns X a_1) a_2) (cns X (ap a_1 a_2))) True % 4.18/4.33 Clause #14 (by clausification #[13]): ∀ (a : a) (a_1 a_2 : lst), Eq (Eq (ap (cns a a_1) a_2) (cns a (ap a_1 a_2))) True % 4.18/4.33 Clause #15 (by clausification #[14]): ∀ (a : a) (a_1 a_2 : lst), Eq (ap (cns a a_1) a_2) (cns a (ap a_1 a_2)) % 4.18/4.33 Clause #19 (by clausification #[0]): ∀ (a_1 : lst), % 4.18/4.33 Eq % 4.18/4.33 ((∀ (Ys Zs : lst), Eq (ap nl (ap Ys Zs)) (ap (ap nl Ys) Zs)) → % 4.18/4.33 (∀ (A : a) (Lst2 : lst), % 4.18/4.33 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.33 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) → % 4.18/4.33 ∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2)) % 4.18/4.33 True % 4.18/4.33 Clause #20 (by clausification #[19]): ∀ (a_1 : lst), % 4.18/4.33 Or (Eq (∀ (Ys Zs : lst), Eq (ap nl (ap Ys Zs)) (ap (ap nl Ys) Zs)) False) % 4.18/4.33 (Eq % 4.18/4.33 ((∀ (A : a) (Lst2 : lst), % 4.18/4.33 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.33 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) → % 4.18/4.33 ∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2)) % 4.18/4.33 True) % 4.18/4.33 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : lst), % 4.18/4.33 Or % 4.18/4.33 (Eq % 4.18/4.33 ((∀ (A : a) (Lst2 : lst), % 4.18/4.33 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.33 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) → % 4.18/4.33 ∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2)) % 4.18/4.33 True) % 4.18/4.33 (Eq (Not (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_2) Zs)) (ap (ap nl (skS.0 2 a_2)) Zs))) True) % 4.18/4.33 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 : lst), % 4.18/4.33 Or (Eq (Not (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_1) Zs)) (ap (ap nl (skS.0 2 a_1)) Zs))) True) % 4.18/4.33 (Or % 4.18/4.33 (Eq % 4.18/4.33 (∀ (A : a) (Lst2 : lst), % 4.18/4.33 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.33 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) % 4.18/4.33 False) % 4.18/4.33 (Eq (∀ (Ys3 Zs2 : lst), Eq (ap a_2 (ap Ys3 Zs2)) (ap (ap a_2 Ys3) Zs2)) True)) % 4.18/4.35 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 : lst), % 4.18/4.35 Or % 4.18/4.35 (Eq % 4.18/4.35 (∀ (A : a) (Lst2 : lst), % 4.18/4.35 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.35 ∀ (Ys Zs : lst), Eq (ap (cns A Lst2) (ap Ys Zs)) (ap (ap (cns A Lst2) Ys) Zs)) % 4.18/4.35 False) % 4.18/4.35 (Or (Eq (∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2)) True) % 4.18/4.35 (Eq (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_2) Zs)) (ap (ap nl (skS.0 2 a_2)) Zs)) False)) % 4.18/4.35 Clause #24 (by clausification #[23]): ∀ (a_1 a_2 : lst) (a_3 : a), % 4.18/4.35 Or (Eq (∀ (Ys3 Zs2 : lst), Eq (ap a_1 (ap Ys3 Zs2)) (ap (ap a_1 Ys3) Zs2)) True) % 4.18/4.35 (Or (Eq (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_2) Zs)) (ap (ap nl (skS.0 2 a_2)) Zs)) False) % 4.18/4.35 (Eq % 4.18/4.35 (Not % 4.18/4.35 (∀ (Lst2 : lst), % 4.18/4.35 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.35 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_3) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_3) Lst2) Ys) Zs))) % 4.18/4.35 True)) % 4.18/4.35 Clause #25 (by clausification #[24]): ∀ (a_1 : lst) (a_2 : a) (a_3 a_4 : lst), % 4.18/4.35 Or (Eq (∀ (Zs : lst), Eq (ap nl (ap (skS.0 2 a_1) Zs)) (ap (ap nl (skS.0 2 a_1)) Zs)) False) % 4.18/4.35 (Or % 4.18/4.35 (Eq % 4.18/4.35 (Not % 4.18/4.35 (∀ (Lst2 : lst), % 4.18/4.35 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.35 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_2) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_2) Lst2) Ys) Zs))) % 4.18/4.35 True) % 4.18/4.35 (Eq (∀ (Zs2 : lst), Eq (ap a_3 (ap a_4 Zs2)) (ap (ap a_3 a_4) Zs2)) True)) % 4.18/4.35 Clause #26 (by clausification #[25]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : lst), % 4.18/4.35 Or % 4.18/4.35 (Eq % 4.18/4.35 (Not % 4.18/4.35 (∀ (Lst2 : lst), % 4.18/4.35 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.35 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_1) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_1) Lst2) Ys) Zs))) % 4.18/4.35 True) % 4.18/4.35 (Or (Eq (∀ (Zs2 : lst), Eq (ap a_2 (ap a_3 Zs2)) (ap (ap a_2 a_3) Zs2)) True) % 4.18/4.35 (Eq (Not (Eq (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5)))) True)) % 4.18/4.35 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 a_3 a_4 : lst) (a_5 : a), % 4.18/4.35 Or (Eq (∀ (Zs2 : lst), Eq (ap a_1 (ap a_2 Zs2)) (ap (ap a_1 a_2) Zs2)) True) % 4.18/4.35 (Or (Eq (Not (Eq (ap nl (ap (skS.0 2 a_3) (skS.0 4 a_3 a_4))) (ap (ap nl (skS.0 2 a_3)) (skS.0 4 a_3 a_4)))) True) % 4.18/4.35 (Eq % 4.18/4.35 (∀ (Lst2 : lst), % 4.18/4.35 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.35 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_5) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_5) Lst2) Ys) Zs)) % 4.18/4.35 False)) % 4.18/4.35 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 : lst) (a_3 : a) (a_4 a_5 a_6 : lst), % 4.18/4.35 Or (Eq (Not (Eq (ap nl (ap (skS.0 2 a_1) (skS.0 4 a_1 a_2))) (ap (ap nl (skS.0 2 a_1)) (skS.0 4 a_1 a_2)))) True) % 4.18/4.35 (Or % 4.18/4.35 (Eq % 4.18/4.35 (∀ (Lst2 : lst), % 4.18/4.35 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.35 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_3) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_3) Lst2) Ys) Zs)) % 4.18/4.35 False) % 4.18/4.35 (Eq (Eq (ap a_4 (ap a_5 a_6)) (ap (ap a_4 a_5) a_6)) True)) % 4.18/4.35 Clause #29 (by clausification #[28]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 a_6 : lst), % 4.18/4.35 Or % 4.18/4.35 (Eq % 4.18/4.35 (∀ (Lst2 : lst), % 4.18/4.35 (∀ (Ys3 Zs2 : lst), Eq (ap Lst2 (ap Ys3 Zs2)) (ap (ap Lst2 Ys3) Zs2)) → % 4.18/4.35 ∀ (Ys Zs : lst), Eq (ap (cns (skS.0 3 a_1) Lst2) (ap Ys Zs)) (ap (ap (cns (skS.0 3 a_1) Lst2) Ys) Zs)) % 4.18/4.35 False) % 4.18/4.35 (Or (Eq (Eq (ap a_2 (ap a_3 a_4)) (ap (ap a_2 a_3) a_4)) True) % 4.18/4.35 (Eq (Eq (ap nl (ap (skS.0 2 a_5) (skS.0 4 a_5 a_6))) (ap (ap nl (skS.0 2 a_5)) (skS.0 4 a_5 a_6))) False)) % 4.18/4.35 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 : lst), % 4.18/4.35 Or (Eq (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) True) % 4.18/4.35 (Or (Eq (Eq (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) False) % 4.18/4.35 (Eq % 4.18/4.35 (Not % 4.18/4.35 ((∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_6 a_7) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_6 a_7) Ys3) Zs2)) → % 4.23/4.38 ∀ (Ys Zs : lst), % 4.23/4.38 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap Ys Zs)) % 4.23/4.38 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) Ys) Zs))) % 4.23/4.38 True)) % 4.23/4.38 Clause #31 (by clausification #[30]): ∀ (a_1 a_2 : lst) (a_3 : a) (a_4 a_5 a_6 a_7 : lst), % 4.23/4.38 Or (Eq (Eq (ap nl (ap (skS.0 2 a_1) (skS.0 4 a_1 a_2))) (ap (ap nl (skS.0 2 a_1)) (skS.0 4 a_1 a_2))) False) % 4.23/4.38 (Or % 4.23/4.38 (Eq % 4.23/4.38 (Not % 4.23/4.38 ((∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_3 a_4) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_3 a_4) Ys3) Zs2)) → % 4.23/4.38 ∀ (Ys Zs : lst), % 4.23/4.38 Eq (ap (cns (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ap Ys Zs)) % 4.23/4.38 (ap (ap (cns (skS.0 3 a_3) (skS.0 5 a_3 a_4)) Ys) Zs))) % 4.23/4.38 True) % 4.23/4.38 (Eq (ap a_5 (ap a_6 a_7)) (ap (ap a_5 a_6) a_7))) % 4.23/4.38 Clause #32 (by clausification #[31]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 a_6 a_7 : lst), % 4.23/4.38 Or % 4.23/4.38 (Eq % 4.23/4.38 (Not % 4.23/4.38 ((∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_1 a_2) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_1 a_2) Ys3) Zs2)) → % 4.23/4.38 ∀ (Ys Zs : lst), % 4.23/4.38 Eq (ap (cns (skS.0 3 a_1) (skS.0 5 a_1 a_2)) (ap Ys Zs)) % 4.23/4.38 (ap (ap (cns (skS.0 3 a_1) (skS.0 5 a_1 a_2)) Ys) Zs))) % 4.23/4.38 True) % 4.23/4.38 (Or (Eq (ap a_3 (ap a_4 a_5)) (ap (ap a_3 a_4) a_5)) % 4.23/4.38 (Ne (ap nl (ap (skS.0 2 a_6) (skS.0 4 a_6 a_7))) (ap (ap nl (skS.0 2 a_6)) (skS.0 4 a_6 a_7)))) % 4.23/4.38 Clause #33 (by clausification #[32]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 : lst), % 4.23/4.38 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.38 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.38 (Eq % 4.23/4.38 ((∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_6 a_7) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_6 a_7) Ys3) Zs2)) → % 4.23/4.38 ∀ (Ys Zs : lst), % 4.23/4.38 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap Ys Zs)) % 4.23/4.38 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) Ys) Zs)) % 4.23/4.38 False)) % 4.23/4.38 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 : lst), % 4.23/4.38 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.38 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.38 (Eq (∀ (Ys3 Zs2 : lst), Eq (ap (skS.0 5 a_6 a_7) (ap Ys3 Zs2)) (ap (ap (skS.0 5 a_6 a_7) Ys3) Zs2)) True)) % 4.23/4.38 Clause #35 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 : lst), % 4.23/4.38 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.38 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.38 (Eq % 4.23/4.38 (∀ (Ys Zs : lst), % 4.23/4.38 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap Ys Zs)) % 4.23/4.38 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) Ys) Zs)) % 4.23/4.38 False)) % 4.23/4.38 Clause #36 (by clausification #[34]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 : lst), % 4.23/4.38 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.38 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.38 (Eq (∀ (Zs2 : lst), Eq (ap (skS.0 5 a_6 a_7) (ap a_8 Zs2)) (ap (ap (skS.0 5 a_6 a_7) a_8) Zs2)) True)) % 4.23/4.38 Clause #37 (by clausification #[36]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.38 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.38 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.38 (Eq (Eq (ap (skS.0 5 a_6 a_7) (ap a_8 a_9)) (ap (ap (skS.0 5 a_6 a_7) a_8) a_9)) True)) % 4.23/4.38 Clause #38 (by clausification #[37]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.38 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.38 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.38 (Eq (ap (skS.0 5 a_6 a_7) (ap a_8 a_9)) (ap (ap (skS.0 5 a_6 a_7) a_8) a_9))) % 4.23/4.38 Clause #39 (by forward demodulation #[38, 5]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.38 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.38 (Or (Ne (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.38 (Eq (ap (skS.0 5 a_6 a_7) (ap a_8 a_9)) (ap (ap (skS.0 5 a_6 a_7) a_8) a_9))) % 4.23/4.41 Clause #40 (by forward demodulation #[39, 5]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Or (Ne (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)) (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) % 4.23/4.41 (Eq (ap (skS.0 5 a_6 a_7) (ap a_8 a_9)) (ap (ap (skS.0 5 a_6 a_7) a_8) a_9))) % 4.23/4.41 Clause #41 (by eliminate resolved literals #[40]): ∀ (a_1 a_2 a_3 : lst) (a_4 : a) (a_5 a_6 a_7 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Eq (ap (skS.0 5 a_4 a_5) (ap a_6 a_7)) (ap (ap (skS.0 5 a_4 a_5) a_6) a_7)) % 4.23/4.41 Clause #42 (by superposition #[41, 11]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 a_6 : lst), % 4.23/4.41 Or (Eq (ap (skS.0 5 a_1 a_2) (ap a_3 a_4)) (ap (ap (skS.0 5 a_1 a_2) a_3) a_4)) % 4.23/4.41 (Ne (ap xs (ap (skS.0 0 a_5) (skS.0 1 a_5 a_6))) (ap xs (ap (skS.0 0 a_5) (skS.0 1 a_5 a_6)))) % 4.23/4.41 Clause #61 (by clausification #[35]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.41 (Eq % 4.23/4.41 (Not % 4.23/4.41 (∀ (Zs : lst), % 4.23/4.41 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) Zs)) % 4.23/4.41 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) Zs))) % 4.23/4.41 True)) % 4.23/4.41 Clause #62 (by clausification #[61]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.41 (Eq % 4.23/4.41 (∀ (Zs : lst), % 4.23/4.41 Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) Zs)) % 4.23/4.41 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) Zs)) % 4.23/4.41 False)) % 4.23/4.41 Clause #63 (by clausification #[62]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.41 (Eq % 4.23/4.41 (Not % 4.23/4.41 (Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9))) % 4.23/4.41 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9)))) % 4.23/4.41 True)) % 4.23/4.41 Clause #64 (by clausification #[63]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.41 (Eq % 4.23/4.41 (Eq (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9))) % 4.23/4.41 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9))) % 4.23/4.41 False)) % 4.23/4.41 Clause #65 (by clausification #[64]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Or (Ne (ap nl (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.41 (Ne (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9))) % 4.23/4.41 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9)))) % 4.23/4.41 Clause #66 (by forward demodulation #[65, 5]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Or (Ne (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)) (ap (ap nl (skS.0 2 a_4)) (skS.0 4 a_4 a_5))) % 4.23/4.41 (Ne (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9))) % 4.23/4.41 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9)))) % 4.23/4.41 Clause #67 (by forward demodulation #[66, 5]): ∀ (a_1 a_2 a_3 a_4 a_5 : lst) (a_6 : a) (a_7 a_8 a_9 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Or (Ne (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5)) (ap (skS.0 2 a_4) (skS.0 4 a_4 a_5))) % 4.23/4.41 (Ne (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (ap (skS.0 6 a_6 a_7 a_8) (skS.0 7 a_6 a_7 a_8 a_9))) % 4.23/4.41 (ap (ap (cns (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (skS.0 6 a_6 a_7 a_8)) (skS.0 7 a_6 a_7 a_8 a_9)))) % 4.23/4.41 Clause #68 (by eliminate resolved literals #[67]): ∀ (a_1 a_2 a_3 : lst) (a_4 : a) (a_5 a_6 a_7 : lst), % 4.23/4.41 Or (Eq (ap a_1 (ap a_2 a_3)) (ap (ap a_1 a_2) a_3)) % 4.23/4.41 (Ne (ap (cns (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ap (skS.0 6 a_4 a_5 a_6) (skS.0 7 a_4 a_5 a_6 a_7))) % 4.23/4.41 (ap (ap (cns (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (skS.0 6 a_4 a_5 a_6)) (skS.0 7 a_4 a_5 a_6 a_7))) % 4.23/4.41 Clause #90 (by eliminate resolved literals #[42]): ∀ (a_1 : a) (a_2 a_3 a_4 : lst), Eq (ap (skS.0 5 a_1 a_2) (ap a_3 a_4)) (ap (ap (skS.0 5 a_1 a_2) a_3) a_4) % 4.23/4.41 Clause #91 (by superposition #[90, 15]): ∀ (a_1 a_2 : a) (a_3 a_4 a_5 : lst), % 4.23/4.41 Eq (ap (cns a_1 (ap (skS.0 5 a_2 a_3) a_4)) a_5) (cns a_1 (ap (skS.0 5 a_2 a_3) (ap a_4 a_5))) % 4.23/4.41 Clause #92 (by forward demodulation #[91, 15]): ∀ (a_1 a_2 : a) (a_3 a_4 a_5 : lst), % 4.23/4.41 Eq (ap (ap (cns a_1 (skS.0 5 a_2 a_3)) a_4) a_5) (cns a_1 (ap (skS.0 5 a_2 a_3) (ap a_4 a_5))) % 4.23/4.41 Clause #93 (by superposition #[92, 15]): ∀ (a_1 a_2 : a) (a_3 a_4 a_5 : lst), % 4.23/4.41 Eq (ap (cns a_1 (skS.0 5 a_2 a_3)) (ap a_4 a_5)) (ap (ap (cns a_1 (skS.0 5 a_2 a_3)) a_4) a_5) % 4.23/4.41 Clause #109 (by backward contextual literal cutting #[93, 68]): ∀ (a a_1 a_2 : lst), Eq (ap a (ap a_1 a_2)) (ap (ap a a_1) a_2) % 4.23/4.41 Clause #113 (by backward contextual literal cutting #[109, 11]): False % 4.23/4.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------