%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV196^5 : 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 08:02:56 PM UTC 2025 % Result : Theorem 4.03s 4.21s % Output : Proof 4.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEV196^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n015.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 01:14:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.03/4.21 SZS status Theorem for theBenchmark.p % 4.03/4.21 SZS output start Proof for theBenchmark.p % 4.03/4.21 Clause #0 (by assumption #[]): Eq % 4.03/4.21 (Not % 4.03/4.21 (∀ (R : a → a → a → Prop), % 4.03/4.21 And True % 4.03/4.21 (∀ (Xa Xb Xc : a), % 4.03/4.21 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 4.03/4.21 (Exists fun Xx1 => % 4.03/4.21 Exists fun Xx2 => % 4.03/4.21 Exists fun Xy1 => % 4.03/4.21 Exists fun Xy2 => % 4.03/4.21 Exists fun Xz1 => % 4.03/4.21 Exists fun Xz2 => % 4.03/4.21 And % 4.03/4.21 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.03/4.21 (R Xx1 Xy1 Xz1)) % 4.03/4.21 (R Xx2 Xy2 Xz2)) → % 4.03/4.21 R Xa Xb Xc) → % 4.03/4.21 R (cP x c0) (cP c0 y) (cP x y))) % 4.03/4.21 True % 4.03/4.21 Clause #1 (by clausification #[0]): Eq % 4.03/4.21 (∀ (R : a → a → a → Prop), % 4.03/4.21 And True % 4.03/4.21 (∀ (Xa Xb Xc : a), % 4.03/4.21 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 4.03/4.21 (Exists fun Xx1 => % 4.03/4.21 Exists fun Xx2 => % 4.03/4.21 Exists fun Xy1 => % 4.03/4.21 Exists fun Xy2 => % 4.03/4.21 Exists fun Xz1 => % 4.03/4.21 Exists fun Xz2 => % 4.03/4.21 And % 4.03/4.21 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.03/4.21 (R Xx1 Xy1 Xz1)) % 4.03/4.21 (R Xx2 Xy2 Xz2)) → % 4.03/4.21 R Xa Xb Xc) → % 4.03/4.21 R (cP x c0) (cP c0 y) (cP x y)) % 4.03/4.21 False % 4.03/4.21 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → a → Prop), % 4.03/4.21 Eq % 4.03/4.21 (Not % 4.03/4.21 (And True % 4.03/4.21 (∀ (Xa Xb Xc : a), % 4.03/4.21 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 4.03/4.21 (Exists fun Xx1 => % 4.03/4.21 Exists fun Xx2 => % 4.03/4.21 Exists fun Xy1 => % 4.03/4.21 Exists fun Xy2 => % 4.03/4.21 Exists fun Xz1 => % 4.03/4.21 Exists fun Xz2 => % 4.03/4.21 And % 4.03/4.21 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.03/4.21 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 4.03/4.21 (skS.0 0 a_1 Xx2 Xy2 Xz2)) → % 4.03/4.21 skS.0 0 a_1 Xa Xb Xc) → % 4.03/4.21 skS.0 0 a_1 (cP x c0) (cP c0 y) (cP x y))) % 4.03/4.21 True % 4.03/4.21 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → a → Prop), % 4.03/4.21 Eq % 4.03/4.21 (And True % 4.03/4.21 (∀ (Xa Xb Xc : a), % 4.03/4.21 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 4.03/4.21 (Exists fun Xx1 => % 4.03/4.21 Exists fun Xx2 => % 4.03/4.21 Exists fun Xy1 => % 4.03/4.21 Exists fun Xy2 => % 4.03/4.21 Exists fun Xz1 => % 4.03/4.21 Exists fun Xz2 => % 4.03/4.21 And % 4.03/4.21 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.03/4.21 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 4.03/4.21 (skS.0 0 a_1 Xx2 Xy2 Xz2)) → % 4.03/4.21 skS.0 0 a_1 Xa Xb Xc) → % 4.03/4.21 skS.0 0 a_1 (cP x c0) (cP c0 y) (cP x y)) % 4.03/4.21 False % 4.03/4.21 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop), % 4.03/4.21 Eq % 4.03/4.21 (And True % 4.03/4.21 (∀ (Xa Xb Xc : a), % 4.03/4.21 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 4.03/4.21 (Exists fun Xx1 => % 4.03/4.21 Exists fun Xx2 => % 4.03/4.21 Exists fun Xy1 => % 4.03/4.21 Exists fun Xy2 => % 4.03/4.21 Exists fun Xz1 => % 4.03/4.21 Exists fun Xz2 => % 4.03/4.21 And % 4.03/4.21 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.03/4.21 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 4.03/4.21 (skS.0 0 a_1 Xx2 Xy2 Xz2)) → % 4.03/4.21 skS.0 0 a_1 Xa Xb Xc)) % 4.03/4.21 True % 4.03/4.21 Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop), Eq (skS.0 0 a_1 (cP x c0) (cP c0 y) (cP x y)) False % 4.03/4.21 Clause #6 (by clausification #[4]): ∀ (a_1 : a → a → a → Prop), % 4.03/4.21 Eq % 4.03/4.21 (∀ (Xa Xb Xc : a), % 4.03/4.21 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 4.07/4.23 (Exists fun Xx1 => % 4.07/4.23 Exists fun Xx2 => % 4.07/4.23 Exists fun Xy1 => % 4.07/4.23 Exists fun Xy2 => % 4.07/4.23 Exists fun Xz1 => % 4.07/4.23 Exists fun Xz2 => % 4.07/4.23 And % 4.07/4.23 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.07/4.23 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 4.07/4.23 (skS.0 0 a_1 Xx2 Xy2 Xz2)) → % 4.07/4.23 skS.0 0 a_1 Xa Xb Xc) % 4.07/4.23 True % 4.07/4.23 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : a → a → a → Prop), % 4.07/4.23 Eq % 4.07/4.23 (∀ (Xb Xc : a), % 4.07/4.23 Or (Or (And (Eq a_1 c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq a_1 Xc))) % 4.07/4.23 (Exists fun Xx1 => % 4.07/4.23 Exists fun Xx2 => % 4.07/4.23 Exists fun Xy1 => % 4.07/4.23 Exists fun Xy2 => % 4.07/4.23 Exists fun Xz1 => % 4.07/4.23 Exists fun Xz2 => % 4.07/4.23 And % 4.07/4.23 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.07/4.23 (skS.0 0 a_2 Xx1 Xy1 Xz1)) % 4.07/4.23 (skS.0 0 a_2 Xx2 Xy2 Xz2)) → % 4.07/4.23 skS.0 0 a_2 a_1 Xb Xc) % 4.07/4.23 True % 4.07/4.23 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 : a) (a_3 : a → a → a → Prop), % 4.07/4.23 Eq % 4.07/4.23 (∀ (Xc : a), % 4.07/4.23 Or (Or (And (Eq a_1 c0) (Eq a_2 Xc)) (And (Eq a_2 c0) (Eq a_1 Xc))) % 4.07/4.23 (Exists fun Xx1 => % 4.07/4.23 Exists fun Xx2 => % 4.07/4.23 Exists fun Xy1 => % 4.07/4.23 Exists fun Xy2 => % 4.07/4.23 Exists fun Xz1 => % 4.07/4.23 Exists fun Xz2 => % 4.07/4.23 And % 4.07/4.23 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.07/4.23 (skS.0 0 a_3 Xx1 Xy1 Xz1)) % 4.07/4.23 (skS.0 0 a_3 Xx2 Xy2 Xz2)) → % 4.07/4.23 skS.0 0 a_3 a_1 a_2 Xc) % 4.07/4.23 True % 4.07/4.23 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop), % 4.07/4.23 Eq % 4.07/4.23 (Or (Or (And (Eq a_1 c0) (Eq a_2 a_3)) (And (Eq a_2 c0) (Eq a_1 a_3))) % 4.07/4.23 (Exists fun Xx1 => % 4.07/4.23 Exists fun Xx2 => % 4.07/4.23 Exists fun Xy1 => % 4.07/4.23 Exists fun Xy2 => % 4.07/4.23 Exists fun Xz1 => % 4.07/4.23 Exists fun Xz2 => % 4.07/4.23 And % 4.07/4.23 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2))) % 4.07/4.23 (skS.0 0 a_4 Xx1 Xy1 Xz1)) % 4.07/4.23 (skS.0 0 a_4 Xx2 Xy2 Xz2)) → % 4.07/4.23 skS.0 0 a_4 a_1 a_2 a_3) % 4.07/4.23 True % 4.07/4.23 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop), % 4.07/4.23 Or % 4.07/4.23 (Eq % 4.07/4.23 (Or (Or (And (Eq a_1 c0) (Eq a_2 a_3)) (And (Eq a_2 c0) (Eq a_1 a_3))) % 4.07/4.23 (Exists fun Xx1 => % 4.07/4.23 Exists fun Xx2 => % 4.07/4.23 Exists fun Xy1 => % 4.07/4.23 Exists fun Xy2 => % 4.07/4.23 Exists fun Xz1 => % 4.07/4.23 Exists fun Xz2 => % 4.07/4.23 And % 4.07/4.23 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2))) % 4.07/4.23 (skS.0 0 a_4 Xx1 Xy1 Xz1)) % 4.07/4.23 (skS.0 0 a_4 Xx2 Xy2 Xz2))) % 4.07/4.23 False) % 4.07/4.23 (Eq (skS.0 0 a_4 a_1 a_2 a_3) True) % 4.07/4.23 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.07/4.23 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.07/4.23 (Eq % 4.07/4.23 (Exists fun Xx1 => % 4.07/4.23 Exists fun Xx2 => % 4.07/4.23 Exists fun Xy1 => % 4.07/4.23 Exists fun Xy2 => % 4.07/4.23 Exists fun Xz1 => % 4.07/4.23 Exists fun Xz2 => % 4.07/4.23 And % 4.07/4.23 (And (And (And (Eq a_2 (cP Xx1 Xx2)) (Eq a_3 (cP Xy1 Xy2))) (Eq a_4 (cP Xz1 Xz2))) % 4.07/4.23 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 4.07/4.23 (skS.0 0 a_1 Xx2 Xy2 Xz2)) % 4.07/4.23 False) % 4.07/4.23 Clause #13 (by clausification #[11]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.07/4.23 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Eq (Or (And (Eq a_2 c0) (Eq a_3 a_4)) (And (Eq a_3 c0) (Eq a_2 a_4))) False) % 4.07/4.23 Clause #14 (by clausification #[12]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 : a), % 4.07/4.23 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.07/4.23 (Eq % 4.07/4.23 (Exists fun Xx2 => % 4.07/4.23 Exists fun Xy1 => % 4.07/4.23 Exists fun Xy2 => % 4.07/4.23 Exists fun Xz1 => % 4.08/4.26 Exists fun Xz2 => % 4.08/4.26 And % 4.08/4.26 (And (And (And (Eq a_2 (cP a_5 Xx2)) (Eq a_3 (cP Xy1 Xy2))) (Eq a_4 (cP Xz1 Xz2))) % 4.08/4.26 (skS.0 0 a_1 a_5 Xy1 Xz1)) % 4.08/4.26 (skS.0 0 a_1 Xx2 Xy2 Xz2)) % 4.08/4.26 False) % 4.08/4.26 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Eq % 4.08/4.26 (Exists fun Xy1 => % 4.08/4.26 Exists fun Xy2 => % 4.08/4.26 Exists fun Xz1 => % 4.08/4.26 Exists fun Xz2 => % 4.08/4.26 And % 4.08/4.26 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP Xy1 Xy2))) (Eq a_4 (cP Xz1 Xz2))) % 4.08/4.26 (skS.0 0 a_1 a_5 Xy1 Xz1)) % 4.08/4.26 (skS.0 0 a_1 a_6 Xy2 Xz2)) % 4.08/4.26 False) % 4.08/4.26 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Eq % 4.08/4.26 (Exists fun Xy2 => % 4.08/4.26 Exists fun Xz1 => % 4.08/4.26 Exists fun Xz2 => % 4.08/4.26 And % 4.08/4.26 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 Xy2))) (Eq a_4 (cP Xz1 Xz2))) % 4.08/4.26 (skS.0 0 a_1 a_5 a_7 Xz1)) % 4.08/4.26 (skS.0 0 a_1 a_6 Xy2 Xz2)) % 4.08/4.26 False) % 4.08/4.26 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Eq % 4.08/4.26 (Exists fun Xz1 => % 4.08/4.26 Exists fun Xz2 => % 4.08/4.26 And % 4.08/4.26 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 a_8))) (Eq a_4 (cP Xz1 Xz2))) % 4.08/4.26 (skS.0 0 a_1 a_5 a_7 Xz1)) % 4.08/4.26 (skS.0 0 a_1 a_6 a_8 Xz2)) % 4.08/4.26 False) % 4.08/4.26 Clause #18 (by clausification #[17]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Eq % 4.08/4.26 (Exists fun Xz2 => % 4.08/4.26 And % 4.08/4.26 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 a_8))) (Eq a_4 (cP a_9 Xz2))) (skS.0 0 a_1 a_5 a_7 a_9)) % 4.08/4.26 (skS.0 0 a_1 a_6 a_8 Xz2)) % 4.08/4.26 False) % 4.08/4.26 Clause #19 (by clausification #[18]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Eq % 4.08/4.26 (And % 4.08/4.26 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 a_8))) (Eq a_4 (cP a_9 a_10))) (skS.0 0 a_1 a_5 a_7 a_9)) % 4.08/4.26 (skS.0 0 a_1 a_6 a_8 a_10)) % 4.08/4.26 False) % 4.08/4.26 Clause #20 (by clausification #[19]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Or % 4.08/4.26 (Eq (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 a_8))) (Eq a_4 (cP a_9 a_10))) (skS.0 0 a_1 a_5 a_7 a_9)) % 4.08/4.26 False) % 4.08/4.26 (Eq (skS.0 0 a_1 a_6 a_8 a_10) False)) % 4.08/4.26 Clause #21 (by clausification #[20]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False) % 4.08/4.26 (Or (Eq (And (And (Eq a_2 (cP a_8 a_5)) (Eq a_3 (cP a_9 a_6))) (Eq a_4 (cP a_10 a_7))) False) % 4.08/4.26 (Eq (skS.0 0 a_1 a_8 a_9 a_10) False))) % 4.08/4.26 Clause #22 (by clausification #[21]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False) % 4.08/4.26 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False) % 4.08/4.26 (Or (Eq (And (Eq a_2 (cP a_8 a_5)) (Eq a_3 (cP a_9 a_6))) False) (Eq (Eq a_4 (cP a_10 a_7)) False)))) % 4.08/4.26 Clause #23 (by clausification #[22]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False) % 4.08/4.26 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False) % 4.08/4.26 (Or (Eq (Eq a_4 (cP a_10 a_7)) False) (Or (Eq (Eq a_2 (cP a_8 a_5)) False) (Eq (Eq a_3 (cP a_9 a_6)) False))))) % 4.08/4.26 Clause #24 (by clausification #[23]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a), % 4.08/4.26 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.26 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False) % 4.08/4.26 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False) % 4.08/4.26 (Or (Eq (Eq a_2 (cP a_8 a_5)) False) (Or (Eq (Eq a_3 (cP a_9 a_6)) False) (Ne a_4 (cP a_10 a_7)))))) % 4.08/4.29 Clause #25 (by clausification #[24]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.29 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False) % 4.08/4.29 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False) % 4.08/4.29 (Or (Eq (Eq a_3 (cP a_9 a_6)) False) (Or (Ne a_4 (cP a_10 a_7)) (Ne a_2 (cP a_8 a_5)))))) % 4.08/4.29 Clause #26 (by clausification #[25]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) % 4.08/4.29 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False) % 4.08/4.29 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False) % 4.08/4.29 (Or (Ne a_4 (cP a_10 a_7)) (Or (Ne a_2 (cP a_8 a_5)) (Ne a_3 (cP a_9 a_6)))))) % 4.08/4.29 Clause #27 (by destructive equality resolution #[26]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 (cP a_4 a_5)) True) % 4.08/4.29 (Or (Eq (skS.0 0 a_1 a_6 a_7 a_5) False) % 4.08/4.29 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_4) False) (Or (Ne a_2 (cP a_8 a_6)) (Ne a_3 (cP a_9 a_7))))) % 4.08/4.29 Clause #28 (by destructive equality resolution #[27]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 (cP a_2 a_3) a_4 (cP a_5 a_6)) True) % 4.08/4.29 (Or (Eq (skS.0 0 a_1 a_3 a_7 a_6) False) (Or (Eq (skS.0 0 a_1 a_2 a_8 a_5) False) (Ne a_4 (cP a_8 a_7)))) % 4.08/4.29 Clause #29 (by destructive equality resolution #[28]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 (cP a_2 a_3) (cP a_4 a_5) (cP a_6 a_7)) True) % 4.08/4.29 (Or (Eq (skS.0 0 a_1 a_3 a_5 a_7) False) (Eq (skS.0 0 a_1 a_2 a_4 a_6) False)) % 4.08/4.29 Clause #30 (by clausification #[13]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Eq (And (Eq a_3 c0) (Eq a_2 a_4)) False) % 4.08/4.29 Clause #31 (by clausification #[13]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Eq (And (Eq a_2 c0) (Eq a_3 a_4)) False) % 4.08/4.29 Clause #32 (by clausification #[30]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_3 c0) False) (Eq (Eq a_2 a_4) False)) % 4.08/4.29 Clause #33 (by clausification #[32]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_2 a_4) False) (Ne a_3 c0)) % 4.08/4.29 Clause #34 (by clausification #[33]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Ne a_3 c0) (Ne a_2 a_4)) % 4.08/4.29 Clause #35 (by destructive equality resolution #[34]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 c0 a_3) True) (Ne a_2 a_3) % 4.08/4.29 Clause #36 (by destructive equality resolution #[35]): ∀ (a_1 : a → a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 a_2 c0 a_2) True % 4.08/4.29 Clause #38 (by clausification #[31]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_2 c0) False) (Eq (Eq a_3 a_4) False)) % 4.08/4.29 Clause #39 (by clausification #[38]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_3 a_4) False) (Ne a_2 c0)) % 4.08/4.29 Clause #40 (by clausification #[39]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Ne a_2 c0) (Ne a_3 a_4)) % 4.08/4.29 Clause #41 (by destructive equality resolution #[40]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 c0 a_2 a_3) True) (Ne a_2 a_3) % 4.08/4.29 Clause #42 (by destructive equality resolution #[41]): ∀ (a_1 : a → a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 c0 a_2 a_2) True % 4.08/4.29 Clause #43 (by superposition #[42, 29]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 (cP a_2 c0) (cP a_3 a_4) (cP a_5 a_4)) True) % 4.08/4.29 (Or (Eq True False) (Eq (skS.0 0 a_1 a_2 a_3 a_5) False)) % 4.08/4.29 Clause #64 (by clausification #[43]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 (cP a_2 c0) (cP a_3 a_4) (cP a_5 a_4)) True) (Eq (skS.0 0 a_1 a_2 a_3 a_5) False) % 4.08/4.29 Clause #70 (by superposition #[64, 36]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), % 4.08/4.29 Or (Eq (skS.0 0 (fun x x_1 x_2 => a_1 x x_1 x_2) (cP a_2 c0) (cP c0 a_3) (cP a_2 a_3)) True) (Eq False True) % 4.08/4.29 Clause #85 (by betaEtaReduce #[70]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), % 4.08/4.29 Or (Eq (skS.0 0 a_1 (cP a_2 c0) (cP c0 a_3) (cP a_2 a_3)) True) (Eq False True) % 4.08/4.29 Clause #86 (by clausification #[85]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (cP a_2 c0) (cP c0 a_3) (cP a_2 a_3)) True % 4.08/4.29 Clause #87 (by superposition #[86, 5]): Eq True False % 4.08/4.29 Clause #91 (by clausification #[87]): False % 4.08/4.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------