%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV200^5 : 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 08:02:56 PM UTC 2025 % Result : Theorem 4.15s 4.37s % Output : Proof 4.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV200^5 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.14 % Command : duper %s % 0.13/0.35 % Computer : n018.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 01:33:08 EDT 2025 % 0.20/0.35 % CPUTime : % 4.15/4.37 SZS status Theorem for theBenchmark.p % 4.15/4.37 SZS output start Proof for theBenchmark.p % 4.15/4.37 Clause #0 (by assumption #[]): Eq % 4.15/4.37 (Not % 4.15/4.37 (And % 4.15/4.37 (And (∀ (Xx0 Xy : a), Ne (cP Xx0 Xy) cZ) % 4.15/4.37 (∀ (Xx0 Xy Xu Xv : a), Eq (cP Xx0 Xu) (cP Xy Xv) → And (Eq Xx0 Xy) (Eq Xu Xv))) % 4.15/4.37 (∀ (X : a → Prop), And (X cZ) (∀ (Xx0 Xy : a), And (X Xx0) (X Xy) → X (cP Xx0 Xy)) → ∀ (Xx0 : a), X Xx0) → % 4.15/4.37 ∀ (R : a → a → a → Prop), % 4.15/4.37 And True % 4.15/4.37 (∀ (Xa Xb Xc : a), % 4.15/4.37 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc))) % 4.15/4.37 (Exists fun Xx1 => % 4.15/4.37 Exists fun Xx2 => % 4.15/4.37 Exists fun Xy1 => % 4.15/4.37 Exists fun Xy2 => % 4.15/4.37 Exists fun Xz1 => % 4.15/4.37 Exists fun Xz2 => % 4.15/4.37 And % 4.15/4.37 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.15/4.37 (R Xx1 Xy1 Xz1)) % 4.15/4.37 (R Xx2 Xy2 Xz2)) → % 4.15/4.37 R Xa Xb Xc) → % 4.15/4.37 R cZ x x)) % 4.15/4.37 True % 4.15/4.37 Clause #1 (by clausification #[0]): Eq % 4.15/4.37 (And % 4.15/4.37 (And (∀ (Xx0 Xy : a), Ne (cP Xx0 Xy) cZ) % 4.15/4.37 (∀ (Xx0 Xy Xu Xv : a), Eq (cP Xx0 Xu) (cP Xy Xv) → And (Eq Xx0 Xy) (Eq Xu Xv))) % 4.15/4.37 (∀ (X : a → Prop), And (X cZ) (∀ (Xx0 Xy : a), And (X Xx0) (X Xy) → X (cP Xx0 Xy)) → ∀ (Xx0 : a), X Xx0) → % 4.15/4.37 ∀ (R : a → a → a → Prop), % 4.15/4.37 And True % 4.15/4.37 (∀ (Xa Xb Xc : a), % 4.15/4.37 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc))) % 4.15/4.37 (Exists fun Xx1 => % 4.15/4.37 Exists fun Xx2 => % 4.15/4.37 Exists fun Xy1 => % 4.15/4.37 Exists fun Xy2 => % 4.15/4.37 Exists fun Xz1 => % 4.15/4.37 Exists fun Xz2 => % 4.15/4.37 And % 4.15/4.37 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.15/4.37 (R Xx1 Xy1 Xz1)) % 4.15/4.37 (R Xx2 Xy2 Xz2)) → % 4.15/4.38 R Xa Xb Xc) → % 4.15/4.38 R cZ x x) % 4.15/4.38 False % 4.15/4.38 Clause #3 (by clausification #[1]): Eq % 4.15/4.38 (∀ (R : a → a → a → Prop), % 4.15/4.38 And True % 4.15/4.38 (∀ (Xa Xb Xc : a), % 4.15/4.38 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc))) % 4.15/4.38 (Exists fun Xx1 => % 4.15/4.38 Exists fun Xx2 => % 4.15/4.38 Exists fun Xy1 => % 4.15/4.38 Exists fun Xy2 => % 4.15/4.38 Exists fun Xz1 => % 4.15/4.38 Exists fun Xz2 => % 4.15/4.38 And % 4.15/4.38 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.15/4.38 (R Xx1 Xy1 Xz1)) % 4.15/4.38 (R Xx2 Xy2 Xz2)) → % 4.15/4.38 R Xa Xb Xc) → % 4.15/4.38 R cZ x x) % 4.15/4.38 False % 4.15/4.38 Clause #26 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop), % 4.15/4.38 Eq % 4.15/4.38 (Not % 4.15/4.38 (And True % 4.15/4.38 (∀ (Xa Xb Xc : a), % 4.15/4.38 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc))) % 4.15/4.38 (Exists fun Xx1 => % 4.15/4.38 Exists fun Xx2 => % 4.15/4.38 Exists fun Xy1 => % 4.15/4.38 Exists fun Xy2 => % 4.15/4.38 Exists fun Xz1 => % 4.15/4.38 Exists fun Xz2 => % 4.15/4.38 And % 4.15/4.38 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.15/4.38 (skS.0 2 a_1 Xx1 Xy1 Xz1)) % 4.15/4.38 (skS.0 2 a_1 Xx2 Xy2 Xz2)) → % 4.15/4.38 skS.0 2 a_1 Xa Xb Xc) → % 4.15/4.38 skS.0 2 a_1 cZ x x)) % 4.15/4.38 True % 4.15/4.38 Clause #27 (by clausification #[26]): ∀ (a_1 : a → a → a → Prop), % 4.15/4.38 Eq % 4.15/4.38 (And True % 4.15/4.38 (∀ (Xa Xb Xc : a), % 4.15/4.38 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc))) % 4.15/4.38 (Exists fun Xx1 => % 4.15/4.38 Exists fun Xx2 => % 4.15/4.38 Exists fun Xy1 => % 4.15/4.38 Exists fun Xy2 => % 4.15/4.38 Exists fun Xz1 => % 4.15/4.38 Exists fun Xz2 => % 4.15/4.38 And % 4.15/4.38 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.22/4.40 (skS.0 2 a_1 Xx1 Xy1 Xz1)) % 4.22/4.40 (skS.0 2 a_1 Xx2 Xy2 Xz2)) → % 4.22/4.40 skS.0 2 a_1 Xa Xb Xc) → % 4.22/4.40 skS.0 2 a_1 cZ x x) % 4.22/4.40 False % 4.22/4.40 Clause #28 (by clausification #[27]): ∀ (a_1 : a → a → a → Prop), % 4.22/4.40 Eq % 4.22/4.40 (And True % 4.22/4.40 (∀ (Xa Xb Xc : a), % 4.22/4.40 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc))) % 4.22/4.40 (Exists fun Xx1 => % 4.22/4.40 Exists fun Xx2 => % 4.22/4.40 Exists fun Xy1 => % 4.22/4.40 Exists fun Xy2 => % 4.22/4.40 Exists fun Xz1 => % 4.22/4.40 Exists fun Xz2 => % 4.22/4.40 And % 4.22/4.40 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.22/4.40 (skS.0 2 a_1 Xx1 Xy1 Xz1)) % 4.22/4.40 (skS.0 2 a_1 Xx2 Xy2 Xz2)) → % 4.22/4.40 skS.0 2 a_1 Xa Xb Xc)) % 4.22/4.40 True % 4.22/4.40 Clause #29 (by clausification #[27]): ∀ (a_1 : a → a → a → Prop), Eq (skS.0 2 a_1 cZ x x) False % 4.22/4.40 Clause #30 (by clausification #[28]): ∀ (a_1 : a → a → a → Prop), % 4.22/4.40 Eq % 4.22/4.40 (∀ (Xa Xb Xc : a), % 4.22/4.40 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc))) % 4.22/4.40 (Exists fun Xx1 => % 4.22/4.40 Exists fun Xx2 => % 4.22/4.40 Exists fun Xy1 => % 4.22/4.40 Exists fun Xy2 => % 4.22/4.40 Exists fun Xz1 => % 4.22/4.40 Exists fun Xz2 => % 4.22/4.40 And % 4.22/4.40 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.22/4.40 (skS.0 2 a_1 Xx1 Xy1 Xz1)) % 4.22/4.40 (skS.0 2 a_1 Xx2 Xy2 Xz2)) → % 4.22/4.40 skS.0 2 a_1 Xa Xb Xc) % 4.22/4.40 True % 4.22/4.40 Clause #32 (by clausification #[30]): ∀ (a_1 : a) (a_2 : a → a → a → Prop), % 4.22/4.40 Eq % 4.22/4.40 (∀ (Xb Xc : a), % 4.22/4.40 Or (Or (And (Eq a_1 cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq a_1 Xc))) % 4.22/4.40 (Exists fun Xx1 => % 4.22/4.40 Exists fun Xx2 => % 4.22/4.40 Exists fun Xy1 => % 4.22/4.40 Exists fun Xy2 => % 4.22/4.40 Exists fun Xz1 => % 4.22/4.40 Exists fun Xz2 => % 4.22/4.40 And % 4.22/4.40 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.22/4.40 (skS.0 2 a_2 Xx1 Xy1 Xz1)) % 4.22/4.40 (skS.0 2 a_2 Xx2 Xy2 Xz2)) → % 4.22/4.40 skS.0 2 a_2 a_1 Xb Xc) % 4.22/4.40 True % 4.22/4.40 Clause #33 (by clausification #[32]): ∀ (a_1 a_2 : a) (a_3 : a → a → a → Prop), % 4.22/4.40 Eq % 4.22/4.40 (∀ (Xc : a), % 4.22/4.40 Or (Or (And (Eq a_1 cZ) (Eq a_2 Xc)) (And (Eq a_2 cZ) (Eq a_1 Xc))) % 4.22/4.40 (Exists fun Xx1 => % 4.22/4.40 Exists fun Xx2 => % 4.22/4.40 Exists fun Xy1 => % 4.22/4.40 Exists fun Xy2 => % 4.22/4.40 Exists fun Xz1 => % 4.22/4.40 Exists fun Xz2 => % 4.22/4.40 And % 4.22/4.40 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 4.22/4.40 (skS.0 2 a_3 Xx1 Xy1 Xz1)) % 4.22/4.40 (skS.0 2 a_3 Xx2 Xy2 Xz2)) → % 4.22/4.40 skS.0 2 a_3 a_1 a_2 Xc) % 4.22/4.40 True % 4.22/4.40 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop), % 4.22/4.40 Eq % 4.22/4.40 (Or (Or (And (Eq a_1 cZ) (Eq a_2 a_3)) (And (Eq a_2 cZ) (Eq a_1 a_3))) % 4.22/4.40 (Exists fun Xx1 => % 4.22/4.40 Exists fun Xx2 => % 4.22/4.40 Exists fun Xy1 => % 4.22/4.40 Exists fun Xy2 => % 4.22/4.40 Exists fun Xz1 => % 4.22/4.40 Exists fun Xz2 => % 4.22/4.40 And % 4.22/4.40 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2))) % 4.22/4.40 (skS.0 2 a_4 Xx1 Xy1 Xz1)) % 4.22/4.40 (skS.0 2 a_4 Xx2 Xy2 Xz2)) → % 4.22/4.40 skS.0 2 a_4 a_1 a_2 a_3) % 4.22/4.40 True % 4.22/4.40 Clause #35 (by clausification #[34]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop), % 4.22/4.40 Or % 4.22/4.40 (Eq % 4.22/4.40 (Or (Or (And (Eq a_1 cZ) (Eq a_2 a_3)) (And (Eq a_2 cZ) (Eq a_1 a_3))) % 4.22/4.40 (Exists fun Xx1 => % 4.22/4.40 Exists fun Xx2 => % 4.22/4.40 Exists fun Xy1 => % 4.22/4.40 Exists fun Xy2 => % 4.22/4.40 Exists fun Xz1 => % 4.22/4.40 Exists fun Xz2 => % 4.22/4.40 And % 4.22/4.40 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2))) % 4.22/4.41 (skS.0 2 a_4 Xx1 Xy1 Xz1)) % 4.22/4.41 (skS.0 2 a_4 Xx2 Xy2 Xz2))) % 4.22/4.41 False) % 4.22/4.41 (Eq (skS.0 2 a_4 a_1 a_2 a_3) True) % 4.22/4.41 Clause #37 (by clausification #[35]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.22/4.41 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Eq (Or (And (Eq a_2 cZ) (Eq a_3 a_4)) (And (Eq a_3 cZ) (Eq a_2 a_4))) False) % 4.22/4.41 Clause #189 (by clausification #[37]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.22/4.41 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Eq (And (Eq a_2 cZ) (Eq a_3 a_4)) False) % 4.22/4.41 Clause #217 (by clausification #[189]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.22/4.41 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_2 cZ) False) (Eq (Eq a_3 a_4) False)) % 4.22/4.41 Clause #218 (by clausification #[217]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 4.22/4.41 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_3 a_4) False) (Ne a_2 cZ)) % 4.22/4.41 Clause #219 (by clausification #[218]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Ne a_2 cZ) (Ne a_3 a_4)) % 4.22/4.41 Clause #220 (by destructive equality resolution #[219]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 2 a_1 cZ a_2 a_3) True) (Ne a_2 a_3) % 4.22/4.41 Clause #221 (by destructive equality resolution #[220]): ∀ (a_1 : a → a → a → Prop) (a_2 : a), Eq (skS.0 2 a_1 cZ a_2 a_2) True % 4.22/4.41 Clause #222 (by superposition #[221, 29]): Eq True False % 4.22/4.41 Clause #230 (by clausification #[222]): False % 4.22/4.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------