%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV194^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 3.98s 4.14s % Output : Proof 3.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV194^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n003.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 01:50:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.98/4.14 SZS status Theorem for theBenchmark.p % 3.98/4.14 SZS output start Proof for theBenchmark.p % 3.98/4.14 Clause #0 (by assumption #[]): Eq % 3.98/4.14 (Not % 3.98/4.14 (∀ (R : a → a → a → Prop), % 3.98/4.14 And True % 3.98/4.14 (∀ (Xa Xb Xc : a), % 3.98/4.14 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 3.98/4.14 (Exists fun Xx1 => % 3.98/4.14 Exists fun Xx2 => % 3.98/4.14 Exists fun Xy1 => % 3.98/4.14 Exists fun Xy2 => % 3.98/4.14 Exists fun Xz1 => % 3.98/4.14 Exists fun Xz2 => % 3.98/4.14 And % 3.98/4.14 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 3.98/4.14 (R Xx1 Xy1 Xz1)) % 3.98/4.14 (R Xx2 Xy2 Xz2)) → % 3.98/4.14 R Xa Xb Xc) → % 3.98/4.14 R c0 x x)) % 3.98/4.14 True % 3.98/4.14 Clause #1 (by clausification #[0]): Eq % 3.98/4.14 (∀ (R : a → a → a → Prop), % 3.98/4.14 And True % 3.98/4.14 (∀ (Xa Xb Xc : a), % 3.98/4.14 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 3.98/4.14 (Exists fun Xx1 => % 3.98/4.14 Exists fun Xx2 => % 3.98/4.14 Exists fun Xy1 => % 3.98/4.14 Exists fun Xy2 => % 3.98/4.14 Exists fun Xz1 => % 3.98/4.14 Exists fun Xz2 => % 3.98/4.14 And % 3.98/4.14 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 3.98/4.14 (R Xx1 Xy1 Xz1)) % 3.98/4.14 (R Xx2 Xy2 Xz2)) → % 3.98/4.14 R Xa Xb Xc) → % 3.98/4.14 R c0 x x) % 3.98/4.14 False % 3.98/4.14 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → a → Prop), % 3.98/4.14 Eq % 3.98/4.14 (Not % 3.98/4.14 (And True % 3.98/4.14 (∀ (Xa Xb Xc : a), % 3.98/4.14 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 3.98/4.14 (Exists fun Xx1 => % 3.98/4.14 Exists fun Xx2 => % 3.98/4.14 Exists fun Xy1 => % 3.98/4.14 Exists fun Xy2 => % 3.98/4.14 Exists fun Xz1 => % 3.98/4.14 Exists fun Xz2 => % 3.98/4.14 And % 3.98/4.14 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 3.98/4.14 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 3.98/4.14 (skS.0 0 a_1 Xx2 Xy2 Xz2)) → % 3.98/4.14 skS.0 0 a_1 Xa Xb Xc) → % 3.98/4.14 skS.0 0 a_1 c0 x x)) % 3.98/4.14 True % 3.98/4.14 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → a → Prop), % 3.98/4.14 Eq % 3.98/4.14 (And True % 3.98/4.14 (∀ (Xa Xb Xc : a), % 3.98/4.14 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 3.98/4.14 (Exists fun Xx1 => % 3.98/4.14 Exists fun Xx2 => % 3.98/4.14 Exists fun Xy1 => % 3.98/4.14 Exists fun Xy2 => % 3.98/4.14 Exists fun Xz1 => % 3.98/4.14 Exists fun Xz2 => % 3.98/4.14 And % 3.98/4.14 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 3.98/4.14 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 3.98/4.14 (skS.0 0 a_1 Xx2 Xy2 Xz2)) → % 3.98/4.14 skS.0 0 a_1 Xa Xb Xc) → % 3.98/4.14 skS.0 0 a_1 c0 x x) % 3.98/4.14 False % 3.98/4.14 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop), % 3.98/4.14 Eq % 3.98/4.14 (And True % 3.98/4.14 (∀ (Xa Xb Xc : a), % 3.98/4.14 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 3.98/4.14 (Exists fun Xx1 => % 3.98/4.14 Exists fun Xx2 => % 3.98/4.14 Exists fun Xy1 => % 3.98/4.14 Exists fun Xy2 => % 3.98/4.14 Exists fun Xz1 => % 3.98/4.14 Exists fun Xz2 => % 3.98/4.14 And % 3.98/4.14 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 3.98/4.14 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 3.98/4.14 (skS.0 0 a_1 Xx2 Xy2 Xz2)) → % 3.98/4.14 skS.0 0 a_1 Xa Xb Xc)) % 3.98/4.14 True % 3.98/4.14 Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop), Eq (skS.0 0 a_1 c0 x x) False % 3.98/4.14 Clause #6 (by clausification #[4]): ∀ (a_1 : a → a → a → Prop), % 3.98/4.14 Eq % 3.98/4.14 (∀ (Xa Xb Xc : a), % 3.98/4.14 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc))) % 3.98/4.14 (Exists fun Xx1 => % 3.98/4.14 Exists fun Xx2 => % 3.98/4.14 Exists fun Xy1 => % 3.98/4.16 Exists fun Xy2 => % 3.98/4.16 Exists fun Xz1 => % 3.98/4.16 Exists fun Xz2 => % 3.98/4.16 And % 3.98/4.16 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 3.98/4.16 (skS.0 0 a_1 Xx1 Xy1 Xz1)) % 3.98/4.16 (skS.0 0 a_1 Xx2 Xy2 Xz2)) → % 3.98/4.16 skS.0 0 a_1 Xa Xb Xc) % 3.98/4.16 True % 3.98/4.16 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : a → a → a → Prop), % 3.98/4.16 Eq % 3.98/4.16 (∀ (Xb Xc : a), % 3.98/4.16 Or (Or (And (Eq a_1 c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq a_1 Xc))) % 3.98/4.16 (Exists fun Xx1 => % 3.98/4.16 Exists fun Xx2 => % 3.98/4.16 Exists fun Xy1 => % 3.98/4.16 Exists fun Xy2 => % 3.98/4.16 Exists fun Xz1 => % 3.98/4.16 Exists fun Xz2 => % 3.98/4.16 And % 3.98/4.16 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 3.98/4.16 (skS.0 0 a_2 Xx1 Xy1 Xz1)) % 3.98/4.16 (skS.0 0 a_2 Xx2 Xy2 Xz2)) → % 3.98/4.16 skS.0 0 a_2 a_1 Xb Xc) % 3.98/4.16 True % 3.98/4.16 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 : a) (a_3 : a → a → a → Prop), % 3.98/4.16 Eq % 3.98/4.16 (∀ (Xc : a), % 3.98/4.16 Or (Or (And (Eq a_1 c0) (Eq a_2 Xc)) (And (Eq a_2 c0) (Eq a_1 Xc))) % 3.98/4.16 (Exists fun Xx1 => % 3.98/4.16 Exists fun Xx2 => % 3.98/4.16 Exists fun Xy1 => % 3.98/4.16 Exists fun Xy2 => % 3.98/4.16 Exists fun Xz1 => % 3.98/4.16 Exists fun Xz2 => % 3.98/4.16 And % 3.98/4.16 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2))) % 3.98/4.16 (skS.0 0 a_3 Xx1 Xy1 Xz1)) % 3.98/4.16 (skS.0 0 a_3 Xx2 Xy2 Xz2)) → % 3.98/4.16 skS.0 0 a_3 a_1 a_2 Xc) % 3.98/4.16 True % 3.98/4.16 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop), % 3.98/4.16 Eq % 3.98/4.16 (Or (Or (And (Eq a_1 c0) (Eq a_2 a_3)) (And (Eq a_2 c0) (Eq a_1 a_3))) % 3.98/4.16 (Exists fun Xx1 => % 3.98/4.16 Exists fun Xx2 => % 3.98/4.16 Exists fun Xy1 => % 3.98/4.16 Exists fun Xy2 => % 3.98/4.16 Exists fun Xz1 => % 3.98/4.16 Exists fun Xz2 => % 3.98/4.16 And % 3.98/4.16 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2))) % 3.98/4.16 (skS.0 0 a_4 Xx1 Xy1 Xz1)) % 3.98/4.16 (skS.0 0 a_4 Xx2 Xy2 Xz2)) → % 3.98/4.16 skS.0 0 a_4 a_1 a_2 a_3) % 3.98/4.16 True % 3.98/4.16 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop), % 3.98/4.16 Or % 3.98/4.16 (Eq % 3.98/4.16 (Or (Or (And (Eq a_1 c0) (Eq a_2 a_3)) (And (Eq a_2 c0) (Eq a_1 a_3))) % 3.98/4.16 (Exists fun Xx1 => % 3.98/4.16 Exists fun Xx2 => % 3.98/4.16 Exists fun Xy1 => % 3.98/4.16 Exists fun Xy2 => % 3.98/4.16 Exists fun Xz1 => % 3.98/4.16 Exists fun Xz2 => % 3.98/4.16 And % 3.98/4.16 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2))) % 3.98/4.16 (skS.0 0 a_4 Xx1 Xy1 Xz1)) % 3.98/4.16 (skS.0 0 a_4 Xx2 Xy2 Xz2))) % 3.98/4.16 False) % 3.98/4.16 (Eq (skS.0 0 a_4 a_1 a_2 a_3) True) % 3.98/4.16 Clause #13 (by clausification #[11]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 3.98/4.16 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) % 3.98/4.16 Clause #31 (by clausification #[13]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 3.98/4.16 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) % 3.98/4.16 Clause #38 (by clausification #[31]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 3.98/4.16 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)) % 3.98/4.16 Clause #39 (by clausification #[38]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), % 3.98/4.16 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)) % 3.98/4.16 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)) % 3.98/4.16 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) % 3.98/4.16 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 % 3.98/4.16 Clause #43 (by superposition #[42, 5]): Eq True False % 3.98/4.16 Clause #48 (by clausification #[43]): False % 3.98/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------