%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU846^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:02:33 PM UTC 2025 % Result : Theorem 3.57s 3.78s % Output : Proof 3.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU846^5 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n007.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 : Fri Oct 3 05:14:23 EDT 2025 % 0.14/0.34 % CPUTime : % 3.57/3.78 SZS status Theorem for theBenchmark.p % 3.57/3.78 SZS output start Proof for theBenchmark.p % 3.57/3.78 Clause #0 (by assumption #[]): Eq % 3.57/3.78 (Not % 3.57/3.78 (∀ (S T U : a → Prop), % 3.57/3.78 And (And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx)) (∀ (Xx : a), S Xx → T Xx) → % 3.57/3.78 ∀ (Xx : a), And (U Xx) (Not (T Xx)) → And (U Xx) (Not (S Xx)))) % 3.57/3.78 True % 3.57/3.78 Clause #1 (by clausification #[0]): Eq % 3.57/3.78 (∀ (S T U : a → Prop), % 3.57/3.78 And (And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx)) (∀ (Xx : a), S Xx → T Xx) → % 3.57/3.78 ∀ (Xx : a), And (U Xx) (Not (T Xx)) → And (U Xx) (Not (S Xx))) % 3.57/3.78 False % 3.57/3.78 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.57/3.78 Eq % 3.57/3.78 (Not % 3.57/3.78 (∀ (T U : a → Prop), % 3.57/3.78 And (And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx)) (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) → % 3.57/3.78 ∀ (Xx : a), And (U Xx) (Not (T Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx)))) % 3.57/3.78 True % 3.57/3.78 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.57/3.78 Eq % 3.57/3.78 (∀ (T U : a → Prop), % 3.57/3.78 And (And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx)) (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) → % 3.57/3.78 ∀ (Xx : a), And (U Xx) (Not (T Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx))) % 3.57/3.78 False % 3.57/3.78 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.57/3.78 Eq % 3.57/3.78 (Not % 3.57/3.78 (∀ (U : a → Prop), % 3.57/3.78 And (And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx)) % 3.57/3.78 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.57/3.78 ∀ (Xx : a), And (U Xx) (Not (skS.0 1 a_1 a_2 Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx)))) % 3.57/3.78 True % 3.57/3.78 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.57/3.78 Eq % 3.57/3.78 (∀ (U : a → Prop), % 3.57/3.78 And (And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx)) % 3.57/3.78 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.57/3.78 ∀ (Xx : a), And (U Xx) (Not (skS.0 1 a_1 a_2 Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx))) % 3.57/3.78 False % 3.57/3.78 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.57/3.78 Eq % 3.57/3.78 (Not % 3.57/3.78 (And % 3.57/3.78 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 3.57/3.78 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 3.57/3.78 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.57/3.78 ∀ (Xx : a), % 3.57/3.78 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → % 3.57/3.78 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))) % 3.57/3.78 True % 3.57/3.78 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.57/3.78 Eq % 3.57/3.78 (And % 3.57/3.78 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 3.57/3.78 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 3.57/3.78 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) → % 3.57/3.78 ∀ (Xx : a), % 3.57/3.78 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))) % 3.57/3.78 False % 3.57/3.78 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.57/3.78 Eq % 3.57/3.78 (And % 3.57/3.78 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) % 3.57/3.78 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx)) % 3.57/3.78 (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)) % 3.57/3.78 True % 3.57/3.78 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.57/3.78 Eq % 3.57/3.78 (∀ (Xx : a), % 3.57/3.78 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))) % 3.57/3.78 False % 3.57/3.78 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True % 3.57/3.78 Clause #12 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Eq (skS.0 0 a_1 a_2 → skS.0 1 a_1 a_3 a_2) True % 3.57/3.78 Clause #13 (by clausification #[12]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 1 a_1 a_3 a_2) True) % 3.57/3.78 Clause #14 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.57/3.78 Eq % 3.57/3.78 (Not % 3.57/3.78 (And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) → % 3.57/3.78 And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))))) % 3.57/3.80 True % 3.57/3.80 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.57/3.80 Eq % 3.57/3.80 (And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) → % 3.57/3.80 And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)))) % 3.57/3.80 False % 3.57/3.80 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.57/3.80 Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)))) True % 3.57/3.80 Clause #17 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.57/3.80 Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)))) False % 3.57/3.80 Clause #18 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) True % 3.57/3.80 Clause #19 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True % 3.57/3.80 Clause #20 (by clausification #[18]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) False % 3.57/3.80 Clause #27 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.57/3.80 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) False) % 3.57/3.80 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.57/3.80 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) % 3.57/3.80 Clause #29 (by superposition #[28, 19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.57/3.80 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True) % 3.57/3.80 (Eq False True) % 3.57/3.80 Clause #30 (by betaEtaReduce #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq False True) % 3.57/3.80 Clause #31 (by clausification #[30]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True % 3.57/3.80 Clause #33 (by superposition #[31, 13]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4 a_5)) True) % 3.57/3.80 Clause #35 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4 a_5)) True % 3.57/3.80 Clause #36 (by superposition #[35, 20]): Eq True False % 3.57/3.80 Clause #37 (by clausification #[36]): False % 3.57/3.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------