%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV228^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 08:02:58 PM UTC 2025 % Result : Theorem 4.61s 4.79s % Output : Proof 4.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEV228^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n025.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 01:13:38 EDT 2025 % 0.13/0.35 % CPUTime : % 4.61/4.79 SZS status Theorem for theBenchmark.p % 4.61/4.79 SZS output start Proof for theBenchmark.p % 4.61/4.79 Clause #0 (by assumption #[]): Eq (Not (∀ (Xx : a), cS Xx → Exists fun S_11 => And (∀ (Xx0 : a), S_11 Xx0 → cS Xx0) (S_11 Xx))) True % 4.61/4.79 Clause #1 (by clausification #[0]): Eq (∀ (Xx : a), cS Xx → Exists fun S_11 => And (∀ (Xx0 : a), S_11 Xx0 → cS Xx0) (S_11 Xx)) False % 4.61/4.79 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 4.61/4.79 Eq (Not (cS (skS.0 0 a_1) → Exists fun S_11 => And (∀ (Xx0 : a), S_11 Xx0 → cS Xx0) (S_11 (skS.0 0 a_1)))) True % 4.61/4.79 Clause #3 (by clausification #[2]): ∀ (a_1 : a), Eq (cS (skS.0 0 a_1) → Exists fun S_11 => And (∀ (Xx0 : a), S_11 Xx0 → cS Xx0) (S_11 (skS.0 0 a_1))) False % 4.61/4.79 Clause #4 (by clausification #[3]): ∀ (a_1 : a), Eq (cS (skS.0 0 a_1)) True % 4.61/4.79 Clause #5 (by clausification #[3]): ∀ (a_1 : a), Eq (Exists fun S_11 => And (∀ (Xx0 : a), S_11 Xx0 → cS Xx0) (S_11 (skS.0 0 a_1))) False % 4.61/4.79 Clause #6 (by clausification #[5]): ∀ (a_1 : a → Prop) (a_2 : a), Eq (And (∀ (Xx0 : a), a_1 Xx0 → cS Xx0) (a_1 (skS.0 0 a_2))) False % 4.61/4.79 Clause #7 (by clausification #[6]): ∀ (a_1 : a → Prop) (a_2 : a), Or (Eq (∀ (Xx0 : a), a_1 Xx0 → cS Xx0) False) (Eq (a_1 (skS.0 0 a_2)) False) % 4.61/4.79 Clause #8 (by clausification #[7]): ∀ (a_1 : a → Prop) (a_2 a_3 : a), % 4.61/4.79 Or (Eq (a_1 (skS.0 0 a_2)) False) (Eq (Not (a_1 (skS.0 1 a_1 a_3) → cS (skS.0 1 a_1 a_3))) True) % 4.61/4.79 Clause #9 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 a_3 : a), % 4.61/4.79 Or (Eq (a_1 (skS.0 0 a_2)) False) (Eq (a_1 (skS.0 1 a_1 a_3) → cS (skS.0 1 a_1 a_3)) False) % 4.61/4.79 Clause #10 (by clausification #[9]): ∀ (a_1 : a → Prop) (a_2 a_3 : a), Or (Eq (a_1 (skS.0 0 a_2)) False) (Eq (a_1 (skS.0 1 a_1 a_3)) True) % 4.61/4.79 Clause #11 (by clausification #[9]): ∀ (a_1 : a → Prop) (a_2 a_3 : a), Or (Eq (a_1 (skS.0 0 a_2)) False) (Eq (cS (skS.0 1 a_1 a_3)) False) % 4.61/4.79 Clause #12 (by superposition #[10, 4]): ∀ (a_1 : a), Or (Eq ((fun x => cS x) (skS.0 1 (fun x => cS x) a_1)) True) (Eq False True) % 4.61/4.79 Clause #21 (by betaEtaReduce #[12]): ∀ (a_1 : a), Or (Eq (cS (skS.0 1 cS a_1)) True) (Eq False True) % 4.61/4.79 Clause #22 (by clausification #[21]): ∀ (a_1 : a), Eq (cS (skS.0 1 cS a_1)) True % 4.61/4.79 Clause #25 (by superposition #[11, 4]): ∀ (a_1 : a), Or (Eq (cS (skS.0 1 (fun x => cS x) a_1)) False) (Eq False True) % 4.61/4.79 Clause #39 (by betaEtaReduce #[25]): ∀ (a_1 : a), Or (Eq (cS (skS.0 1 cS a_1)) False) (Eq False True) % 4.61/4.79 Clause #40 (by clausification #[39]): ∀ (a_1 : a), Eq (cS (skS.0 1 cS a_1)) False % 4.61/4.79 Clause #41 (by superposition #[40, 22]): Eq False True % 4.61/4.79 Clause #44 (by clausification #[41]): False % 4.61/4.79 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------