%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV233^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 7.49s 7.70s % Output : Proof 7.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.10 % Problem : SEV233^5 : TPTP v9.2.0. Released v4.0.0. % 0.09/0.11 % Command : duper %s % 0.11/0.31 % Computer : n021.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Fri Oct 3 01:32:08 EDT 2025 % 0.11/0.31 % CPUTime : % 7.49/7.70 SZS status Theorem for theBenchmark.p % 7.49/7.70 SZS output start Proof for theBenchmark.p % 7.49/7.70 Clause #0 (by assumption #[]): Eq % 7.49/7.70 (Not % 7.49/7.70 (∀ (Xx : Iota → Prop), % 7.49/7.70 (∀ (Xx0 : Iota), Xx Xx0 → And (cD Xx0) (cE Xx0)) → % 7.49/7.70 And (∀ (Xx0 : Iota), Xx Xx0 → cD Xx0) (∀ (Xx0 : Iota), Xx Xx0 → cE Xx0))) % 7.49/7.70 True % 7.49/7.70 Clause #1 (by clausification #[0]): Eq % 7.49/7.70 (∀ (Xx : Iota → Prop), % 7.49/7.70 (∀ (Xx0 : Iota), Xx Xx0 → And (cD Xx0) (cE Xx0)) → % 7.49/7.70 And (∀ (Xx0 : Iota), Xx Xx0 → cD Xx0) (∀ (Xx0 : Iota), Xx Xx0 → cE Xx0)) % 7.49/7.70 False % 7.49/7.70 Clause #2 (by clausification #[1]): ∀ (a : Iota → Prop), % 7.49/7.70 Eq % 7.49/7.70 (Not % 7.49/7.70 ((∀ (Xx0 : Iota), skS.0 0 a Xx0 → And (cD Xx0) (cE Xx0)) → % 7.49/7.70 And (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cD Xx0) (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0))) % 7.49/7.70 True % 7.49/7.70 Clause #3 (by clausification #[2]): ∀ (a : Iota → Prop), % 7.49/7.70 Eq % 7.49/7.70 ((∀ (Xx0 : Iota), skS.0 0 a Xx0 → And (cD Xx0) (cE Xx0)) → % 7.49/7.70 And (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cD Xx0) (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0)) % 7.49/7.70 False % 7.49/7.70 Clause #4 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (∀ (Xx0 : Iota), skS.0 0 a Xx0 → And (cD Xx0) (cE Xx0)) True % 7.49/7.70 Clause #5 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (And (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cD Xx0) (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0)) False % 7.49/7.70 Clause #6 (by clausification #[4]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (skS.0 0 a a_1 → And (cD a_1) (cE a_1)) True % 7.49/7.70 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a a_1) False) (Eq (And (cD a_1) (cE a_1)) True) % 7.49/7.70 Clause #8 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a a_1) False) (Eq (cE a_1) True) % 7.49/7.70 Clause #9 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a a_1) False) (Eq (cD a_1) True) % 7.49/7.70 Clause #10 (by clausification #[5]): ∀ (a : Iota → Prop), % 7.49/7.70 Or (Eq (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cD Xx0) False) (Eq (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0) False) % 7.49/7.70 Clause #11 (by clausification #[10]): ∀ (a : Iota → Prop) (a_1 : Iota), % 7.49/7.70 Or (Eq (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0) False) % 7.49/7.70 (Eq (Not (skS.0 0 a (skS.0 1 a a_1) → cD (skS.0 1 a a_1))) True) % 7.49/7.70 Clause #12 (by clausification #[11]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.70 Or (Eq (Not (skS.0 0 a (skS.0 1 a a_1) → cD (skS.0 1 a a_1))) True) % 7.49/7.70 (Eq (Not (skS.0 0 a (skS.0 2 a a_2) → cE (skS.0 2 a a_2))) True) % 7.49/7.70 Clause #13 (by clausification #[12]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.70 Or (Eq (Not (skS.0 0 a (skS.0 2 a a_1) → cE (skS.0 2 a a_1))) True) % 7.49/7.70 (Eq (skS.0 0 a (skS.0 1 a a_2) → cD (skS.0 1 a a_2)) False) % 7.49/7.70 Clause #14 (by clausification #[13]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.70 Or (Eq (skS.0 0 a (skS.0 1 a a_1) → cD (skS.0 1 a a_1)) False) % 7.49/7.70 (Eq (skS.0 0 a (skS.0 2 a a_2) → cE (skS.0 2 a a_2)) False) % 7.49/7.70 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.70 Or (Eq (skS.0 0 a (skS.0 2 a a_1) → cE (skS.0 2 a a_1)) False) (Eq (skS.0 0 a (skS.0 1 a a_2)) True) % 7.49/7.70 Clause #16 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.70 Or (Eq (skS.0 0 a (skS.0 2 a a_1) → cE (skS.0 2 a a_1)) False) (Eq (cD (skS.0 1 a a_2)) False) % 7.49/7.70 Clause #17 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Eq (skS.0 0 a (skS.0 2 a a_2)) True) % 7.49/7.70 Clause #18 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Eq (cE (skS.0 2 a a_2)) False) % 7.49/7.70 Clause #20 (by superposition #[17, 8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.70 Or (Eq (skS.0 0 (fun x => a x) (skS.0 1 (fun x => a x) a_1)) True) (Or (Eq True False) (Eq (cE (skS.0 2 a a_2)) True)) % 7.49/7.70 Clause #23 (by clausification #[16]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cD (skS.0 1 a a_1)) False) (Eq (skS.0 0 a (skS.0 2 a a_2)) True) % 7.49/7.70 Clause #24 (by clausification #[16]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cD (skS.0 1 a a_1)) False) (Eq (cE (skS.0 2 a a_2)) False) % 7.49/7.70 Clause #59 (by betaEtaReduce #[20]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.75 Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Or (Eq True False) (Eq (cE (skS.0 2 a a_2)) True)) % 7.49/7.75 Clause #60 (by clausification #[59]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Eq (cE (skS.0 2 a a_2)) True) % 7.49/7.75 Clause #62 (by superposition #[60, 9]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.75 Or (Eq (cE (skS.0 2 (fun x => a x) a_1)) True) (Or (Eq True False) (Eq (cD (skS.0 1 a a_2)) True)) % 7.49/7.75 Clause #71 (by betaEtaReduce #[62]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.75 Or (Eq (cE (skS.0 2 a a_1)) True) (Or (Eq True False) (Eq (cD (skS.0 1 a a_2)) True)) % 7.49/7.75 Clause #72 (by clausification #[71]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Eq (cD (skS.0 1 a a_2)) True) % 7.49/7.75 Clause #74 (by superposition #[72, 23]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.75 Or (Eq (cE (skS.0 2 (fun x => a x) a_1)) True) (Or (Eq True False) (Eq (skS.0 0 a (skS.0 2 a a_2)) True)) % 7.49/7.75 Clause #118 (by betaEtaReduce #[74]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.75 Or (Eq (cE (skS.0 2 a a_1)) True) (Or (Eq True False) (Eq (skS.0 0 a (skS.0 2 a a_2)) True)) % 7.49/7.75 Clause #119 (by clausification #[118]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Eq (skS.0 0 a (skS.0 2 a a_2)) True) % 7.49/7.75 Clause #122 (by superposition #[119, 8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.75 Or (Eq (cE (skS.0 2 (fun x => a x) a_1)) True) (Or (Eq True False) (Eq (cE (skS.0 2 a a_2)) True)) % 7.49/7.75 Clause #126 (by betaEtaReduce #[122]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 7.49/7.75 Or (Eq (cE (skS.0 2 a a_1)) True) (Or (Eq True False) (Eq (cE (skS.0 2 a a_2)) True)) % 7.49/7.75 Clause #127 (by clausification #[126]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Eq (cE (skS.0 2 a a_2)) True) % 7.49/7.75 Clause #130 (by equality factoring #[127]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Ne True True) (Eq (cE (skS.0 2 a a_1)) True) % 7.49/7.75 Clause #136 (by clausification #[130]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Or (Eq True False) (Eq True False)) % 7.49/7.75 Clause #138 (by clausification #[136]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Eq True False) % 7.49/7.75 Clause #139 (by clausification #[138]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cE (skS.0 2 a a_1)) True % 7.49/7.75 Clause #140 (by superposition #[139, 18]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Eq True False) % 7.49/7.75 Clause #143 (by clausification #[140]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (skS.0 0 a (skS.0 1 a a_1)) True % 7.49/7.75 Clause #145 (by superposition #[143, 9]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq True False) (Eq (cD (skS.0 1 a a_1)) True) % 7.49/7.75 Clause #146 (by clausification #[145]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cD (skS.0 1 a a_1)) True % 7.49/7.75 Clause #148 (by superposition #[146, 24]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq True False) (Eq (cE (skS.0 2 a a_1)) False) % 7.49/7.75 Clause #149 (by clausification #[148]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cE (skS.0 2 a a_1)) False % 7.49/7.75 Clause #150 (by superposition #[149, 139]): Eq False True % 7.49/7.75 Clause #152 (by clausification #[150]): False % 7.49/7.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------