%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO308^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 08:08:53 PM UTC 2025 % Result : Theorem 3.34s 3.49s % Output : Proof 3.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SYO308^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.15 % Command : duper %s % 0.15/0.36 % Computer : n012.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 14:29:23 EDT 2025 % 0.15/0.36 % CPUTime : % 3.34/3.49 SZS status Theorem for theBenchmark.p % 3.34/3.49 SZS output start Proof for theBenchmark.p % 3.34/3.49 Clause #0 (by assumption #[]): Eq % 3.34/3.49 (Not % 3.34/3.49 (∀ (Z1 : Iota → Prop), % 3.34/3.49 Or (∀ (Z3 : Iota), Z1 Z3 → cA Z3) (∀ (Z4 : Iota), Z1 Z4 → cB Z4) → ∀ (Z5 : Iota), Z1 Z5 → Or (cA Z5) (cB Z5))) % 3.34/3.49 True % 3.34/3.49 Clause #1 (by clausification #[0]): Eq % 3.34/3.49 (∀ (Z1 : Iota → Prop), % 3.34/3.49 Or (∀ (Z3 : Iota), Z1 Z3 → cA Z3) (∀ (Z4 : Iota), Z1 Z4 → cB Z4) → ∀ (Z5 : Iota), Z1 Z5 → Or (cA Z5) (cB Z5)) % 3.34/3.49 False % 3.34/3.49 Clause #2 (by clausification #[1]): ∀ (a : Iota → Prop), % 3.34/3.49 Eq % 3.34/3.49 (Not % 3.34/3.49 (Or (∀ (Z3 : Iota), skS.0 0 a Z3 → cA Z3) (∀ (Z4 : Iota), skS.0 0 a Z4 → cB Z4) → % 3.34/3.49 ∀ (Z5 : Iota), skS.0 0 a Z5 → Or (cA Z5) (cB Z5))) % 3.34/3.49 True % 3.34/3.49 Clause #3 (by clausification #[2]): ∀ (a : Iota → Prop), % 3.34/3.49 Eq % 3.34/3.49 (Or (∀ (Z3 : Iota), skS.0 0 a Z3 → cA Z3) (∀ (Z4 : Iota), skS.0 0 a Z4 → cB Z4) → % 3.34/3.49 ∀ (Z5 : Iota), skS.0 0 a Z5 → Or (cA Z5) (cB Z5)) % 3.34/3.49 False % 3.34/3.49 Clause #4 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (Or (∀ (Z3 : Iota), skS.0 0 a Z3 → cA Z3) (∀ (Z4 : Iota), skS.0 0 a Z4 → cB Z4)) True % 3.34/3.49 Clause #5 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (∀ (Z5 : Iota), skS.0 0 a Z5 → Or (cA Z5) (cB Z5)) False % 3.34/3.49 Clause #6 (by clausification #[4]): ∀ (a : Iota → Prop), Or (Eq (∀ (Z3 : Iota), skS.0 0 a Z3 → cA Z3) True) (Eq (∀ (Z4 : Iota), skS.0 0 a Z4 → cB Z4) True) % 3.34/3.49 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (∀ (Z4 : Iota), skS.0 0 a Z4 → cB Z4) True) (Eq (skS.0 0 a a_1 → cA a_1) True) % 3.34/3.49 Clause #8 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (skS.0 0 a a_1 → cA a_1) True) (Eq (skS.0 0 a a_2 → cB a_2) True) % 3.34/3.49 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.34/3.49 Or (Eq (skS.0 0 a a_1 → cB a_1) True) (Or (Eq (skS.0 0 a a_2) False) (Eq (cA a_2) True)) % 3.34/3.49 Clause #10 (by clausification #[9]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.34/3.49 Or (Eq (skS.0 0 a a_1) False) (Or (Eq (cA a_1) True) (Or (Eq (skS.0 0 a a_2) False) (Eq (cB a_2) True))) % 3.34/3.49 Clause #11 (by clausification #[5]): ∀ (a : Iota → Prop) (a_1 : Iota), % 3.34/3.49 Eq (Not (skS.0 0 a (skS.0 1 a a_1) → Or (cA (skS.0 1 a a_1)) (cB (skS.0 1 a a_1)))) True % 3.34/3.49 Clause #12 (by clausification #[11]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (skS.0 0 a (skS.0 1 a a_1) → Or (cA (skS.0 1 a a_1)) (cB (skS.0 1 a a_1))) False % 3.34/3.49 Clause #13 (by clausification #[12]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (skS.0 0 a (skS.0 1 a a_1)) True % 3.34/3.49 Clause #14 (by clausification #[12]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (Or (cA (skS.0 1 a a_1)) (cB (skS.0 1 a a_1))) False % 3.34/3.49 Clause #15 (by superposition #[13, 10]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.34/3.49 Or (Eq True False) (Or (Eq (cA (skS.0 1 a a_1)) True) (Or (Eq (skS.0 0 a a_2) False) (Eq (cB a_2) True))) % 3.34/3.49 Clause #16 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cB (skS.0 1 a a_1)) False % 3.34/3.49 Clause #17 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cA (skS.0 1 a a_1)) False % 3.34/3.49 Clause #18 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.34/3.49 Or (Eq (cA (skS.0 1 a a_1)) True) (Or (Eq (skS.0 0 a a_2) False) (Eq (cB a_2) True)) % 3.34/3.49 Clause #19 (by superposition #[18, 13]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.34/3.49 Or (Eq (cA (skS.0 1 (fun x => a x) a_1)) True) (Or (Eq (cB (skS.0 1 a a_2)) True) (Eq False True)) % 3.34/3.49 Clause #20 (by betaEtaReduce #[19]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.34/3.49 Or (Eq (cA (skS.0 1 a a_1)) True) (Or (Eq (cB (skS.0 1 a a_2)) True) (Eq False True)) % 3.34/3.49 Clause #21 (by clausification #[20]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cA (skS.0 1 a a_1)) True) (Eq (cB (skS.0 1 a a_2)) True) % 3.34/3.49 Clause #23 (by superposition #[21, 16]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cA (skS.0 1 (fun x => a x) a_1)) True) (Eq True False) % 3.34/3.49 Clause #24 (by betaEtaReduce #[23]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cA (skS.0 1 a a_1)) True) (Eq True False) % 3.34/3.49 Clause #25 (by clausification #[24]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cA (skS.0 1 a a_1)) True % 3.34/3.49 Clause #26 (by superposition #[25, 17]): Eq True False % 3.34/3.49 Clause #27 (by clausification #[26]): False % 3.34/3.49 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------