%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO375^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:08:57 PM UTC 2025 % Result : Theorem 5.05s 5.22s % Output : Proof 5.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SYO375^5 : TPTP v9.2.0. Released v4.0.0. % 0.14/0.14 % Command : duper %s % 0.14/0.35 % Computer : n031.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 14:14:53 EDT 2025 % 0.14/0.35 % CPUTime : % 5.05/5.22 SZS status Theorem for theBenchmark.p % 5.05/5.22 SZS output start Proof for theBenchmark.p % 5.05/5.22 Clause #0 (by assumption #[]): Eq (Not (∀ (X Y : Iota → Prop), (∀ (W : Iota), Iff (X W) (Y W)) → ∀ (Xx : Iota), Iff (X Xx) (Y Xx))) True % 5.05/5.22 Clause #1 (by clausification #[0]): Eq (∀ (X Y : Iota → Prop), (∀ (W : Iota), Iff (X W) (Y W)) → ∀ (Xx : Iota), Iff (X Xx) (Y Xx)) False % 5.05/5.22 Clause #2 (by clausification #[1]): ∀ (a : Iota → Prop), % 5.05/5.22 Eq (Not (∀ (Y : Iota → Prop), (∀ (W : Iota), Iff (skS.0 0 a W) (Y W)) → ∀ (Xx : Iota), Iff (skS.0 0 a Xx) (Y Xx))) % 5.05/5.22 True % 5.05/5.22 Clause #3 (by clausification #[2]): ∀ (a : Iota → Prop), % 5.05/5.22 Eq (∀ (Y : Iota → Prop), (∀ (W : Iota), Iff (skS.0 0 a W) (Y W)) → ∀ (Xx : Iota), Iff (skS.0 0 a Xx) (Y Xx)) False % 5.05/5.22 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota → Prop), % 5.05/5.22 Eq (Not ((∀ (W : Iota), Iff (skS.0 0 a W) (skS.0 1 a a_1 W)) → ∀ (Xx : Iota), Iff (skS.0 0 a Xx) (skS.0 1 a a_1 Xx))) % 5.05/5.22 True % 5.05/5.22 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota → Prop), % 5.05/5.22 Eq ((∀ (W : Iota), Iff (skS.0 0 a W) (skS.0 1 a a_1 W)) → ∀ (Xx : Iota), Iff (skS.0 0 a Xx) (skS.0 1 a a_1 Xx)) False % 5.05/5.22 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota → Prop), Eq (∀ (W : Iota), Iff (skS.0 0 a W) (skS.0 1 a a_1 W)) True % 5.05/5.22 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota → Prop), Eq (∀ (Xx : Iota), Iff (skS.0 0 a Xx) (skS.0 1 a a_1 Xx)) False % 5.05/5.22 Clause #8 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 : Iota) (a_2 : Iota → Prop), Eq (Iff (skS.0 0 a a_1) (skS.0 1 a a_2 a_1)) True % 5.05/5.22 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (skS.0 0 a a_1) True) (Eq (skS.0 1 a a_2 a_1) False) % 5.05/5.22 Clause #10 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (skS.0 0 a a_1) False) (Eq (skS.0 1 a a_2 a_1) True) % 5.05/5.22 Clause #11 (by clausification #[7]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), % 5.05/5.22 Eq (Not (Iff (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)))) True % 5.05/5.22 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), Eq (Iff (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1 (skS.0 2 a a_1 a_2))) False % 5.05/5.22 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), % 5.05/5.22 Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) False) (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) False) % 5.05/5.22 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), % 5.05/5.22 Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) True) % 5.05/5.22 Clause #15 (by superposition #[14, 9]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), % 5.05/5.22 Or (Eq (skS.0 0 (fun x => a x) (skS.0 2 (fun x => a x) (fun x => a_1 x) a_2)) True) % 5.05/5.22 (Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Eq True False)) % 5.05/5.22 Clause #16 (by betaEtaReduce #[15]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), % 5.05/5.22 Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Eq True False)) % 5.05/5.22 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), % 5.05/5.22 Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) % 5.05/5.22 Clause #18 (by eliminate duplicate literals #[17]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True % 5.05/5.22 Clause #19 (by backward demodulation #[18, 13]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), Or (Eq True False) (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) False) % 5.05/5.22 Clause #21 (by superposition #[18, 10]): ∀ (a a_1 a_2 : Iota → Prop) (a_3 : Iota), Or (Eq True False) (Eq (skS.0 1 a a_1 (skS.0 2 a a_2 a_3)) True) % 5.05/5.22 Clause #22 (by clausification #[19]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) False % 5.05/5.22 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota → Prop) (a_3 : Iota), Eq (skS.0 1 a a_1 (skS.0 2 a a_2 a_3)) True % 5.05/5.22 Clause #24 (by superposition #[23, 22]): Eq True False % 5.05/5.22 Clause #26 (by clausification #[24]): False % 5.05/5.22 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------