%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO296^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:08:51 PM UTC 2025 % Result : Theorem 3.31s 3.50s % Output : Proof 3.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYO296^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.12 % Command : duper %s % 0.12/0.33 % Computer : n003.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Oct 3 13:39:08 EDT 2025 % 0.12/0.33 % CPUTime : % 3.31/3.50 SZS status Theorem for theBenchmark.p % 3.31/3.50 SZS output start Proof for theBenchmark.p % 3.31/3.50 Clause #0 (by assumption #[]): Eq (Not (Exists fun A => ∀ (Xx Xy : Iota), Or (A Xx) (A Xy) → And (p Xx) (q Xy))) True % 3.31/3.50 Clause #1 (by clausification #[0]): Eq (Exists fun A => ∀ (Xx Xy : Iota), Or (A Xx) (A Xy) → And (p Xx) (q Xy)) False % 3.31/3.50 Clause #2 (by clausification #[1]): ∀ (a : Iota → Prop), Eq (∀ (Xx Xy : Iota), Or (a Xx) (a Xy) → And (p Xx) (q Xy)) False % 3.31/3.50 Clause #3 (by clausification #[2]): ∀ (a : Iota → Prop) (a_1 : Iota), % 3.31/3.50 Eq (Not (∀ (Xy : Iota), Or (a (skS.0 0 a a_1)) (a Xy) → And (p (skS.0 0 a a_1)) (q Xy))) True % 3.31/3.50 Clause #4 (by clausification #[3]): ∀ (a : Iota → Prop) (a_1 : Iota), % 3.31/3.50 Eq (∀ (Xy : Iota), Or (a (skS.0 0 a a_1)) (a Xy) → And (p (skS.0 0 a a_1)) (q Xy)) False % 3.31/3.50 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.31/3.50 Eq (Not (Or (a (skS.0 0 a a_1)) (a (skS.0 1 a a_1 a_2)) → And (p (skS.0 0 a a_1)) (q (skS.0 1 a a_1 a_2)))) True % 3.31/3.50 Clause #6 (by clausification #[5]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.31/3.50 Eq (Or (a (skS.0 0 a a_1)) (a (skS.0 1 a a_1 a_2)) → And (p (skS.0 0 a a_1)) (q (skS.0 1 a a_1 a_2))) False % 3.31/3.50 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Eq (Or (a (skS.0 0 a a_1)) (a (skS.0 1 a a_1 a_2))) True % 3.31/3.50 Clause #9 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a (skS.0 0 a a_1)) True) (Eq (a (skS.0 1 a a_1 a_2)) True) % 3.31/3.50 Clause #16 (by equality factoring #[9]): ∀ (a : Prop) (a_1 : Iota), Or (Ne True True) (Eq ((fun x => a) (skS.0 0 (fun x => a) a_1)) True) % 3.31/3.50 Clause #42 (by betaEtaReduce #[16]): ∀ (a : Prop), Or (Ne True True) (Eq a True) % 3.31/3.50 Clause #43 (by clausification #[42]): ∀ (a : Prop), Or (Eq a True) (Or (Eq True False) (Eq True False)) % 3.31/3.50 Clause #45 (by clausification #[43]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 3.31/3.50 Clause #46 (by clausification #[45]): ∀ (a : Prop), Eq a True % 3.31/3.50 Clause #47 (by falseElim #[46]): False % 3.31/3.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------