%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU967^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:02:41 PM UTC 2025 % Result : Theorem 4.43s 4.63s % Output : Proof 4.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU967^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.14 % Command : duper %s % 0.14/0.35 % Computer : n013.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 06:37:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.43/4.63 SZS status Theorem for theBenchmark.p % 4.43/4.63 SZS output start Proof for theBenchmark.p % 4.43/4.63 Clause #0 (by assumption #[]): Eq % 4.43/4.63 (Not % 4.43/4.63 (Not % 4.43/4.63 (∀ (Xm_5 : (Iota → Iota) → Iota → Prop), % 4.43/4.63 And % 4.43/4.63 (And (Exists fun Xw_2 => Xm_5 (cG_0 fun Xw_1144 => Exists fun Xw_20 => Xm_5 Xw_1144 Xw_20) Xw_2) % 4.43/4.63 (Exists fun Xw_2 => Xm_5 (cH_0 fun Xw_1144 => Exists fun Xw_20 => Xm_5 Xw_1144 Xw_20) Xw_2)) % 4.43/4.63 (Or % 4.43/4.63 (Not % 4.43/4.63 (Exists fun Xw_2 => % 4.43/4.63 Xm_5 % 4.43/4.63 (fun Xx => % 4.43/4.63 cG_0 (fun Xw_1144 => Exists fun Xw_20 => Xm_5 Xw_1144 Xw_20) % 4.43/4.63 (cH_0 (fun Xw_1144 => Exists fun Xw_20 => Xm_5 Xw_1144 Xw_20) Xx)) % 4.43/4.63 Xw_2)) % 4.43/4.63 (And (cP_0 (cY_0 fun Xw_1144 => Exists fun Xw_2 => Xm_5 Xw_1144 Xw_2)) % 4.43/4.63 (Not % 4.43/4.63 (cP_0 % 4.43/4.63 (cG_0 (fun Xw_1144 => Exists fun Xw_2 => Xm_5 Xw_1144 Xw_2) % 4.43/4.63 (cY_0 fun Xw_1144 => Exists fun Xw_2 => Xm_5 Xw_1144 Xw_2))))))))) % 4.43/4.63 True % 4.43/4.63 Clause #1 (by betaEtaReduce #[0]): Eq % 4.43/4.63 (Not % 4.43/4.63 (Not % 4.43/4.63 (∀ (Xm_5 : (Iota → Iota) → Iota → Prop), % 4.43/4.63 And % 4.43/4.63 (And (Exists (Xm_5 (cG_0 fun Xw_1144 => Exists (Xm_5 Xw_1144)))) % 4.43/4.63 (Exists (Xm_5 (cH_0 fun Xw_1144 => Exists (Xm_5 Xw_1144))))) % 4.43/4.63 (Or % 4.43/4.63 (Not % 4.43/4.63 (Exists % 4.43/4.63 (Xm_5 fun Xx => % 4.43/4.63 cG_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) (cH_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) Xx)))) % 4.43/4.63 (And (cP_0 (cY_0 fun Xw_1144 => Exists (Xm_5 Xw_1144))) % 4.43/4.63 (Not % 4.43/4.63 (cP_0 (cG_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) (cY_0 fun Xw_1144 => Exists (Xm_5 Xw_1144)))))))))) % 4.43/4.63 True % 4.43/4.63 Clause #2 (by clausification #[1]): Eq % 4.43/4.63 (Not % 4.43/4.63 (∀ (Xm_5 : (Iota → Iota) → Iota → Prop), % 4.43/4.63 And % 4.43/4.63 (And (Exists (Xm_5 (cG_0 fun Xw_1144 => Exists (Xm_5 Xw_1144)))) % 4.43/4.63 (Exists (Xm_5 (cH_0 fun Xw_1144 => Exists (Xm_5 Xw_1144))))) % 4.43/4.63 (Or % 4.43/4.63 (Not % 4.43/4.63 (Exists % 4.43/4.63 (Xm_5 fun Xx => % 4.43/4.63 cG_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) (cH_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) Xx)))) % 4.43/4.63 (And (cP_0 (cY_0 fun Xw_1144 => Exists (Xm_5 Xw_1144))) % 4.43/4.63 (Not (cP_0 (cG_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) (cY_0 fun Xw_1144 => Exists (Xm_5 Xw_1144))))))))) % 4.43/4.63 False % 4.43/4.63 Clause #3 (by clausification #[2]): Eq % 4.43/4.63 (∀ (Xm_5 : (Iota → Iota) → Iota → Prop), % 4.43/4.63 And % 4.43/4.63 (And (Exists (Xm_5 (cG_0 fun Xw_1144 => Exists (Xm_5 Xw_1144)))) % 4.43/4.63 (Exists (Xm_5 (cH_0 fun Xw_1144 => Exists (Xm_5 Xw_1144))))) % 4.43/4.63 (Or % 4.43/4.63 (Not % 4.43/4.63 (Exists % 4.43/4.63 (Xm_5 fun Xx => % 4.43/4.63 cG_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) (cH_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) Xx)))) % 4.43/4.63 (And (cP_0 (cY_0 fun Xw_1144 => Exists (Xm_5 Xw_1144))) % 4.43/4.63 (Not (cP_0 (cG_0 (fun Xw_1144 => Exists (Xm_5 Xw_1144)) (cY_0 fun Xw_1144 => Exists (Xm_5 Xw_1144)))))))) % 4.43/4.63 True % 4.43/4.63 Clause #4 (by clausification #[3]): ∀ (a : (Iota → Iota) → Iota → Prop), % 4.43/4.63 Eq % 4.43/4.63 (And % 4.43/4.63 (And (Exists (a (cG_0 fun Xw_1144 => Exists (a Xw_1144)))) (Exists (a (cH_0 fun Xw_1144 => Exists (a Xw_1144))))) % 4.43/4.63 (Or % 4.43/4.63 (Not % 4.43/4.63 (Exists (a fun Xx => cG_0 (fun Xw_1144 => Exists (a Xw_1144)) (cH_0 (fun Xw_1144 => Exists (a Xw_1144)) Xx)))) % 4.43/4.63 (And (cP_0 (cY_0 fun Xw_1144 => Exists (a Xw_1144))) % 4.43/4.63 (Not (cP_0 (cG_0 (fun Xw_1144 => Exists (a Xw_1144)) (cY_0 fun Xw_1144 => Exists (a Xw_1144)))))))) % 4.43/4.63 True % 4.43/4.63 Clause #6 (by clausification #[4]): ∀ (a : (Iota → Iota) → Iota → Prop), % 4.43/4.63 Eq (And (Exists (a (cG_0 fun Xw_1144 => Exists (a Xw_1144)))) (Exists (a (cH_0 fun Xw_1144 => Exists (a Xw_1144))))) % 4.43/4.63 True % 4.43/4.63 Clause #21 (by clausification #[6]): ∀ (a : (Iota → Iota) → Iota → Prop), Eq (Exists (a (cG_0 fun Xw_1144 => Exists (a Xw_1144)))) True % 4.43/4.63 Clause #36 (by clausification #[21]): ∀ (a : (Iota → Iota) → Iota → Prop) (a_1 : Iota), Eq (a (cG_0 fun Xw_1144 => Exists (a Xw_1144)) (skS.0 1 a a_1)) True % 4.43/4.63 Clause #52 (by fluidBoolHoist #[36]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.43/4.63 Or (Eq ((fun Xw_1144 x => a x) (cG_0 fun Xw_1144 => False) (skS.0 1 (fun Xw_1144 x => a x) a_1)) True) % 4.43/4.64 (Eq (Exists a) True) % 4.43/4.64 Clause #125 (by betaEtaReduce #[52]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a (skS.0 1 (fun Xw_1144 x => a x) a_1)) True) (Eq (Exists a) True) % 4.43/4.64 Clause #126 (by clausification #[125]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.43/4.64 Or (Eq (a (skS.0 1 (fun Xw_1144 x => a x) a_1)) True) (Eq (a (skS.0 2 a a_2)) True) % 4.43/4.64 Clause #129 (by equality factoring #[126]): ∀ (a : Prop) (a_1 : Iota), Or (Ne True True) (Eq ((fun x => a) (skS.0 2 (fun x => a) a_1)) True) % 4.43/4.64 Clause #193 (by betaEtaReduce #[129]): ∀ (a : Prop), Or (Ne True True) (Eq a True) % 4.43/4.64 Clause #194 (by clausification #[193]): ∀ (a : Prop), Or (Eq a True) (Or (Eq True False) (Eq True False)) % 4.43/4.64 Clause #196 (by clausification #[194]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 4.43/4.64 Clause #197 (by clausification #[196]): ∀ (a : Prop), Eq a True % 4.43/4.64 Clause #199 (by falseElim #[197]): False % 4.43/4.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------