%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ANA095^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 07:44:33 PM UTC 2025 % Result : Theorem 239.47s 239.64s % Output : Proof 240.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ANA095^1 : TPTP v9.2.0. Released v7.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n007.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 22:07:23 EDT 2025 % 0.14/0.36 % CPUTime : % 239.47/239.64 SZS status Theorem for theBenchmark.p % 239.47/239.64 SZS output start Proof for theBenchmark.p % 239.47/239.64 Clause #0 (by assumption #[]): Eq (∀ (A : Type), Eq («const/iterate/sum» A) («const/iterate/iterate» A «type/realax/real» «const/realax/real_add»)) % 239.47/239.64 True % 239.47/239.64 Clause #1 (by assumption #[]): Eq % 239.47/239.64 (∀ (A A0 : Type) (A1 : A0 → A0 → A0), % 239.47/239.64 «const/iterate/monoidal» A0 A1 → % 239.47/239.64 ∀ (A2 : A → A0) (A3 A4 : A → Prop), % 239.47/239.64 And (And («const/sets/FINITE» A A3) («const/sets/FINITE» A A4)) («const/sets/DISJOINT» A A3 A4) → % 239.47/239.64 Eq («const/iterate/iterate» A A0 A1 («const/sets/UNION» A A3 A4) A2) % 239.47/239.64 (A1 («const/iterate/iterate» A A0 A1 A3 A2) («const/iterate/iterate» A A0 A1 A4 A2))) % 239.47/239.64 True % 239.47/239.64 Clause #2 (by assumption #[]): Eq («const/iterate/monoidal» «type/realax/real» «const/realax/real_add») True % 239.47/239.64 Clause #3 (by assumption #[]): Eq % 239.47/239.64 (Not % 239.47/239.64 (∀ (A : Type) (A0 : A → «type/realax/real») (A1 A2 : A → Prop), % 239.47/239.64 And (And («const/sets/FINITE» A A1) («const/sets/FINITE» A A2)) («const/sets/DISJOINT» A A1 A2) → % 239.47/239.64 Eq («const/iterate/sum» A («const/sets/UNION» A A1 A2) A0) % 239.47/239.64 («const/realax/real_add» («const/iterate/sum» A A1 A0) («const/iterate/sum» A A2 A0)))) % 239.47/239.64 True % 239.47/239.64 Clause #4 (by clausification #[0]): ∀ (a : Type), % 239.47/239.64 Eq (Eq («const/iterate/sum» a) («const/iterate/iterate» a «type/realax/real» «const/realax/real_add»)) True % 239.47/239.64 Clause #5 (by clausification #[4]): ∀ (a : Type), Eq («const/iterate/sum» a) («const/iterate/iterate» a «type/realax/real» «const/realax/real_add») % 239.47/239.64 Clause #7 (by argument congruence #[5]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : a → «type/realax/real»), % 239.47/239.64 Eq («const/iterate/sum» a a_1 a_2) («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» a_1 a_2) % 239.47/239.64 Clause #8 (by clausification #[3]): Eq % 239.47/239.64 (∀ (A : Type) (A0 : A → «type/realax/real») (A1 A2 : A → Prop), % 239.47/239.64 And (And («const/sets/FINITE» A A1) («const/sets/FINITE» A A2)) («const/sets/DISJOINT» A A1 A2) → % 239.47/239.64 Eq («const/iterate/sum» A («const/sets/UNION» A A1 A2) A0) % 239.47/239.64 («const/realax/real_add» («const/iterate/sum» A A1 A0) («const/iterate/sum» A A2 A0))) % 239.47/239.64 False % 239.47/239.64 Clause #9 (by clausification #[8]): ∀ (a : Type), % 239.47/239.64 Eq % 239.47/239.64 (Not % 239.47/239.64 (∀ (A0 : skS.0 0 a → «type/realax/real») (A1 A2 : skS.0 0 a → Prop), % 239.47/239.64 And (And («const/sets/FINITE» (skS.0 0 a) A1) («const/sets/FINITE» (skS.0 0 a) A2)) % 239.47/239.64 («const/sets/DISJOINT» (skS.0 0 a) A1 A2) → % 239.47/239.64 Eq («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) A1 A2) A0) % 239.47/239.64 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) A1 A0) («const/iterate/sum» (skS.0 0 a) A2 A0)))) % 239.47/239.64 True % 239.47/239.64 Clause #10 (by clausification #[9]): ∀ (a : Type), % 239.47/239.64 Eq % 239.47/239.64 (∀ (A0 : skS.0 0 a → «type/realax/real») (A1 A2 : skS.0 0 a → Prop), % 239.47/239.64 And (And («const/sets/FINITE» (skS.0 0 a) A1) («const/sets/FINITE» (skS.0 0 a) A2)) % 239.47/239.64 («const/sets/DISJOINT» (skS.0 0 a) A1 A2) → % 239.47/239.64 Eq («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) A1 A2) A0) % 239.47/239.64 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) A1 A0) («const/iterate/sum» (skS.0 0 a) A2 A0))) % 239.47/239.64 False % 239.47/239.64 Clause #11 (by clausification #[10]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real»), % 239.47/239.64 Eq % 239.47/239.64 (Not % 239.47/239.64 (∀ (A1 A2 : skS.0 0 a → Prop), % 239.47/239.64 And (And («const/sets/FINITE» (skS.0 0 a) A1) («const/sets/FINITE» (skS.0 0 a) A2)) % 239.47/239.64 («const/sets/DISJOINT» (skS.0 0 a) A1 A2) → % 239.47/239.64 Eq («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) A1 A2) (skS.0 1 a a_1)) % 239.47/239.64 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) A1 (skS.0 1 a a_1)) % 239.47/239.64 («const/iterate/sum» (skS.0 0 a) A2 (skS.0 1 a a_1))))) % 239.47/239.64 True % 239.47/239.64 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real»), % 239.47/239.64 Eq % 239.47/239.64 (∀ (A1 A2 : skS.0 0 a → Prop), % 239.47/239.64 And (And («const/sets/FINITE» (skS.0 0 a) A1) («const/sets/FINITE» (skS.0 0 a) A2)) % 239.47/239.64 («const/sets/DISJOINT» (skS.0 0 a) A1 A2) → % 239.47/239.66 Eq («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) A1 A2) (skS.0 1 a a_1)) % 239.47/239.66 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) A1 (skS.0 1 a a_1)) % 239.47/239.66 («const/iterate/sum» (skS.0 0 a) A2 (skS.0 1 a a_1)))) % 239.47/239.66 False % 239.47/239.66 Clause #13 (by clausification #[12]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 : skS.0 0 a → Prop), % 239.47/239.66 Eq % 239.47/239.66 (Not % 239.47/239.66 (∀ (A2 : skS.0 0 a → Prop), % 239.47/239.66 And (And («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) («const/sets/FINITE» (skS.0 0 a) A2)) % 239.47/239.66 («const/sets/DISJOINT» (skS.0 0 a) (skS.0 2 a a_1 a_2) A2) → % 239.47/239.66 Eq («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) A2) (skS.0 1 a a_1)) % 239.47/239.66 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 239.47/239.66 («const/iterate/sum» (skS.0 0 a) A2 (skS.0 1 a a_1))))) % 239.47/239.66 True % 239.47/239.66 Clause #14 (by clausification #[13]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 : skS.0 0 a → Prop), % 239.47/239.66 Eq % 239.47/239.66 (∀ (A2 : skS.0 0 a → Prop), % 239.47/239.66 And (And («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) («const/sets/FINITE» (skS.0 0 a) A2)) % 239.47/239.66 («const/sets/DISJOINT» (skS.0 0 a) (skS.0 2 a a_1 a_2) A2) → % 239.47/239.66 Eq («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) A2) (skS.0 1 a a_1)) % 239.47/239.66 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 239.47/239.66 («const/iterate/sum» (skS.0 0 a) A2 (skS.0 1 a a_1)))) % 239.47/239.66 False % 239.47/239.66 Clause #15 (by clausification #[14]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop), % 239.47/239.66 Eq % 239.47/239.66 (Not % 239.47/239.66 (And % 239.47/239.66 (And («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 239.47/239.66 («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) % 239.47/239.66 («const/sets/DISJOINT» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) → % 239.47/239.67 Eq % 239.47/239.67 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 239.47/239.67 (skS.0 1 a a_1)) % 239.47/239.67 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 239.47/239.67 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1))))) % 239.47/239.67 True % 239.47/239.67 Clause #16 (by clausification #[15]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop), % 239.47/239.67 Eq % 239.47/239.67 (And % 239.47/239.67 (And («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 239.47/239.67 («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) % 239.47/239.67 («const/sets/DISJOINT» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) → % 239.47/239.67 Eq % 239.47/239.67 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 239.47/239.67 (skS.0 1 a a_1)) % 239.47/239.67 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 239.47/239.67 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)))) % 239.47/239.67 False % 239.47/239.67 Clause #17 (by clausification #[16]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop), % 239.47/239.67 Eq % 239.47/239.67 (And % 239.47/239.67 (And («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 239.47/239.67 («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) % 239.47/239.67 («const/sets/DISJOINT» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 239.47/239.67 True % 239.47/239.67 Clause #18 (by clausification #[16]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop), % 239.47/239.67 Eq % 239.47/239.67 (Eq % 239.47/239.67 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 239.47/239.67 (skS.0 1 a a_1)) % 239.47/239.67 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 239.47/239.67 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)))) % 239.47/239.67 False % 239.47/239.67 Clause #19 (by clausification #[17]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop), % 239.47/239.68 Eq («const/sets/DISJOINT» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) True % 239.47/239.68 Clause #20 (by clausification #[17]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop), % 239.47/239.68 Eq % 239.47/239.68 (And («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 239.47/239.68 («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) % 239.47/239.68 True % 239.47/239.68 Clause #21 (by clausification #[1]): ∀ (a : Type), % 239.47/239.68 Eq % 239.47/239.68 (∀ (A0 : Type) (A1 : A0 → A0 → A0), % 239.47/239.68 «const/iterate/monoidal» A0 A1 → % 239.47/239.68 ∀ (A2 : a → A0) (A3 A4 : a → Prop), % 239.47/239.68 And (And («const/sets/FINITE» a A3) («const/sets/FINITE» a A4)) («const/sets/DISJOINT» a A3 A4) → % 239.47/239.68 Eq («const/iterate/iterate» a A0 A1 («const/sets/UNION» a A3 A4) A2) % 239.47/239.68 (A1 («const/iterate/iterate» a A0 A1 A3 A2) («const/iterate/iterate» a A0 A1 A4 A2))) % 239.47/239.68 True % 239.47/239.68 Clause #22 (by clausification #[21]): ∀ (a a_1 : Type), % 239.47/239.68 Eq % 239.47/239.68 (∀ (A1 : a → a → a), % 239.47/239.68 «const/iterate/monoidal» a A1 → % 239.47/239.68 ∀ (A2 : a_1 → a) (A3 A4 : a_1 → Prop), % 239.47/239.68 And (And («const/sets/FINITE» a_1 A3) («const/sets/FINITE» a_1 A4)) («const/sets/DISJOINT» a_1 A3 A4) → % 239.47/239.68 Eq («const/iterate/iterate» a_1 a A1 («const/sets/UNION» a_1 A3 A4) A2) % 239.47/239.68 (A1 («const/iterate/iterate» a_1 a A1 A3 A2) («const/iterate/iterate» a_1 a A1 A4 A2))) % 239.47/239.68 True % 239.47/239.68 Clause #23 (by clausification #[22]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type), % 239.47/239.68 Eq % 239.47/239.68 («const/iterate/monoidal» a a_1 → % 239.47/239.68 ∀ (A2 : a_2 → a) (A3 A4 : a_2 → Prop), % 239.47/239.68 And (And («const/sets/FINITE» a_2 A3) («const/sets/FINITE» a_2 A4)) («const/sets/DISJOINT» a_2 A3 A4) → % 239.47/239.68 Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 A3 A4) A2) % 239.47/239.68 (a_1 («const/iterate/iterate» a_2 a a_1 A3 A2) («const/iterate/iterate» a_2 a a_1 A4 A2))) % 239.47/239.68 True % 239.47/239.68 Clause #24 (by clausification #[23]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type), % 239.47/239.68 Or (Eq («const/iterate/monoidal» a a_1) False) % 239.47/239.68 (Eq % 239.47/239.68 (∀ (A2 : a_2 → a) (A3 A4 : a_2 → Prop), % 239.47/239.68 And (And («const/sets/FINITE» a_2 A3) («const/sets/FINITE» a_2 A4)) («const/sets/DISJOINT» a_2 A3 A4) → % 239.47/239.68 Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 A3 A4) A2) % 239.47/239.68 (a_1 («const/iterate/iterate» a_2 a a_1 A3 A2) («const/iterate/iterate» a_2 a a_1 A4 A2))) % 239.47/239.68 True) % 239.47/239.68 Clause #25 (by clausification #[24]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type) (a_3 : a_2 → a), % 239.47/239.68 Or (Eq («const/iterate/monoidal» a a_1) False) % 239.47/239.68 (Eq % 239.47/239.68 (∀ (A3 A4 : a_2 → Prop), % 239.47/239.68 And (And («const/sets/FINITE» a_2 A3) («const/sets/FINITE» a_2 A4)) («const/sets/DISJOINT» a_2 A3 A4) → % 239.47/239.68 Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 A3 A4) a_3) % 239.47/239.68 (a_1 («const/iterate/iterate» a_2 a a_1 A3 a_3) («const/iterate/iterate» a_2 a a_1 A4 a_3))) % 239.47/239.68 True) % 239.47/239.68 Clause #26 (by clausification #[25]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type) (a_3 : a_2 → Prop) (a_4 : a_2 → a), % 239.47/239.68 Or (Eq («const/iterate/monoidal» a a_1) False) % 239.47/239.68 (Eq % 239.47/239.68 (∀ (A4 : a_2 → Prop), % 239.47/239.68 And (And («const/sets/FINITE» a_2 a_3) («const/sets/FINITE» a_2 A4)) («const/sets/DISJOINT» a_2 a_3 A4) → % 239.47/239.68 Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 a_3 A4) a_4) % 239.47/239.68 (a_1 («const/iterate/iterate» a_2 a a_1 a_3 a_4) («const/iterate/iterate» a_2 a a_1 A4 a_4))) % 239.47/239.68 True) % 239.47/239.68 Clause #27 (by clausification #[26]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type) (a_3 a_4 : a_2 → Prop) (a_5 : a_2 → a), % 239.47/239.68 Or (Eq («const/iterate/monoidal» a a_1) False) % 239.47/239.68 (Eq % 239.47/239.68 (And (And («const/sets/FINITE» a_2 a_3) («const/sets/FINITE» a_2 a_4)) («const/sets/DISJOINT» a_2 a_3 a_4) → % 239.47/239.68 Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 a_3 a_4) a_5) % 239.47/239.68 (a_1 («const/iterate/iterate» a_2 a a_1 a_3 a_5) («const/iterate/iterate» a_2 a a_1 a_4 a_5))) % 239.47/239.68 True) % 239.47/239.68 Clause #28 (by clausification #[27]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type) (a_3 a_4 : a_2 → Prop) (a_5 : a_2 → a), % 239.47/239.70 Or (Eq («const/iterate/monoidal» a a_1) False) % 239.47/239.70 (Or % 239.47/239.70 (Eq (And (And («const/sets/FINITE» a_2 a_3) («const/sets/FINITE» a_2 a_4)) («const/sets/DISJOINT» a_2 a_3 a_4)) % 239.47/239.70 False) % 239.47/239.70 (Eq % 239.47/239.70 (Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 a_3 a_4) a_5) % 239.47/239.70 (a_1 («const/iterate/iterate» a_2 a a_1 a_3 a_5) («const/iterate/iterate» a_2 a a_1 a_4 a_5))) % 239.47/239.70 True)) % 239.47/239.70 Clause #29 (by clausification #[28]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type) (a_3 a_4 : a_2 → Prop) (a_5 : a_2 → a), % 239.47/239.70 Or (Eq («const/iterate/monoidal» a a_1) False) % 239.47/239.70 (Or % 239.47/239.70 (Eq % 239.47/239.70 (Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 a_3 a_4) a_5) % 239.47/239.70 (a_1 («const/iterate/iterate» a_2 a a_1 a_3 a_5) («const/iterate/iterate» a_2 a a_1 a_4 a_5))) % 239.47/239.70 True) % 239.47/239.70 (Or (Eq (And («const/sets/FINITE» a_2 a_3) («const/sets/FINITE» a_2 a_4)) False) % 239.47/239.70 (Eq («const/sets/DISJOINT» a_2 a_3 a_4) False))) % 239.47/239.70 Clause #30 (by clausification #[29]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type) (a_3 a_4 : a_2 → Prop) (a_5 : a_2 → a), % 239.47/239.70 Or (Eq («const/iterate/monoidal» a a_1) False) % 239.47/239.70 (Or (Eq (And («const/sets/FINITE» a_2 a_3) («const/sets/FINITE» a_2 a_4)) False) % 239.47/239.70 (Or (Eq («const/sets/DISJOINT» a_2 a_3 a_4) False) % 239.47/239.70 (Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 a_3 a_4) a_5) % 239.47/239.70 (a_1 («const/iterate/iterate» a_2 a a_1 a_3 a_5) («const/iterate/iterate» a_2 a a_1 a_4 a_5))))) % 239.47/239.70 Clause #31 (by clausification #[30]): ∀ (a : Type) (a_1 : a → a → a) (a_2 : Type) (a_3 a_4 : a_2 → Prop) (a_5 : a_2 → a), % 239.47/239.70 Or (Eq («const/iterate/monoidal» a a_1) False) % 239.47/239.70 (Or (Eq («const/sets/DISJOINT» a_2 a_3 a_4) False) % 239.47/239.70 (Or % 239.47/239.70 (Eq («const/iterate/iterate» a_2 a a_1 («const/sets/UNION» a_2 a_3 a_4) a_5) % 239.47/239.70 (a_1 («const/iterate/iterate» a_2 a a_1 a_3 a_5) («const/iterate/iterate» a_2 a a_1 a_4 a_5))) % 239.47/239.70 (Or (Eq («const/sets/FINITE» a_2 a_3) False) (Eq («const/sets/FINITE» a_2 a_4) False)))) % 239.47/239.70 Clause #32 (by superposition #[31, 2]): ∀ (a : Type) (a_1 a_2 : a → Prop) (a_3 : a → «type/realax/real»), % 239.47/239.70 Or (Eq («const/sets/DISJOINT» a a_1 a_2) False) % 239.47/239.70 (Or % 239.47/239.70 (Eq % 239.47/239.70 («const/iterate/iterate» a «type/realax/real» (fun x x_1 => «const/realax/real_add» x x_1) % 239.47/239.70 («const/sets/UNION» a a_1 a_2) a_3) % 239.47/239.70 ((fun x x_1 => «const/realax/real_add» x x_1) % 239.47/239.70 («const/iterate/iterate» a «type/realax/real» (fun x x_1 => «const/realax/real_add» x x_1) a_1 a_3) % 239.47/239.70 («const/iterate/iterate» a «type/realax/real» (fun x x_1 => «const/realax/real_add» x x_1) a_2 a_3))) % 239.47/239.70 (Or (Eq («const/sets/FINITE» a a_1) False) (Or (Eq («const/sets/FINITE» a a_2) False) (Eq False True)))) % 239.47/239.70 Clause #43 (by clausification #[20]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop), % 239.47/239.70 Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) True % 239.47/239.70 Clause #44 (by clausification #[20]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 : skS.0 0 a → Prop), % 239.47/239.70 Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 239.47/239.70 Clause #84 (by clausification #[18]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop), % 239.47/239.70 Ne % 239.47/239.70 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 239.47/239.70 (skS.0 1 a a_1)) % 239.47/239.70 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 239.47/239.70 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1))) % 239.47/239.70 Clause #120 (by betaEtaReduce #[32]): ∀ (a : Type) (a_1 a_2 : a → Prop) (a_3 : a → «type/realax/real»), % 239.47/239.70 Or (Eq («const/sets/DISJOINT» a a_1 a_2) False) % 239.47/239.70 (Or % 239.47/239.70 (Eq («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» («const/sets/UNION» a a_1 a_2) a_3) % 239.47/239.70 («const/realax/real_add» («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» a_1 a_3) % 239.47/239.72 («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» a_2 a_3))) % 239.47/239.72 (Or (Eq («const/sets/FINITE» a a_1) False) (Or (Eq («const/sets/FINITE» a a_2) False) (Eq False True)))) % 239.47/239.72 Clause #121 (by clausification #[120]): ∀ (a : Type) (a_1 a_2 : a → Prop) (a_3 : a → «type/realax/real»), % 239.47/239.72 Or (Eq («const/sets/DISJOINT» a a_1 a_2) False) % 239.47/239.72 (Or % 239.47/239.72 (Eq («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» («const/sets/UNION» a a_1 a_2) a_3) % 239.47/239.72 («const/realax/real_add» («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» a_1 a_3) % 239.47/239.72 («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» a_2 a_3))) % 239.47/239.72 (Or (Eq («const/sets/FINITE» a a_1) False) (Eq («const/sets/FINITE» a a_2) False))) % 239.47/239.72 Clause #122 (by forward demodulation #[121, 7]): ∀ (a : Type) (a_1 a_2 : a → Prop) (a_3 : a → «type/realax/real»), % 239.47/239.72 Or (Eq («const/sets/DISJOINT» a a_1 a_2) False) % 239.47/239.72 (Or % 239.47/239.72 (Eq («const/iterate/sum» a («const/sets/UNION» a a_1 a_2) a_3) % 239.47/239.72 («const/realax/real_add» («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» a_1 a_3) % 239.47/239.72 («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» a_2 a_3))) % 239.47/239.72 (Or (Eq («const/sets/FINITE» a a_1) False) (Eq («const/sets/FINITE» a a_2) False))) % 239.47/239.72 Clause #123 (by forward demodulation #[122, 7]): ∀ (a : Type) (a_1 a_2 : a → Prop) (a_3 : a → «type/realax/real»), % 239.47/239.72 Or (Eq («const/sets/DISJOINT» a a_1 a_2) False) % 239.47/239.72 (Or % 239.47/239.72 (Eq («const/iterate/sum» a («const/sets/UNION» a a_1 a_2) a_3) % 239.47/239.72 («const/realax/real_add» («const/iterate/iterate» a «type/realax/real» «const/realax/real_add» a_1 a_3) % 239.47/239.72 («const/iterate/sum» a a_2 a_3))) % 239.47/239.72 (Or (Eq («const/sets/FINITE» a a_1) False) (Eq («const/sets/FINITE» a a_2) False))) % 239.47/239.72 Clause #124 (by forward demodulation #[123, 7]): ∀ (a : Type) (a_1 a_2 : a → Prop) (a_3 : a → «type/realax/real»), % 239.47/239.72 Or (Eq («const/sets/DISJOINT» a a_1 a_2) False) % 239.47/239.72 (Or % 239.47/239.72 (Eq («const/iterate/sum» a («const/sets/UNION» a a_1 a_2) a_3) % 239.47/239.72 («const/realax/real_add» («const/iterate/sum» a a_1 a_3) («const/iterate/sum» a a_2 a_3))) % 239.47/239.72 (Or (Eq («const/sets/FINITE» a a_1) False) (Eq («const/sets/FINITE» a a_2) False))) % 239.47/239.72 Clause #125 (by superposition #[124, 19]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop) (a_4 : skS.0 0 a → «type/realax/real»), % 239.47/239.72 Or % 239.47/239.72 (Eq % 239.47/239.72 («const/iterate/sum» (skS.0 0 a) % 239.47/239.72 («const/sets/UNION» (skS.0 0 a) (fun x => skS.0 2 a a_1 a_2 x) fun x => skS.0 3 a a_1 a_2 a_3 x) a_4) % 239.47/239.72 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (fun x => skS.0 2 a a_1 a_2 x) a_4) % 239.47/239.72 («const/iterate/sum» (skS.0 0 a) (fun x => skS.0 3 a a_1 a_2 a_3 x) a_4))) % 239.47/239.72 (Or (Eq («const/sets/FINITE» (skS.0 0 a) fun x => skS.0 2 a a_1 a_2 x) False) % 239.47/239.72 (Or (Eq («const/sets/FINITE» (skS.0 0 a) fun x => skS.0 3 a a_1 a_2 a_3 x) False) (Eq False True))) % 239.47/239.72 Clause #4111 (by betaEtaReduce #[125]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop) (a_4 : skS.0 0 a → «type/realax/real»), % 239.47/239.72 Or % 239.47/239.72 (Eq % 239.47/239.72 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4) % 239.47/239.72 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) a_4) % 239.47/239.72 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) a_4))) % 239.47/239.72 (Or (Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) False) % 239.47/239.72 (Or (Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) False) (Eq False True))) % 239.47/239.72 Clause #4112 (by clausification #[4111]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop) (a_4 : skS.0 0 a → «type/realax/real»), % 239.47/239.72 Or % 239.47/239.72 (Eq % 239.47/239.72 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4) % 240.78/241.00 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) a_4) % 240.78/241.00 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) a_4))) % 240.78/241.00 (Or (Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 2 a a_1 a_2)) False) % 240.78/241.00 (Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) False)) % 240.78/241.00 Clause #4113 (by forward demodulation #[4112, 44]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop) (a_4 : skS.0 0 a → «type/realax/real»), % 240.78/241.00 Or % 240.78/241.00 (Eq % 240.78/241.00 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4) % 240.78/241.00 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) a_4) % 240.78/241.00 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) a_4))) % 240.78/241.00 (Or (Eq True False) (Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) False)) % 240.78/241.00 Clause #4114 (by clausification #[4113]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop) (a_4 : skS.0 0 a → «type/realax/real»), % 240.78/241.00 Or % 240.78/241.00 (Eq % 240.78/241.00 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4) % 240.78/241.00 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) a_4) % 240.78/241.00 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) a_4))) % 240.78/241.00 (Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) False) % 240.78/241.00 Clause #4115 (by forward demodulation #[4114, 43]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop) (a_4 : skS.0 0 a → «type/realax/real»), % 240.78/241.00 Or % 240.78/241.00 (Eq % 240.78/241.00 («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4) % 240.78/241.00 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) a_4) % 240.78/241.00 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) a_4))) % 240.78/241.00 (Eq True False) % 240.78/241.00 Clause #4116 (by clausification #[4115]): ∀ (a : Type) (a_1 : skS.0 0 a → «type/realax/real») (a_2 a_3 : skS.0 0 a → Prop) (a_4 : skS.0 0 a → «type/realax/real»), % 240.78/241.00 Eq («const/iterate/sum» (skS.0 0 a) («const/sets/UNION» (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4) % 240.78/241.00 («const/realax/real_add» («const/iterate/sum» (skS.0 0 a) (skS.0 2 a a_1 a_2) a_4) % 240.78/241.00 («const/iterate/sum» (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) a_4)) % 240.78/241.00 Clause #4118 (by backward contextual literal cutting #[4116, 84]): False % 240.78/241.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------