%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU666^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:02:10 PM UTC 2025 % Result : Theorem 4.37s 4.57s % Output : Proof 4.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.09 % Problem : SEU666^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.10 % Command : duper %s % 0.09/0.30 % Computer : n008.cluster.edu % 0.09/0.30 % Model : x86_64 x86_64 % 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.30 % Memory : 8042.1875MB % 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.30 % CPULimit : 300 % 0.09/0.30 % WCLimit : 300 % 0.09/0.30 % DateTime : Fri Oct 3 06:14:38 EDT 2025 % 0.09/0.30 % CPUTime : % 4.37/4.57 SZS status Theorem for theBenchmark.p % 4.37/4.57 SZS output start Proof for theBenchmark.p % 4.37/4.57 Clause #0 (by assumption #[]): Eq (Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → in Xx A)) % 4.37/4.57 True % 4.37/4.57 Clause #1 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 4.37/4.57 Clause #2 (by assumption #[]): Eq % 4.37/4.57 (Eq dpsetconstr fun A B Xphi => % 4.37/4.57 dsetconstr (cartprod A B) fun Xu => % 4.37/4.57 Exists fun Xx => And (in Xx A) (Exists fun Xy => And (And (in Xy B) (Xphi Xx Xy)) (Eq Xu (kpair Xx Xy)))) % 4.37/4.57 True % 4.37/4.57 Clause #3 (by assumption #[]): Eq % 4.37/4.57 (Not % 4.37/4.57 (dsetconstrEL → % 4.37/4.57 subsetI2 → % 4.37/4.57 ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B fun Xx Xy => Xphi Xx Xy) (cartprod A B))) % 4.37/4.57 True % 4.37/4.57 Clause #4 (by clausification #[1]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.37/4.57 Clause #6 (by clausify Prop equality #[4]): Or (Eq subsetI2 False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) True) % 4.37/4.57 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq subsetI2 False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True) % 4.37/4.57 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True) % 4.37/4.57 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True)) % 4.37/4.57 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.37/4.57 Or (Eq subsetI2 False) % 4.37/4.57 (Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1)) True)) % 4.37/4.57 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.37/4.57 Or (Eq subsetI2 False) % 4.37/4.57 (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1) False)) % 4.37/4.57 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 4.37/4.57 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 4.37/4.57 Clause #23 (by betaEtaReduce #[0]): Eq (Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A)) True % 4.37/4.57 Clause #24 (by clausification #[23]): Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A) % 4.37/4.57 Clause #28 (by clausification #[2]): Eq dpsetconstr fun A B Xphi => % 4.37/4.57 dsetconstr (cartprod A B) fun Xu => % 4.37/4.57 Exists fun Xx => And (in Xx A) (Exists fun Xy => And (And (in Xy B) (Xphi Xx Xy)) (Eq Xu (kpair Xx Xy))) % 4.37/4.57 Clause #31 (by argument congruence #[28]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), % 4.37/4.57 Eq (dpsetconstr a a_1 a_2) % 4.37/4.57 ((fun A B Xphi => % 4.37/4.57 dsetconstr (cartprod A B) fun Xu => % 4.37/4.57 Exists fun Xx => And (in Xx A) (Exists fun Xy => And (And (in Xy B) (Xphi Xx Xy)) (Eq Xu (kpair Xx Xy)))) % 4.37/4.57 a a_1 a_2) % 4.37/4.57 Clause #44 (by betaEtaReduce #[3]): Eq % 4.37/4.57 (Not % 4.37/4.57 (dsetconstrEL → % 4.37/4.57 subsetI2 → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B))) % 4.37/4.57 True % 4.37/4.57 Clause #45 (by clausification #[44]): Eq (dsetconstrEL → subsetI2 → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B)) % 4.37/4.57 False % 4.37/4.57 Clause #46 (by clausification #[45]): Eq dsetconstrEL True % 4.37/4.57 Clause #47 (by clausification #[45]): Eq (subsetI2 → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B)) False % 4.37/4.57 Clause #48 (by backward demodulation #[46, 24]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A) % 4.37/4.57 Clause #51 (by clausification #[48]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → in Xx a) True % 4.37/4.57 Clause #52 (by clausification #[51]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → in Xx a) True % 4.37/4.57 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → in a a_1) True % 4.42/4.59 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (in a a_1) True) % 4.42/4.59 Clause #55 (by clausification #[47]): Eq subsetI2 True % 4.42/4.59 Clause #56 (by clausification #[47]): Eq (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B)) False % 4.42/4.59 Clause #58 (by backward demodulation #[55, 13]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 4.42/4.59 Clause #61 (by backward demodulation #[55, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 4.42/4.59 Clause #70 (by clausification #[56]): ∀ (a : Iota), % 4.42/4.59 Eq (Not (∀ (B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr (skS.0 7 a) B Xphi) (cartprod (skS.0 7 a) B))) % 4.42/4.59 True % 4.42/4.59 Clause #71 (by clausification #[70]): ∀ (a : Iota), % 4.42/4.59 Eq (∀ (B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr (skS.0 7 a) B Xphi) (cartprod (skS.0 7 a) B)) False % 4.42/4.59 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), % 4.42/4.59 Eq % 4.42/4.59 (Not % 4.42/4.59 (∀ (Xphi : Iota → Iota → Prop), % 4.42/4.59 subset (dpsetconstr (skS.0 7 a) (skS.0 8 a a_1) Xphi) (cartprod (skS.0 7 a) (skS.0 8 a a_1)))) % 4.42/4.59 True % 4.42/4.59 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), % 4.42/4.59 Eq % 4.42/4.59 (∀ (Xphi : Iota → Iota → Prop), % 4.42/4.59 subset (dpsetconstr (skS.0 7 a) (skS.0 8 a a_1) Xphi) (cartprod (skS.0 7 a) (skS.0 8 a a_1))) % 4.42/4.59 False % 4.42/4.59 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), % 4.42/4.59 Eq (Not (subset (dpsetconstr (skS.0 7 a) (skS.0 8 a a_1) (skS.0 9 a a_1 a_2)) (cartprod (skS.0 7 a) (skS.0 8 a a_1)))) % 4.42/4.59 True % 4.42/4.59 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), % 4.42/4.59 Eq (subset (dpsetconstr (skS.0 7 a) (skS.0 8 a a_1) (skS.0 9 a a_1 a_2)) (cartprod (skS.0 7 a) (skS.0 8 a a_1))) False % 4.42/4.59 Clause #89 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False) % 4.42/4.59 Clause #95 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True) % 4.42/4.59 Clause #96 (by superposition #[95, 54]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 a_3 : Iota), % 4.42/4.59 Or (Eq (subset (dsetconstr a a_1) a_2) True) % 4.42/4.59 (Or (Eq True False) (Eq (in (skS.0 0 (dsetconstr a a_1) a_2 a_3) a) True)) % 4.42/4.59 Clause #100 (by clausification #[96]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 a_3 : Iota), % 4.42/4.59 Or (Eq (subset (dsetconstr a a_1) a_2) True) (Eq (in (skS.0 0 (dsetconstr a a_1) a_2 a_3) a) True) % 4.42/4.59 Clause #102 (by superposition #[100, 89]): ∀ (a : Iota) (a_1 : Iota → Prop), % 4.42/4.59 Or (Eq (subset (dsetconstr a a_1) a) True) (Or (Eq (subset (dsetconstr a a_1) a) True) (Eq True False)) % 4.42/4.59 Clause #105 (by betaEtaReduce #[31]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), % 4.42/4.59 Eq (dpsetconstr a a_1 a_2) % 4.42/4.59 (dsetconstr (cartprod a a_1) fun Xu => % 4.42/4.59 Exists fun Xx => And (in Xx a) (Exists fun Xy => And (And (in Xy a_1) (a_2 Xx Xy)) (Eq Xu (kpair Xx Xy)))) % 4.42/4.59 Clause #176 (by clausification #[102]): ∀ (a : Iota) (a_1 : Iota → Prop), Or (Eq (subset (dsetconstr a a_1) a) True) (Eq (subset (dsetconstr a a_1) a) True) % 4.42/4.59 Clause #177 (by eliminate duplicate literals #[176]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (subset (dsetconstr a a_1) a) True % 4.42/4.59 Clause #178 (by superposition #[177, 105]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), Eq (subset (dpsetconstr a a_1 a_2) (cartprod a a_1)) True % 4.42/4.59 Clause #185 (by superposition #[178, 75]): Eq True False % 4.42/4.59 Clause #193 (by clausification #[185]): False % 4.42/4.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------