%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU080+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:00:51 PM UTC 2025 % Result : Theorem 48.50s 48.65s % Output : Proof 48.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU080+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 04:56:08 EDT 2025 % 0.13/0.34 % CPUTime : % 48.50/48.65 SZS status Theorem for theBenchmark.p % 48.50/48.65 SZS output start Proof for theBenchmark.p % 48.50/48.65 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq A B) (And (subset A B) (subset B A))) True % 48.50/48.65 Clause #22 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 48.50/48.65 Clause #23 (by assumption #[]): Eq % 48.50/48.65 (∀ (A B C : Iota), % 48.50/48.65 And (relation C) (function C) → % 48.50/48.65 And (subset (relation_inverse_image C A) (relation_inverse_image C B)) (subset A (relation_rng C)) → subset A B) % 48.50/48.65 True % 48.50/48.65 Clause #24 (by assumption #[]): Eq % 48.50/48.65 (Not % 48.50/48.65 (∀ (A B C : Iota), % 48.50/48.65 And (relation C) (function C) → % 48.50/48.65 And (And (Eq (relation_inverse_image C A) (relation_inverse_image C B)) (subset A (relation_rng C))) % 48.50/48.65 (subset B (relation_rng C)) → % 48.50/48.65 Eq A B)) % 48.50/48.65 True % 48.50/48.65 Clause #51 (by clausification #[22]): ∀ (a : Iota), Eq (Iota → subset a a) True % 48.50/48.65 Clause #52 (by clausification #[51]): ∀ (a : Iota), Iota → Eq (subset a a) True % 48.50/48.65 Clause #82 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq a B) (And (subset a B) (subset B a))) True % 48.50/48.65 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 48.50/48.65 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 48.50/48.65 Clause #86 (by clausification #[84]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 48.50/48.65 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 48.50/48.65 Clause #136 (by clausification #[23]): ∀ (a : Iota), % 48.50/48.65 Eq % 48.50/48.65 (∀ (B C : Iota), % 48.50/48.65 And (relation C) (function C) → % 48.50/48.65 And (subset (relation_inverse_image C a) (relation_inverse_image C B)) (subset a (relation_rng C)) → subset a B) % 48.50/48.65 True % 48.50/48.65 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), % 48.50/48.65 Eq % 48.50/48.65 (∀ (C : Iota), % 48.50/48.65 And (relation C) (function C) → % 48.50/48.65 And (subset (relation_inverse_image C a) (relation_inverse_image C a_1)) (subset a (relation_rng C)) → % 48.50/48.65 subset a a_1) % 48.50/48.65 True % 48.50/48.65 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 : Iota), % 48.50/48.65 Eq % 48.50/48.65 (And (relation a) (function a) → % 48.50/48.65 And (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) (subset a_1 (relation_rng a)) → % 48.50/48.65 subset a_1 a_2) % 48.50/48.65 True % 48.50/48.65 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 : Iota), % 48.50/48.65 Or (Eq (And (relation a) (function a)) False) % 48.50/48.65 (Eq % 48.50/48.65 (And (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) (subset a_1 (relation_rng a)) → % 48.50/48.65 subset a_1 a_2) % 48.50/48.65 True) % 48.50/48.65 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 : Iota), % 48.50/48.65 Or % 48.50/48.65 (Eq % 48.50/48.65 (And (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) (subset a_1 (relation_rng a)) → % 48.50/48.65 subset a_1 a_2) % 48.50/48.65 True) % 48.50/48.65 (Or (Eq (relation a) False) (Eq (function a) False)) % 48.50/48.65 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota), % 48.50/48.65 Or (Eq (relation a) False) % 48.50/48.65 (Or (Eq (function a) False) % 48.50/48.65 (Or % 48.50/48.65 (Eq (And (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) (subset a_1 (relation_rng a))) % 48.50/48.65 False) % 48.50/48.65 (Eq (subset a_1 a_2) True))) % 48.50/48.65 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 : Iota), % 48.50/48.65 Or (Eq (relation a) False) % 48.50/48.65 (Or (Eq (function a) False) % 48.50/48.65 (Or (Eq (subset a_1 a_2) True) % 48.50/48.65 (Or (Eq (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) False) % 48.50/48.65 (Eq (subset a_1 (relation_rng a)) False)))) % 48.50/48.65 Clause #200 (by clausification #[24]): Eq % 48.50/48.65 (∀ (A B C : Iota), % 48.50/48.65 And (relation C) (function C) → % 48.50/48.65 And (And (Eq (relation_inverse_image C A) (relation_inverse_image C B)) (subset A (relation_rng C))) % 48.50/48.65 (subset B (relation_rng C)) → % 48.50/48.65 Eq A B) % 48.50/48.65 False % 48.50/48.65 Clause #201 (by clausification #[200]): ∀ (a : Iota), % 48.50/48.65 Eq % 48.50/48.65 (Not % 48.50/48.65 (∀ (B C : Iota), % 48.50/48.65 And (relation C) (function C) → % 48.50/48.65 And % 48.50/48.65 (And (Eq (relation_inverse_image C (skS.0 11 a)) (relation_inverse_image C B)) % 48.50/48.65 (subset (skS.0 11 a) (relation_rng C))) % 48.50/48.65 (subset B (relation_rng C)) → % 48.50/48.68 Eq (skS.0 11 a) B)) % 48.50/48.68 True % 48.50/48.68 Clause #202 (by clausification #[201]): ∀ (a : Iota), % 48.50/48.68 Eq % 48.50/48.68 (∀ (B C : Iota), % 48.50/48.68 And (relation C) (function C) → % 48.50/48.68 And % 48.50/48.68 (And (Eq (relation_inverse_image C (skS.0 11 a)) (relation_inverse_image C B)) % 48.50/48.68 (subset (skS.0 11 a) (relation_rng C))) % 48.50/48.68 (subset B (relation_rng C)) → % 48.50/48.68 Eq (skS.0 11 a) B) % 48.50/48.68 False % 48.50/48.68 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota), % 48.50/48.68 Eq % 48.50/48.68 (Not % 48.50/48.68 (∀ (C : Iota), % 48.50/48.68 And (relation C) (function C) → % 48.50/48.68 And % 48.50/48.68 (And (Eq (relation_inverse_image C (skS.0 11 a)) (relation_inverse_image C (skS.0 12 a a_1))) % 48.50/48.68 (subset (skS.0 11 a) (relation_rng C))) % 48.50/48.68 (subset (skS.0 12 a a_1) (relation_rng C)) → % 48.50/48.68 Eq (skS.0 11 a) (skS.0 12 a a_1))) % 48.50/48.68 True % 48.50/48.68 Clause #204 (by clausification #[203]): ∀ (a a_1 : Iota), % 48.50/48.68 Eq % 48.50/48.68 (∀ (C : Iota), % 48.50/48.68 And (relation C) (function C) → % 48.50/48.68 And % 48.50/48.68 (And (Eq (relation_inverse_image C (skS.0 11 a)) (relation_inverse_image C (skS.0 12 a a_1))) % 48.50/48.68 (subset (skS.0 11 a) (relation_rng C))) % 48.50/48.68 (subset (skS.0 12 a a_1) (relation_rng C)) → % 48.50/48.68 Eq (skS.0 11 a) (skS.0 12 a a_1)) % 48.50/48.68 False % 48.50/48.68 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 : Iota), % 48.50/48.68 Eq % 48.50/48.68 (Not % 48.50/48.68 (And (relation (skS.0 13 a a_1 a_2)) (function (skS.0 13 a a_1 a_2)) → % 48.50/48.68 And % 48.50/48.68 (And % 48.50/48.68 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a)) % 48.50/48.68 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1))) % 48.50/48.68 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2)))) % 48.50/48.68 (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))) → % 48.50/48.68 Eq (skS.0 11 a) (skS.0 12 a a_1))) % 48.50/48.68 True % 48.50/48.68 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 : Iota), % 48.50/48.68 Eq % 48.50/48.68 (And (relation (skS.0 13 a a_1 a_2)) (function (skS.0 13 a a_1 a_2)) → % 48.50/48.68 And % 48.50/48.68 (And % 48.50/48.68 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a)) % 48.50/48.68 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1))) % 48.50/48.68 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2)))) % 48.50/48.68 (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))) → % 48.50/48.68 Eq (skS.0 11 a) (skS.0 12 a a_1)) % 48.50/48.68 False % 48.50/48.68 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 : Iota), Eq (And (relation (skS.0 13 a a_1 a_2)) (function (skS.0 13 a a_1 a_2))) True % 48.50/48.68 Clause #208 (by clausification #[206]): ∀ (a a_1 a_2 : Iota), % 48.50/48.68 Eq % 48.50/48.68 (And % 48.50/48.68 (And % 48.50/48.68 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a)) % 48.50/48.68 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1))) % 48.50/48.68 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2)))) % 48.50/48.68 (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))) → % 48.50/48.68 Eq (skS.0 11 a) (skS.0 12 a a_1)) % 48.50/48.68 False % 48.50/48.68 Clause #209 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), Eq (function (skS.0 13 a a_1 a_2)) True % 48.50/48.68 Clause #210 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), Eq (relation (skS.0 13 a a_1 a_2)) True % 48.50/48.68 Clause #234 (by superposition #[210, 142]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 48.50/48.68 Or (Eq True False) % 48.50/48.68 (Or (Eq (function (skS.0 13 a a_1 a_2)) False) % 48.50/48.68 (Or (Eq (subset a_3 a_4) True) % 48.50/48.68 (Or % 48.50/48.68 (Eq % 48.50/48.68 (subset (relation_inverse_image (skS.0 13 a a_1 a_2) a_3) (relation_inverse_image (skS.0 13 a a_1 a_2) a_4)) % 48.50/48.68 False) % 48.50/48.68 (Eq (subset a_3 (relation_rng (skS.0 13 a a_1 a_2))) False)))) % 48.50/48.68 Clause #347 (by clausification #[208]): ∀ (a a_1 a_2 : Iota), % 48.50/48.68 Eq % 48.50/48.68 (And % 48.50/48.68 (And % 48.50/48.68 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a)) % 48.50/48.68 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1))) % 48.50/48.68 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2)))) % 48.50/48.68 (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2)))) % 48.50/48.68 True % 48.50/48.68 Clause #348 (by clausification #[208]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 11 a) (skS.0 12 a a_1)) False % 48.50/48.68 Clause #349 (by clausification #[347]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))) True % 48.50/48.70 Clause #350 (by clausification #[347]): ∀ (a a_1 a_2 : Iota), % 48.50/48.70 Eq % 48.50/48.70 (And % 48.50/48.70 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a)) % 48.50/48.70 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1))) % 48.50/48.70 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2)))) % 48.50/48.70 True % 48.50/48.70 Clause #353 (by clausification #[348]): ∀ (a a_1 : Iota), Ne (skS.0 11 a) (skS.0 12 a a_1) % 48.50/48.70 Clause #410 (by clausification #[234]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 48.50/48.70 Or (Eq (function (skS.0 13 a a_1 a_2)) False) % 48.50/48.70 (Or (Eq (subset a_3 a_4) True) % 48.50/48.70 (Or % 48.50/48.70 (Eq (subset (relation_inverse_image (skS.0 13 a a_1 a_2) a_3) (relation_inverse_image (skS.0 13 a a_1 a_2) a_4)) % 48.50/48.70 False) % 48.50/48.70 (Eq (subset a_3 (relation_rng (skS.0 13 a a_1 a_2))) False))) % 48.50/48.70 Clause #411 (by forward demodulation #[410, 209]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 48.50/48.70 Or (Eq True False) % 48.50/48.70 (Or (Eq (subset a a_1) True) % 48.50/48.70 (Or % 48.50/48.70 (Eq % 48.50/48.70 (subset (relation_inverse_image (skS.0 13 a_2 a_3 a_4) a) (relation_inverse_image (skS.0 13 a_2 a_3 a_4) a_1)) % 48.50/48.70 False) % 48.50/48.70 (Eq (subset a (relation_rng (skS.0 13 a_2 a_3 a_4))) False))) % 48.50/48.70 Clause #412 (by clausification #[411]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 48.50/48.70 Or (Eq (subset a a_1) True) % 48.50/48.70 (Or % 48.50/48.70 (Eq (subset (relation_inverse_image (skS.0 13 a_2 a_3 a_4) a) (relation_inverse_image (skS.0 13 a_2 a_3 a_4) a_1)) % 48.50/48.70 False) % 48.50/48.70 (Eq (subset a (relation_rng (skS.0 13 a_2 a_3 a_4))) False)) % 48.50/48.70 Clause #468 (by clausification #[350]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))) True % 48.50/48.70 Clause #469 (by clausification #[350]): ∀ (a a_1 a_2 : Iota), % 48.50/48.70 Eq % 48.50/48.70 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a)) % 48.50/48.70 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1))) % 48.50/48.70 True % 48.50/48.70 Clause #771 (by clausification #[469]): ∀ (a a_1 a_2 : Iota), % 48.50/48.70 Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a)) % 48.50/48.70 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1)) % 48.50/48.70 Clause #772 (by superposition #[771, 412]): ∀ (a a_1 a_2 a_3 : Iota), % 48.50/48.70 Or (Eq (subset a (skS.0 12 a_1 a_2)) True) % 48.50/48.70 (Or % 48.50/48.70 (Eq % 48.50/48.70 (subset (relation_inverse_image (skS.0 13 a_1 a_2 a_3) a) % 48.50/48.70 (relation_inverse_image (skS.0 13 a_1 a_2 a_3) (skS.0 11 a_1))) % 48.50/48.70 False) % 48.50/48.70 (Eq (subset a (relation_rng (skS.0 13 a_1 a_2 a_3))) False)) % 48.50/48.70 Clause #773 (by superposition #[771, 412]): ∀ (a a_1 a_2 a_3 : Iota), % 48.50/48.70 Or (Eq (subset (skS.0 12 a a_1) a_2) True) % 48.50/48.70 (Or % 48.50/48.70 (Eq % 48.50/48.70 (subset (relation_inverse_image (skS.0 13 a a_1 a_3) (skS.0 11 a)) % 48.50/48.70 (relation_inverse_image (skS.0 13 a a_1 a_3) a_2)) % 48.50/48.70 False) % 48.50/48.70 (Eq (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_3))) False)) % 48.50/48.70 Clause #5615 (by superposition #[772, 52]): ∀ (a a_1 a_2 : Iota), % 48.50/48.70 Or (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) True) % 48.50/48.70 (Or (Eq (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))) False) (Eq False True)) % 48.50/48.70 Clause #5617 (by clausification #[5615]): ∀ (a a_1 a_2 : Iota), % 48.50/48.70 Or (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) True) % 48.50/48.70 (Eq (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))) False) % 48.50/48.70 Clause #5618 (by superposition #[5617, 468]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) True) (Eq False True) % 48.50/48.70 Clause #5619 (by clausification #[5618]): ∀ (a a_1 : Iota), Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) True % 48.50/48.70 Clause #5629 (by forward demodulation #[773, 349]): ∀ (a a_1 a_2 a_3 : Iota), % 48.50/48.70 Or (Eq (subset (skS.0 12 a a_1) a_2) True) % 48.50/48.70 (Or % 48.50/48.70 (Eq % 48.50/48.70 (subset (relation_inverse_image (skS.0 13 a a_1 a_3) (skS.0 11 a)) % 48.50/48.70 (relation_inverse_image (skS.0 13 a a_1 a_3) a_2)) % 48.50/48.70 False) % 48.50/48.70 (Eq True False)) % 48.50/48.70 Clause #5630 (by clausification #[5629]): ∀ (a a_1 a_2 a_3 : Iota), % 48.50/48.70 Or (Eq (subset (skS.0 12 a a_1) a_2) True) % 48.50/48.70 (Eq % 48.50/48.70 (subset (relation_inverse_image (skS.0 13 a a_1 a_3) (skS.0 11 a)) % 48.50/48.70 (relation_inverse_image (skS.0 13 a a_1 a_3) a_2)) % 48.50/48.70 False) % 48.50/48.70 Clause #5631 (by superposition #[5630, 52]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 12 a a_1) (skS.0 11 a)) True) (Eq False True) % 48.50/48.75 Clause #5633 (by clausification #[5631]): ∀ (a a_1 : Iota), Eq (subset (skS.0 12 a a_1) (skS.0 11 a)) True % 48.50/48.75 Clause #5634 (by superposition #[5633, 87]): ∀ (a a_1 : Iota), % 48.50/48.75 Or (Eq (skS.0 12 a a_1) (skS.0 11 a)) (Or (Eq True False) (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) False)) % 48.50/48.75 Clause #5706 (by clausification #[5634]): ∀ (a a_1 : Iota), Or (Eq (skS.0 12 a a_1) (skS.0 11 a)) (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) False) % 48.50/48.75 Clause #5707 (by forward contextual literal cutting #[5706, 353]): ∀ (a a_1 : Iota), Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) False % 48.50/48.75 Clause #5708 (by superposition #[5707, 5619]): Eq False True % 48.50/48.75 Clause #5709 (by clausification #[5708]): False % 48.50/48.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------