%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET627+3 : TPTP v9.2.0. Released v2.2.0. % 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 08:00:17 PM UTC 2025 % Result : Theorem 3.59s 3.80s % Output : Proof 3.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.15 % Problem : SET627+3 : TPTP v9.2.0. Released v2.2.0. % 0.13/0.16 % Command : duper %s % 0.14/0.38 % Computer : n007.cluster.edu % 0.14/0.38 % Model : x86_64 x86_64 % 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.38 % Memory : 8042.1875MB % 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.38 % CPULimit : 300 % 0.14/0.38 % WCLimit : 300 % 0.14/0.38 % DateTime : Thu Oct 2 15:00:08 EDT 2025 % 0.14/0.38 % CPUTime : % 3.59/3.80 SZS status Theorem for theBenchmark.p % 3.59/3.80 SZS output start Proof for theBenchmark.p % 3.59/3.80 Clause #0 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True % 3.59/3.80 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True % 3.59/3.80 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Iff (disjoint B C) (Not (intersect B C))) True % 3.59/3.80 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), intersect B C → intersect C B) True % 3.59/3.80 Clause #5 (by assumption #[]): Eq (Not (∀ (B : Iota), disjoint B empty_set)) True % 3.59/3.80 Clause #6 (by clausification #[5]): Eq (∀ (B : Iota), disjoint B empty_set) False % 3.59/3.80 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (Not (disjoint (skS.0 0 a) empty_set)) True % 3.59/3.80 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (disjoint (skS.0 0 a) empty_set) False % 3.59/3.80 Clause #9 (by clausification #[0]): ∀ (a : Iota), Eq (Not (member a empty_set)) True % 3.59/3.80 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (member a empty_set) False % 3.59/3.80 Clause #11 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), intersect a C → intersect C a) True % 3.59/3.80 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (intersect a a_1 → intersect a_1 a) True % 3.59/3.80 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (intersect a_1 a) True) % 3.59/3.80 Clause #22 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True % 3.59/3.80 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True % 3.59/3.80 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (Exists fun D => And (member D a) (member D a_1)) True) % 3.59/3.80 Clause #32 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (disjoint a C) (Not (intersect a C))) True % 3.59/3.80 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Not (intersect a a_1))) True % 3.59/3.80 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Not (intersect a a_1)) False) % 3.59/3.80 Clause #36 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (intersect a a_1) True) % 3.59/3.80 Clause #37 (by superposition #[36, 8]): ∀ (a : Iota), Or (Eq (intersect (skS.0 0 a) empty_set) True) (Eq True False) % 3.59/3.80 Clause #41 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 3.59/3.80 Or (Eq (intersect a a_1) False) (Eq (And (member (skS.0 2 a a_1 a_2) a) (member (skS.0 2 a a_1 a_2) a_1)) True) % 3.59/3.80 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 2 a a_1 a_2) a) True) % 3.59/3.80 Clause #44 (by clausification #[37]): ∀ (a : Iota), Eq (intersect (skS.0 0 a) empty_set) True % 3.59/3.80 Clause #45 (by superposition #[44, 13]): ∀ (a : Iota), Or (Eq True False) (Eq (intersect empty_set (skS.0 0 a)) True) % 3.59/3.80 Clause #47 (by clausification #[45]): ∀ (a : Iota), Eq (intersect empty_set (skS.0 0 a)) True % 3.59/3.80 Clause #51 (by superposition #[43, 47]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (member (skS.0 2 empty_set (skS.0 0 a) a_1) empty_set) True) % 3.59/3.80 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (member (skS.0 2 empty_set (skS.0 0 a) a_1) empty_set) True % 3.59/3.80 Clause #53 (by superposition #[52, 10]): Eq True False % 3.59/3.80 Clause #57 (by clausification #[53]): False % 3.59/3.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------