%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET631+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 08:00:18 PM UTC 2025 % Result : Theorem 4.39s 4.61s % Output : Proof 4.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET631+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n028.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 13:37:53 EDT 2025 % 0.14/0.35 % CPUTime : % 4.39/4.61 SZS status Theorem for theBenchmark.p % 4.39/4.61 SZS output start Proof for theBenchmark.p % 4.39/4.61 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (difference B C)) (And (member D B) (Not (member D C)))) True % 4.39/4.61 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True % 4.39/4.61 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), intersect B C → intersect C B) True % 4.39/4.61 Clause #3 (by assumption #[]): Eq (Not (∀ (B C D : Iota), intersect B (difference C D) → intersect B C)) True % 4.39/4.61 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), intersect a C → intersect C a) True % 4.39/4.61 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (intersect a a_1 → intersect a_1 a) True % 4.39/4.61 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (intersect a_1 a) True) % 4.39/4.61 Clause #7 (by clausification #[3]): Eq (∀ (B C D : Iota), intersect B (difference C D) → intersect B C) False % 4.39/4.61 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (C D : Iota), intersect (skS.0 0 a) (difference C D) → intersect (skS.0 0 a) C)) True % 4.39/4.61 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (C D : Iota), intersect (skS.0 0 a) (difference C D) → intersect (skS.0 0 a) C) False % 4.39/4.61 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 4.39/4.61 Eq (Not (∀ (D : Iota), intersect (skS.0 0 a) (difference (skS.0 1 a a_1) D) → intersect (skS.0 0 a) (skS.0 1 a a_1))) % 4.39/4.61 True % 4.39/4.61 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 4.39/4.61 Eq (∀ (D : Iota), intersect (skS.0 0 a) (difference (skS.0 1 a a_1) D) → intersect (skS.0 0 a) (skS.0 1 a a_1)) False % 4.39/4.61 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.39/4.61 Eq % 4.39/4.61 (Not % 4.39/4.61 (intersect (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → intersect (skS.0 0 a) (skS.0 1 a a_1))) % 4.39/4.61 True % 4.39/4.61 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 4.39/4.61 Eq (intersect (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → intersect (skS.0 0 a) (skS.0 1 a a_1)) % 4.39/4.61 False % 4.39/4.61 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Eq (intersect (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 4.39/4.61 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (intersect (skS.0 0 a) (skS.0 1 a a_1)) False % 4.39/4.61 Clause #16 (by superposition #[14, 6]): ∀ (a a_1 a_2 : Iota), % 4.39/4.61 Or (Eq True False) (Eq (intersect (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (skS.0 0 a)) True) % 4.39/4.61 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True % 4.39/4.61 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True % 4.39/4.61 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) True) (Eq (Exists fun D => And (member D a) (member D a_1)) False) % 4.39/4.61 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (Exists fun D => And (member D a) (member D a_1)) True) % 4.39/4.61 Clause #21 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Eq (And (member a_2 a) (member a_2 a_1)) False) % 4.39/4.61 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) False)) % 4.39/4.61 Clause #23 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 4.39/4.61 Or (Eq (intersect a a_1) False) (Eq (And (member (skS.0 3 a a_1 a_2) a) (member (skS.0 3 a a_1 a_2) a_1)) True) % 4.39/4.61 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 3 a a_1 a_2) a_1) True) % 4.39/4.61 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 3 a a_1 a_2) a) True) % 4.39/4.61 Clause #27 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (difference a C)) (And (member D a) (Not (member D C)))) True % 4.39/4.61 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (difference a a_1)) (And (member D a) (Not (member D a_1)))) True % 4.48/4.63 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (difference a_1 a_2)) (And (member a a_1) (Not (member a a_2)))) True % 4.48/4.63 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (And (member a a_1) (Not (member a a_2))) True) % 4.48/4.63 Clause #35 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (member a a_1) True) % 4.48/4.63 Clause #38 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (intersect (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (skS.0 0 a)) True % 4.48/4.63 Clause #40 (by superposition #[38, 24]): ∀ (a a_1 a_2 a_3 : Iota), % 4.48/4.63 Or (Eq True False) % 4.48/4.63 (Eq (member (skS.0 3 (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (skS.0 0 a) a_3) (skS.0 0 a)) True) % 4.48/4.63 Clause #41 (by superposition #[38, 25]): ∀ (a a_1 a_2 a_3 : Iota), % 4.48/4.63 Or (Eq True False) % 4.48/4.63 (Eq % 4.48/4.63 (member (skS.0 3 (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (skS.0 0 a) a_3) % 4.48/4.63 (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.48/4.63 True) % 4.48/4.63 Clause #47 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.48/4.63 Eq (member (skS.0 3 (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (skS.0 0 a) a_3) (skS.0 0 a)) True % 4.48/4.63 Clause #48 (by superposition #[47, 22]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.48/4.63 Or (Eq (intersect (skS.0 0 a) a_1) True) % 4.48/4.63 (Or (Eq True False) % 4.48/4.63 (Eq (member (skS.0 3 (difference (skS.0 1 a a_2) (skS.0 2 a a_2 a_3)) (skS.0 0 a) a_4) a_1) False)) % 4.48/4.63 Clause #57 (by clausification #[48]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.48/4.63 Or (Eq (intersect (skS.0 0 a) a_1) True) % 4.48/4.63 (Eq (member (skS.0 3 (difference (skS.0 1 a a_2) (skS.0 2 a a_2 a_3)) (skS.0 0 a) a_4) a_1) False) % 4.48/4.63 Clause #59 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 4.48/4.63 Eq % 4.48/4.63 (member (skS.0 3 (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (skS.0 0 a) a_3) % 4.48/4.63 (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.48/4.63 True % 4.48/4.63 Clause #61 (by superposition #[59, 35]): ∀ (a a_1 a_2 a_3 : Iota), % 4.48/4.63 Or (Eq True False) % 4.48/4.63 (Eq (member (skS.0 3 (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (skS.0 0 a) a_3) (skS.0 1 a a_1)) True) % 4.48/4.63 Clause #71 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota), % 4.48/4.63 Eq (member (skS.0 3 (difference (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (skS.0 0 a) a_3) (skS.0 1 a a_1)) True % 4.48/4.63 Clause #72 (by superposition #[71, 57]): ∀ (a a_1 : Iota), Or (Eq (intersect (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False) % 4.48/4.63 Clause #79 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (intersect (skS.0 0 a) (skS.0 1 a a_1)) True % 4.48/4.63 Clause #80 (by superposition #[79, 15]): Eq True False % 4.48/4.63 Clause #84 (by clausification #[80]): False % 4.48/4.63 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------