%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET912+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:00:40 PM UTC 2025 % Result : Theorem 4.16s 4.32s % Output : Proof 4.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET912+1 : TPTP v9.2.0. Released v3.2.0. % 0.13/0.13 % Command : duper %s % 0.14/0.34 % Computer : n022.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 13:52:53 EDT 2025 % 0.14/0.34 % CPUTime : % 4.16/4.32 SZS status Theorem for theBenchmark.p % 4.16/4.32 SZS output start Proof for theBenchmark.p % 4.16/4.32 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A B) (set_intersection2 B A)) True % 4.16/4.32 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), subset A B → Eq (set_intersection2 A B) A) True % 4.16/4.32 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (subset (unordered_pair A B) C) (And (in A C) (in B C))) True % 4.16/4.32 Clause #9 (by assumption #[]): Eq (Not (∀ (A B C : Iota), And (in A B) (in C B) → Eq (set_intersection2 (unordered_pair A C) B) (unordered_pair A C))) % 4.16/4.32 True % 4.16/4.32 Clause #26 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a B → Eq (set_intersection2 a B) a) True % 4.16/4.32 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (subset a a_1 → Eq (set_intersection2 a a_1) a) True % 4.16/4.32 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (Eq (set_intersection2 a a_1) a) True) % 4.16/4.32 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_intersection2 a a_1) a) % 4.16/4.32 Clause #31 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a B) (set_intersection2 B a)) True % 4.16/4.32 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)) True % 4.16/4.32 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (set_intersection2 a a_1) (set_intersection2 a_1 a) % 4.16/4.32 Clause #34 (by clausification #[9]): Eq (∀ (A B C : Iota), And (in A B) (in C B) → Eq (set_intersection2 (unordered_pair A C) B) (unordered_pair A C)) False % 4.16/4.32 Clause #35 (by clausification #[34]): ∀ (a : Iota), % 4.16/4.32 Eq % 4.16/4.32 (Not % 4.16/4.32 (∀ (B C : Iota), % 4.16/4.32 And (in (skS.0 2 a) B) (in C B) → % 4.16/4.32 Eq (set_intersection2 (unordered_pair (skS.0 2 a) C) B) (unordered_pair (skS.0 2 a) C))) % 4.16/4.32 True % 4.16/4.32 Clause #36 (by clausification #[35]): ∀ (a : Iota), % 4.16/4.32 Eq % 4.16/4.32 (∀ (B C : Iota), % 4.16/4.32 And (in (skS.0 2 a) B) (in C B) → % 4.16/4.32 Eq (set_intersection2 (unordered_pair (skS.0 2 a) C) B) (unordered_pair (skS.0 2 a) C)) % 4.16/4.32 False % 4.16/4.32 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 4.16/4.32 Eq % 4.16/4.32 (Not % 4.16/4.32 (∀ (C : Iota), % 4.16/4.32 And (in (skS.0 2 a) (skS.0 3 a a_1)) (in C (skS.0 3 a a_1)) → % 4.16/4.32 Eq (set_intersection2 (unordered_pair (skS.0 2 a) C) (skS.0 3 a a_1)) (unordered_pair (skS.0 2 a) C))) % 4.16/4.32 True % 4.16/4.32 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 4.16/4.32 Eq % 4.16/4.32 (∀ (C : Iota), % 4.16/4.32 And (in (skS.0 2 a) (skS.0 3 a a_1)) (in C (skS.0 3 a a_1)) → % 4.16/4.32 Eq (set_intersection2 (unordered_pair (skS.0 2 a) C) (skS.0 3 a a_1)) (unordered_pair (skS.0 2 a) C)) % 4.16/4.32 False % 4.16/4.32 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 4.16/4.32 Eq % 4.16/4.32 (Not % 4.16/4.32 (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) → % 4.16/4.32 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) % 4.16/4.32 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)))) % 4.16/4.32 True % 4.16/4.32 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 4.16/4.32 Eq % 4.16/4.32 (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) → % 4.16/4.32 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) % 4.16/4.32 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 4.16/4.32 False % 4.16/4.32 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1))) True % 4.16/4.32 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.16/4.32 Eq % 4.16/4.32 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) % 4.16/4.32 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 4.16/4.32 False % 4.16/4.32 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) True % 4.16/4.32 Clause #44 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True % 4.16/4.32 Clause #47 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (subset (unordered_pair a B) C) (And (in a C) (in B C))) True % 4.16/4.32 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Iff (subset (unordered_pair a a_1) C) (And (in a C) (in a_1 C))) True % 4.16/4.34 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Eq (Iff (subset (unordered_pair a a_1) a_2) (And (in a a_2) (in a_1 a_2))) True % 4.16/4.34 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) True) (Eq (And (in a a_2) (in a_1 a_2)) False) % 4.16/4.34 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Or (Eq (subset (unordered_pair a a_1) a_2) True) (Or (Eq (in a a_2) False) (Eq (in a_1 a_2) False)) % 4.16/4.34 Clause #54 (by superposition #[52, 44]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Or (Eq (subset (unordered_pair (skS.0 2 a) a_1) (skS.0 3 a a_2)) True) % 4.16/4.34 (Or (Eq (in a_1 (skS.0 3 a a_2)) False) (Eq False True)) % 4.16/4.34 Clause #66 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Ne (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) % 4.16/4.34 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 4.16/4.34 Clause #67 (by forward demodulation #[66, 33]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Ne (set_intersection2 (skS.0 3 a a_1) (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 4.16/4.34 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 4.16/4.34 Clause #97 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Or (Eq (subset (unordered_pair (skS.0 2 a) a_1) (skS.0 3 a a_2)) True) (Eq (in a_1 (skS.0 3 a a_2)) False) % 4.16/4.34 Clause #98 (by superposition #[97, 43]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Or (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) True) (Eq False True) % 4.16/4.34 Clause #108 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) True % 4.16/4.34 Clause #110 (by superposition #[108, 29]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Or (Eq True False) % 4.16/4.34 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) % 4.16/4.34 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 4.16/4.34 Clause #118 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) % 4.16/4.34 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 4.16/4.34 Clause #119 (by superposition #[118, 33]): ∀ (a a_1 a_2 : Iota), % 4.16/4.34 Eq (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 4.16/4.34 (set_intersection2 (skS.0 3 a a_1) (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 4.16/4.34 Clause #121 (by forward contextual literal cutting #[119, 67]): False % 4.16/4.34 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------