%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET873+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:00:37 PM UTC 2025 % Result : Theorem 3.78s 3.97s % Output : Proof 3.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET873+1 : TPTP v9.2.0. Released v3.2.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 : Thu Oct 2 14:56:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.78/3.97 SZS status Theorem for theBenchmark.p % 3.78/3.97 SZS output start Proof for theBenchmark.p % 3.78/3.97 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True % 3.78/3.97 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.78/3.97 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), subset (set_union2 (singleton A) B) B → in A B) True % 3.78/3.97 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 3.78/3.97 Clause #10 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_union2 (singleton A) (singleton B)) (singleton A) → Eq A B)) True % 3.78/3.97 Clause #11 (by clausification #[9]): ∀ (a : Iota), Eq (Iota → subset a a) True % 3.78/3.97 Clause #12 (by clausification #[11]): ∀ (a : Iota), Iota → Eq (subset a a) True % 3.78/3.97 Clause #15 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (set_union2 (singleton a) B) B → in a B) True % 3.78/3.97 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (subset (set_union2 (singleton a) a_1) a_1 → in a a_1) True % 3.78/3.97 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (subset (set_union2 (singleton a) a_1) a_1) False) (Eq (in a a_1) True) % 3.78/3.97 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True % 3.78/3.97 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True % 3.78/3.97 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a) % 3.78/3.97 Clause #27 (by superposition #[26, 17]): ∀ (a a_1 : Iota), Or (Eq (subset (set_union2 a (singleton a_1)) a) False) (Eq (in a_1 a) True) % 3.78/3.97 Clause #34 (by clausification #[10]): Eq (∀ (A B : Iota), Eq (set_union2 (singleton A) (singleton B)) (singleton A) → Eq A B) False % 3.78/3.97 Clause #35 (by clausification #[34]): ∀ (a : Iota), % 3.78/3.97 Eq % 3.78/3.97 (Not % 3.78/3.97 (∀ (B : Iota), Eq (set_union2 (singleton (skS.0 2 a)) (singleton B)) (singleton (skS.0 2 a)) → Eq (skS.0 2 a) B)) % 3.78/3.97 True % 3.78/3.97 Clause #36 (by clausification #[35]): ∀ (a : Iota), % 3.78/3.97 Eq (∀ (B : Iota), Eq (set_union2 (singleton (skS.0 2 a)) (singleton B)) (singleton (skS.0 2 a)) → Eq (skS.0 2 a) B) % 3.78/3.97 False % 3.78/3.97 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.78/3.97 Eq % 3.78/3.97 (Not % 3.78/3.97 (Eq (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) → % 3.78/3.97 Eq (skS.0 2 a) (skS.0 3 a a_1))) % 3.78/3.97 True % 3.78/3.97 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 3.78/3.97 Eq % 3.78/3.97 (Eq (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) → % 3.78/3.97 Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.78/3.97 False % 3.78/3.97 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a))) True % 3.78/3.97 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) False % 3.78/3.97 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) % 3.78/3.97 Clause #50 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.78/3.97 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.78/3.97 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.78/3.97 Clause #69 (by superposition #[27, 41]): ∀ (a a_1 : Iota), % 3.78/3.97 Or (Eq (subset (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) False) % 3.78/3.97 (Eq (in (skS.0 3 a a_1) (singleton (skS.0 2 a))) True) % 3.78/3.97 Clause #70 (by clausification #[53]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.78/3.97 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.78/3.97 Clause #73 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True)) % 3.78/3.97 Clause #76 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 3.78/3.97 Clause #77 (by destructive equality resolution #[76]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 3.78/3.97 Clause #80 (by clausification #[40]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (skS.0 3 a a_1) % 3.78/3.97 Clause #104 (by forward demodulation #[69, 12]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (skS.0 3 a a_1) (singleton (skS.0 2 a))) True) % 3.78/3.97 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a a_1) (singleton (skS.0 2 a))) True % 3.78/3.97 Clause #106 (by superposition #[105, 77]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 3 a a_1) (skS.0 2 a)) % 3.78/3.97 Clause #111 (by clausification #[106]): ∀ (a a_1 : Iota), Eq (skS.0 3 a a_1) (skS.0 2 a) % 3.78/3.97 Clause #112 (by forward contextual literal cutting #[111, 80]): False % 3.78/3.97 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------