%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU139+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:00:56 PM UTC 2025 % Result : Theorem 3.81s 4.00s % Output : Proof 3.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU139+1 : TPTP v9.2.0. Released v3.3.0. % 0.04/0.14 % Command : duper %s % 0.15/0.35 % Computer : n016.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 05:19:08 EDT 2025 % 0.15/0.35 % CPUTime : % 3.81/4.00 SZS status Theorem for theBenchmark.p % 3.81/4.00 SZS output start Proof for theBenchmark.p % 3.81/4.00 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), proper_subset A B → Not (proper_subset B A)) True % 3.81/4.00 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (proper_subset A B) (And (subset A B) (Ne A B))) True % 3.81/4.00 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Iota → Not (proper_subset A A)) True % 3.81/4.00 Clause #5 (by assumption #[]): Eq (Not (∀ (A B : Iota), Not (And (subset A B) (proper_subset B A)))) True % 3.81/4.00 Clause #8 (by clausification #[3]): ∀ (a : Iota), Eq (Iota → Not (proper_subset a a)) True % 3.81/4.00 Clause #9 (by clausification #[8]): ∀ (a : Iota), Iota → Eq (Not (proper_subset a a)) True % 3.81/4.00 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (proper_subset a a) False % 3.81/4.00 Clause #11 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), proper_subset a B → Not (proper_subset B a)) True % 3.81/4.00 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (proper_subset a a_1 → Not (proper_subset a_1 a)) True % 3.81/4.00 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) False) (Eq (Not (proper_subset a_1 a)) True) % 3.81/4.00 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) False) (Eq (proper_subset a_1 a) False) % 3.81/4.00 Clause #15 (by clausification #[5]): Eq (∀ (A B : Iota), Not (And (subset A B) (proper_subset B A))) False % 3.81/4.00 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Not (And (subset (skS.0 0 a) B) (proper_subset B (skS.0 0 a))))) True % 3.81/4.00 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (subset (skS.0 0 a) B) (proper_subset B (skS.0 0 a)))) False % 3.81/4.00 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 3.81/4.00 Eq (Not (Not (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (proper_subset (skS.0 1 a a_1) (skS.0 0 a))))) True % 3.81/4.00 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Not (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (proper_subset (skS.0 1 a a_1) (skS.0 0 a)))) False % 3.81/4.00 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (proper_subset (skS.0 1 a a_1) (skS.0 0 a))) True % 3.81/4.00 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (proper_subset (skS.0 1 a a_1) (skS.0 0 a)) True % 3.81/4.00 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 3.81/4.00 Clause #23 (by superposition #[21, 14]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (proper_subset (skS.0 0 a) (skS.0 1 a a_1)) False) % 3.81/4.00 Clause #31 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (proper_subset a B) (And (subset a B) (Ne a B))) True % 3.81/4.00 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (Iff (proper_subset a a_1) (And (subset a a_1) (Ne a a_1))) True % 3.81/4.00 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Eq (And (subset a a_1) (Ne a a_1)) False) % 3.81/4.00 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Or (Eq (subset a a_1) False) (Eq (Ne a a_1) False)) % 3.81/4.00 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Or (Eq (subset a a_1) False) (Eq a a_1)) % 3.81/4.00 Clause #48 (by superposition #[22, 36]): ∀ (a a_1 : Iota), % 3.81/4.00 Or (Eq (proper_subset (skS.0 0 a) (skS.0 1 a a_1)) True) (Or (Eq (skS.0 0 a) (skS.0 1 a a_1)) (Eq False True)) % 3.81/4.00 Clause #53 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (proper_subset (skS.0 0 a) (skS.0 1 a a_1)) False % 3.81/4.00 Clause #54 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (proper_subset (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (skS.0 0 a) (skS.0 1 a a_1)) % 3.81/4.00 Clause #55 (by superposition #[54, 53]): ∀ (a a_1 : Iota), Or (Eq (skS.0 0 a) (skS.0 1 a a_1)) (Eq True False) % 3.81/4.00 Clause #58 (by clausification #[55]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 1 a a_1) % 3.81/4.00 Clause #59 (by backward demodulation #[58, 21]): ∀ (a : Iota), Eq (proper_subset (skS.0 0 a) (skS.0 0 a)) True % 3.81/4.00 Clause #65 (by superposition #[59, 10]): Eq True False % 3.81/4.00 Clause #68 (by clausification #[65]): False % 3.81/4.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------