%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU355+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:01:27 PM UTC 2025 % Result : Theorem 4.63s 4.78s % Output : Proof 4.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU355+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.33 % Computer : n006.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % 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 : Fri Oct 3 05:37:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.63/4.78 SZS status Theorem for theBenchmark.p % 4.63/4.78 SZS output start Proof for theBenchmark.p % 4.63/4.78 Clause #2 (by assumption #[]): Eq % 4.63/4.78 (∀ (A : Iota), % 4.63/4.78 rel_str A → % 4.63/4.78 ∀ (B C : Iota), % 4.63/4.78 element C (the_carrier A) → % 4.63/4.78 Iff (relstr_element_smaller A B C) (∀ (D : Iota), element D (the_carrier A) → in D B → related A C D)) % 4.63/4.78 True % 4.63/4.78 Clause #3 (by assumption #[]): Eq % 4.63/4.78 (∀ (A : Iota), % 4.63/4.78 rel_str A → % 4.63/4.78 ∀ (B C : Iota), % 4.63/4.78 element C (the_carrier A) → % 4.63/4.78 Iff (relstr_set_smaller A B C) (∀ (D : Iota), element D (the_carrier A) → in D B → related A D C)) % 4.63/4.78 True % 4.63/4.78 Clause #9 (by assumption #[]): Eq (empty empty_set) True % 4.63/4.78 Clause #16 (by assumption #[]): Eq % 4.63/4.78 (Not % 4.63/4.78 (∀ (A : Iota), % 4.63/4.78 rel_str A → % 4.63/4.78 ∀ (B : Iota), % 4.63/4.78 element B (the_carrier A) → And (relstr_set_smaller A empty_set B) (relstr_element_smaller A empty_set B))) % 4.63/4.78 True % 4.63/4.78 Clause #17 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (in A B) (empty B))) True % 4.63/4.78 Clause #43 (by clausification #[2]): ∀ (a : Iota), % 4.63/4.78 Eq % 4.63/4.78 (rel_str a → % 4.63/4.78 ∀ (B C : Iota), % 4.63/4.78 element C (the_carrier a) → % 4.63/4.78 Iff (relstr_element_smaller a B C) (∀ (D : Iota), element D (the_carrier a) → in D B → related a C D)) % 4.63/4.78 True % 4.63/4.78 Clause #44 (by clausification #[43]): ∀ (a : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Eq % 4.63/4.78 (∀ (B C : Iota), % 4.63/4.78 element C (the_carrier a) → % 4.63/4.78 Iff (relstr_element_smaller a B C) (∀ (D : Iota), element D (the_carrier a) → in D B → related a C D)) % 4.63/4.78 True) % 4.63/4.78 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Eq % 4.63/4.78 (∀ (C : Iota), % 4.63/4.78 element C (the_carrier a) → % 4.63/4.78 Iff (relstr_element_smaller a a_1 C) (∀ (D : Iota), element D (the_carrier a) → in D a_1 → related a C D)) % 4.63/4.78 True) % 4.63/4.78 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Eq % 4.63/4.78 (element a_1 (the_carrier a) → % 4.63/4.78 Iff (relstr_element_smaller a a_2 a_1) (∀ (D : Iota), element D (the_carrier a) → in D a_2 → related a a_1 D)) % 4.63/4.78 True) % 4.63/4.78 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.78 (Eq % 4.63/4.78 (Iff (relstr_element_smaller a a_2 a_1) (∀ (D : Iota), element D (the_carrier a) → in D a_2 → related a a_1 D)) % 4.63/4.78 True)) % 4.63/4.78 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.78 (Or (Eq (relstr_element_smaller a a_2 a_1) True) % 4.63/4.78 (Eq (∀ (D : Iota), element D (the_carrier a) → in D a_2 → related a a_1 D) False))) % 4.63/4.78 Clause #50 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.78 (Or (Eq (relstr_element_smaller a a_2 a_1) True) % 4.63/4.78 (Eq % 4.63/4.78 (Not % 4.63/4.78 (element (skS.0 3 a a_2 a_1 a_3) (the_carrier a) → % 4.63/4.78 in (skS.0 3 a a_2 a_1 a_3) a_2 → related a a_1 (skS.0 3 a a_2 a_1 a_3))) % 4.63/4.78 True))) % 4.63/4.78 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.78 (Or (Eq (relstr_element_smaller a a_2 a_1) True) % 4.63/4.78 (Eq % 4.63/4.78 (element (skS.0 3 a a_2 a_1 a_3) (the_carrier a) → % 4.63/4.78 in (skS.0 3 a a_2 a_1 a_3) a_2 → related a a_1 (skS.0 3 a a_2 a_1 a_3)) % 4.63/4.78 False))) % 4.63/4.78 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.78 (Or (Eq (relstr_element_smaller a a_2 a_1) True) % 4.63/4.78 (Eq (in (skS.0 3 a a_2 a_1 a_3) a_2 → related a a_1 (skS.0 3 a a_2 a_1 a_3)) False))) % 4.63/4.78 Clause #68 (by clausification #[3]): ∀ (a : Iota), % 4.63/4.78 Eq % 4.63/4.78 (rel_str a → % 4.63/4.78 ∀ (B C : Iota), % 4.63/4.78 element C (the_carrier a) → % 4.63/4.78 Iff (relstr_set_smaller a B C) (∀ (D : Iota), element D (the_carrier a) → in D B → related a D C)) % 4.63/4.78 True % 4.63/4.78 Clause #69 (by clausification #[68]): ∀ (a : Iota), % 4.63/4.78 Or (Eq (rel_str a) False) % 4.63/4.78 (Eq % 4.63/4.78 (∀ (B C : Iota), % 4.63/4.80 element C (the_carrier a) → % 4.63/4.80 Iff (relstr_set_smaller a B C) (∀ (D : Iota), element D (the_carrier a) → in D B → related a D C)) % 4.63/4.80 True) % 4.63/4.80 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 4.63/4.80 Or (Eq (rel_str a) False) % 4.63/4.80 (Eq % 4.63/4.80 (∀ (C : Iota), % 4.63/4.80 element C (the_carrier a) → % 4.63/4.80 Iff (relstr_set_smaller a a_1 C) (∀ (D : Iota), element D (the_carrier a) → in D a_1 → related a D C)) % 4.63/4.80 True) % 4.63/4.80 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), % 4.63/4.80 Or (Eq (rel_str a) False) % 4.63/4.80 (Eq % 4.63/4.80 (element a_1 (the_carrier a) → % 4.63/4.80 Iff (relstr_set_smaller a a_2 a_1) (∀ (D : Iota), element D (the_carrier a) → in D a_2 → related a D a_1)) % 4.63/4.80 True) % 4.63/4.80 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 4.63/4.80 Or (Eq (rel_str a) False) % 4.63/4.80 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.80 (Eq (Iff (relstr_set_smaller a a_2 a_1) (∀ (D : Iota), element D (the_carrier a) → in D a_2 → related a D a_1)) % 4.63/4.80 True)) % 4.63/4.80 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 4.63/4.80 Or (Eq (rel_str a) False) % 4.63/4.80 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.80 (Or (Eq (relstr_set_smaller a a_2 a_1) True) % 4.63/4.80 (Eq (∀ (D : Iota), element D (the_carrier a) → in D a_2 → related a D a_1) False))) % 4.63/4.80 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), % 4.63/4.80 Or (Eq (rel_str a) False) % 4.63/4.80 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.80 (Or (Eq (relstr_set_smaller a a_2 a_1) True) % 4.63/4.80 (Eq % 4.63/4.80 (Not % 4.63/4.80 (element (skS.0 6 a a_2 a_1 a_3) (the_carrier a) → % 4.63/4.80 in (skS.0 6 a a_2 a_1 a_3) a_2 → related a (skS.0 6 a a_2 a_1 a_3) a_1)) % 4.63/4.80 True))) % 4.63/4.80 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota), % 4.63/4.80 Or (Eq (rel_str a) False) % 4.63/4.80 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.80 (Or (Eq (relstr_set_smaller a a_2 a_1) True) % 4.63/4.80 (Eq % 4.63/4.80 (element (skS.0 6 a a_2 a_1 a_3) (the_carrier a) → % 4.63/4.80 in (skS.0 6 a a_2 a_1 a_3) a_2 → related a (skS.0 6 a a_2 a_1 a_3) a_1) % 4.63/4.80 False))) % 4.63/4.80 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 4.63/4.80 Or (Eq (rel_str a) False) % 4.63/4.80 (Or (Eq (element a_1 (the_carrier a)) False) % 4.63/4.80 (Or (Eq (relstr_set_smaller a a_2 a_1) True) % 4.63/4.80 (Eq (in (skS.0 6 a a_2 a_1 a_3) a_2 → related a (skS.0 6 a a_2 a_1 a_3) a_1) False))) % 4.63/4.80 Clause #80 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (in a B) (empty B))) True % 4.63/4.80 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (Not (And (in a a_1) (empty a_1))) True % 4.63/4.80 Clause #82 (by clausification #[81]): ∀ (a a_1 : Iota), Eq (And (in a a_1) (empty a_1)) False % 4.63/4.80 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (empty a_1) False) % 4.63/4.80 Clause #90 (by clausification #[16]): Eq % 4.63/4.80 (∀ (A : Iota), % 4.63/4.80 rel_str A → % 4.63/4.80 ∀ (B : Iota), % 4.63/4.80 element B (the_carrier A) → And (relstr_set_smaller A empty_set B) (relstr_element_smaller A empty_set B)) % 4.63/4.80 False % 4.63/4.80 Clause #91 (by clausification #[90]): ∀ (a : Iota), % 4.63/4.80 Eq % 4.63/4.80 (Not % 4.63/4.80 (rel_str (skS.0 8 a) → % 4.63/4.80 ∀ (B : Iota), % 4.63/4.80 element B (the_carrier (skS.0 8 a)) → % 4.63/4.80 And (relstr_set_smaller (skS.0 8 a) empty_set B) (relstr_element_smaller (skS.0 8 a) empty_set B))) % 4.63/4.80 True % 4.63/4.80 Clause #92 (by clausification #[91]): ∀ (a : Iota), % 4.63/4.80 Eq % 4.63/4.80 (rel_str (skS.0 8 a) → % 4.63/4.80 ∀ (B : Iota), % 4.63/4.80 element B (the_carrier (skS.0 8 a)) → % 4.63/4.80 And (relstr_set_smaller (skS.0 8 a) empty_set B) (relstr_element_smaller (skS.0 8 a) empty_set B)) % 4.63/4.80 False % 4.63/4.80 Clause #93 (by clausification #[92]): ∀ (a : Iota), Eq (rel_str (skS.0 8 a)) True % 4.63/4.80 Clause #94 (by clausification #[92]): ∀ (a : Iota), % 4.63/4.80 Eq % 4.63/4.80 (∀ (B : Iota), % 4.63/4.80 element B (the_carrier (skS.0 8 a)) → % 4.63/4.80 And (relstr_set_smaller (skS.0 8 a) empty_set B) (relstr_element_smaller (skS.0 8 a) empty_set B)) % 4.63/4.80 False % 4.63/4.80 Clause #123 (by clausification #[94]): ∀ (a a_1 : Iota), % 4.63/4.80 Eq % 4.63/4.80 (Not % 4.63/4.80 (element (skS.0 9 a a_1) (the_carrier (skS.0 8 a)) → % 4.63/4.80 And (relstr_set_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) % 4.68/4.83 (relstr_element_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)))) % 4.68/4.83 True % 4.68/4.83 Clause #124 (by clausification #[123]): ∀ (a a_1 : Iota), % 4.68/4.83 Eq % 4.68/4.83 (element (skS.0 9 a a_1) (the_carrier (skS.0 8 a)) → % 4.68/4.83 And (relstr_set_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) % 4.68/4.83 (relstr_element_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1))) % 4.68/4.83 False % 4.68/4.83 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), Eq (element (skS.0 9 a a_1) (the_carrier (skS.0 8 a))) True % 4.68/4.83 Clause #126 (by clausification #[124]): ∀ (a a_1 : Iota), % 4.68/4.83 Eq % 4.68/4.83 (And (relstr_set_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) % 4.68/4.83 (relstr_element_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1))) % 4.68/4.83 False % 4.68/4.83 Clause #132 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (rel_str a) False) % 4.68/4.83 (Or (Eq (element a_1 (the_carrier a)) False) % 4.68/4.83 (Or (Eq (relstr_element_smaller a a_2 a_1) True) (Eq (in (skS.0 3 a a_2 a_1 a_3) a_2) True))) % 4.68/4.83 Clause #135 (by superposition #[132, 93]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (element a (the_carrier (skS.0 8 a_1))) False) % 4.68/4.83 (Or (Eq (relstr_element_smaller (skS.0 8 a_1) a_2 a) True) % 4.68/4.83 (Or (Eq (in (skS.0 3 (skS.0 8 a_1) a_2 a a_3) a_2) True) (Eq False True))) % 4.68/4.83 Clause #141 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (rel_str a) False) % 4.68/4.83 (Or (Eq (element a_1 (the_carrier a)) False) % 4.68/4.83 (Or (Eq (relstr_set_smaller a a_2 a_1) True) (Eq (in (skS.0 6 a a_2 a_1 a_3) a_2) True))) % 4.68/4.83 Clause #144 (by superposition #[141, 93]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (element a (the_carrier (skS.0 8 a_1))) False) % 4.68/4.83 (Or (Eq (relstr_set_smaller (skS.0 8 a_1) a_2 a) True) % 4.68/4.83 (Or (Eq (in (skS.0 6 (skS.0 8 a_1) a_2 a a_3) a_2) True) (Eq False True))) % 4.68/4.83 Clause #149 (by clausification #[126]): ∀ (a a_1 : Iota), % 4.68/4.83 Or (Eq (relstr_set_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) False) % 4.68/4.83 (Eq (relstr_element_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) False) % 4.68/4.83 Clause #150 (by clausification #[135]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (element a (the_carrier (skS.0 8 a_1))) False) % 4.68/4.83 (Or (Eq (relstr_element_smaller (skS.0 8 a_1) a_2 a) True) (Eq (in (skS.0 3 (skS.0 8 a_1) a_2 a a_3) a_2) True)) % 4.68/4.83 Clause #151 (by superposition #[150, 125]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (relstr_element_smaller (skS.0 8 a) a_1 (skS.0 9 a a_2)) True) % 4.68/4.83 (Or (Eq (in (skS.0 3 (skS.0 8 a) a_1 (skS.0 9 a a_2) a_3) a_1) True) (Eq False True)) % 4.68/4.83 Clause #155 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (element a (the_carrier (skS.0 8 a_1))) False) % 4.68/4.83 (Or (Eq (relstr_set_smaller (skS.0 8 a_1) a_2 a) True) (Eq (in (skS.0 6 (skS.0 8 a_1) a_2 a a_3) a_2) True)) % 4.68/4.83 Clause #156 (by superposition #[155, 125]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (relstr_set_smaller (skS.0 8 a) a_1 (skS.0 9 a a_2)) True) % 4.68/4.83 (Or (Eq (in (skS.0 6 (skS.0 8 a) a_1 (skS.0 9 a a_2) a_3) a_1) True) (Eq False True)) % 4.68/4.83 Clause #167 (by clausification #[151]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (relstr_element_smaller (skS.0 8 a) a_1 (skS.0 9 a a_2)) True) % 4.68/4.83 (Eq (in (skS.0 3 (skS.0 8 a) a_1 (skS.0 9 a a_2) a_3) a_1) True) % 4.68/4.83 Clause #170 (by superposition #[167, 83]): ∀ (a a_1 a_2 : Iota), % 4.68/4.83 Or (Eq (relstr_element_smaller (skS.0 8 a) a_1 (skS.0 9 a a_2)) True) (Or (Eq True False) (Eq (empty a_1) False)) % 4.68/4.83 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 : Iota), Or (Eq (relstr_element_smaller (skS.0 8 a) a_1 (skS.0 9 a a_2)) True) (Eq (empty a_1) False) % 4.68/4.83 Clause #172 (by superposition #[171, 9]): ∀ (a a_1 : Iota), Or (Eq (relstr_element_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) True) (Eq False True) % 4.68/4.83 Clause #176 (by clausification #[172]): ∀ (a a_1 : Iota), Eq (relstr_element_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) True % 4.68/4.83 Clause #177 (by backward demodulation #[176, 149]): ∀ (a a_1 : Iota), Or (Eq (relstr_set_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) False) (Eq True False) % 4.68/4.83 Clause #178 (by clausification #[177]): ∀ (a a_1 : Iota), Eq (relstr_set_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) False % 4.68/4.83 Clause #202 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.83 Or (Eq (relstr_set_smaller (skS.0 8 a) a_1 (skS.0 9 a a_2)) True) % 4.68/4.84 (Eq (in (skS.0 6 (skS.0 8 a) a_1 (skS.0 9 a a_2) a_3) a_1) True) % 4.68/4.84 Clause #205 (by superposition #[202, 83]): ∀ (a a_1 a_2 : Iota), % 4.68/4.84 Or (Eq (relstr_set_smaller (skS.0 8 a) a_1 (skS.0 9 a a_2)) True) (Or (Eq True False) (Eq (empty a_1) False)) % 4.68/4.84 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 : Iota), Or (Eq (relstr_set_smaller (skS.0 8 a) a_1 (skS.0 9 a a_2)) True) (Eq (empty a_1) False) % 4.68/4.84 Clause #207 (by superposition #[206, 9]): ∀ (a a_1 : Iota), Or (Eq (relstr_set_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) True) (Eq False True) % 4.68/4.84 Clause #208 (by clausification #[207]): ∀ (a a_1 : Iota), Eq (relstr_set_smaller (skS.0 8 a) empty_set (skS.0 9 a a_1)) True % 4.68/4.84 Clause #209 (by superposition #[208, 178]): Eq True False % 4.68/4.84 Clause #210 (by clausification #[209]): False % 4.68/4.84 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------