%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU361+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 5.28s 5.45s % Output : Proof 5.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU361+1 : TPTP v9.2.0. Released v3.3.0. % 0.04/0.13 % Command : duper %s % 0.12/0.34 % Computer : n026.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 05:18:38 EDT 2025 % 0.12/0.34 % CPUTime : % 5.28/5.45 SZS status Theorem for theBenchmark.p % 5.28/5.45 SZS output start Proof for theBenchmark.p % 5.28/5.45 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), rel_str A → Eq (bottom_of_relstr A) (join_on_relstr A empty_set)) True % 5.28/5.45 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), rel_str A → element (join_on_relstr A B) (the_carrier A)) True % 5.28/5.45 Clause #18 (by assumption #[]): Eq % 5.28/5.45 (∀ (A : Iota), % 5.28/5.45 And (antisymmetric_relstr A) (rel_str A) → % 5.28/5.45 ∀ (B : Iota), % 5.28/5.45 element B (the_carrier A) → % 5.28/5.45 ∀ (C : Iota), % 5.28/5.45 And % 5.28/5.45 (And (Eq B (join_on_relstr A C)) (ex_sup_of_relstr_set A C) → % 5.28/5.45 And (relstr_set_smaller A C B) % 5.28/5.45 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A C D → related A B D)) % 5.28/5.45 (And (relstr_set_smaller A C B) % 5.28/5.45 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A C D → related A B D) → % 5.28/5.45 And (Eq B (join_on_relstr A C)) (ex_sup_of_relstr_set A C))) % 5.28/5.45 True % 5.28/5.45 Clause #19 (by assumption #[]): Eq % 5.28/5.45 (∀ (A : Iota), % 5.28/5.45 And (And (And (Not (empty_carrier A)) (antisymmetric_relstr A)) (lower_bounded_relstr A)) (rel_str A) → % 5.28/5.45 And (ex_sup_of_relstr_set A empty_set) (ex_inf_of_relstr_set A (the_carrier A))) % 5.28/5.45 True % 5.28/5.45 Clause #20 (by assumption #[]): Eq % 5.28/5.45 (Not % 5.28/5.45 (∀ (A : Iota), % 5.28/5.45 And (And (And (Not (empty_carrier A)) (antisymmetric_relstr A)) (lower_bounded_relstr A)) (rel_str A) → % 5.28/5.45 ∀ (B : Iota), element B (the_carrier A) → related A (bottom_of_relstr A) B)) % 5.28/5.45 True % 5.28/5.45 Clause #22 (by assumption #[]): Eq % 5.28/5.45 (∀ (A : Iota), % 5.28/5.45 rel_str A → % 5.28/5.45 ∀ (B : Iota), % 5.28/5.45 element B (the_carrier A) → And (relstr_set_smaller A empty_set B) (relstr_element_smaller A empty_set B)) % 5.28/5.45 True % 5.28/5.45 Clause #49 (by clausification #[2]): ∀ (a : Iota), Eq (rel_str a → Eq (bottom_of_relstr a) (join_on_relstr a empty_set)) True % 5.28/5.45 Clause #50 (by clausification #[49]): ∀ (a : Iota), Or (Eq (rel_str a) False) (Eq (Eq (bottom_of_relstr a) (join_on_relstr a empty_set)) True) % 5.28/5.45 Clause #51 (by clausification #[50]): ∀ (a : Iota), Or (Eq (rel_str a) False) (Eq (bottom_of_relstr a) (join_on_relstr a empty_set)) % 5.28/5.45 Clause #69 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), rel_str a → element (join_on_relstr a B) (the_carrier a)) True % 5.28/5.45 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), Eq (rel_str a → element (join_on_relstr a a_1) (the_carrier a)) True % 5.28/5.45 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), Or (Eq (rel_str a) False) (Eq (element (join_on_relstr a a_1) (the_carrier a)) True) % 5.28/5.45 Clause #95 (by clausification #[19]): ∀ (a : Iota), % 5.28/5.45 Eq % 5.28/5.45 (And (And (And (Not (empty_carrier a)) (antisymmetric_relstr a)) (lower_bounded_relstr a)) (rel_str a) → % 5.28/5.45 And (ex_sup_of_relstr_set a empty_set) (ex_inf_of_relstr_set a (the_carrier a))) % 5.28/5.45 True % 5.28/5.45 Clause #96 (by clausification #[95]): ∀ (a : Iota), % 5.28/5.45 Or (Eq (And (And (And (Not (empty_carrier a)) (antisymmetric_relstr a)) (lower_bounded_relstr a)) (rel_str a)) False) % 5.28/5.45 (Eq (And (ex_sup_of_relstr_set a empty_set) (ex_inf_of_relstr_set a (the_carrier a))) True) % 5.28/5.45 Clause #97 (by clausification #[96]): ∀ (a : Iota), % 5.28/5.45 Or (Eq (And (ex_sup_of_relstr_set a empty_set) (ex_inf_of_relstr_set a (the_carrier a))) True) % 5.28/5.45 (Or (Eq (And (And (Not (empty_carrier a)) (antisymmetric_relstr a)) (lower_bounded_relstr a)) False) % 5.28/5.45 (Eq (rel_str a) False)) % 5.28/5.45 Clause #99 (by clausification #[97]): ∀ (a : Iota), % 5.28/5.45 Or (Eq (And (And (Not (empty_carrier a)) (antisymmetric_relstr a)) (lower_bounded_relstr a)) False) % 5.28/5.45 (Or (Eq (rel_str a) False) (Eq (ex_sup_of_relstr_set a empty_set) True)) % 5.28/5.45 Clause #104 (by clausification #[20]): Eq % 5.28/5.45 (∀ (A : Iota), % 5.28/5.45 And (And (And (Not (empty_carrier A)) (antisymmetric_relstr A)) (lower_bounded_relstr A)) (rel_str A) → % 5.28/5.45 ∀ (B : Iota), element B (the_carrier A) → related A (bottom_of_relstr A) B) % 5.28/5.45 False % 5.28/5.45 Clause #105 (by clausification #[104]): ∀ (a : Iota), % 5.28/5.45 Eq % 5.28/5.45 (Not % 5.28/5.45 (And % 5.28/5.45 (And (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a))) % 5.28/5.45 (lower_bounded_relstr (skS.0 7 a))) % 5.28/5.47 (rel_str (skS.0 7 a)) → % 5.28/5.47 ∀ (B : Iota), element B (the_carrier (skS.0 7 a)) → related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) B)) % 5.28/5.47 True % 5.28/5.47 Clause #106 (by clausification #[105]): ∀ (a : Iota), % 5.28/5.47 Eq % 5.28/5.47 (And % 5.28/5.47 (And (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a))) % 5.28/5.47 (lower_bounded_relstr (skS.0 7 a))) % 5.28/5.47 (rel_str (skS.0 7 a)) → % 5.28/5.47 ∀ (B : Iota), element B (the_carrier (skS.0 7 a)) → related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) B) % 5.28/5.47 False % 5.28/5.47 Clause #107 (by clausification #[106]): ∀ (a : Iota), % 5.28/5.47 Eq % 5.28/5.47 (And % 5.28/5.47 (And (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a))) % 5.28/5.47 (lower_bounded_relstr (skS.0 7 a))) % 5.28/5.47 (rel_str (skS.0 7 a))) % 5.28/5.47 True % 5.28/5.47 Clause #108 (by clausification #[106]): ∀ (a : Iota), % 5.28/5.47 Eq (∀ (B : Iota), element B (the_carrier (skS.0 7 a)) → related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) B) False % 5.28/5.47 Clause #109 (by clausification #[107]): ∀ (a : Iota), Eq (rel_str (skS.0 7 a)) True % 5.28/5.47 Clause #110 (by clausification #[107]): ∀ (a : Iota), % 5.28/5.47 Eq (And (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a))) (lower_bounded_relstr (skS.0 7 a))) % 5.28/5.47 True % 5.28/5.47 Clause #112 (by superposition #[109, 51]): ∀ (a : Iota), Or (Eq True False) (Eq (bottom_of_relstr (skS.0 7 a)) (join_on_relstr (skS.0 7 a) empty_set)) % 5.28/5.47 Clause #114 (by superposition #[109, 71]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) True) % 5.28/5.47 Clause #116 (by clausification #[18]): ∀ (a : Iota), % 5.28/5.47 Eq % 5.28/5.47 (And (antisymmetric_relstr a) (rel_str a) → % 5.28/5.47 ∀ (B : Iota), % 5.28/5.47 element B (the_carrier a) → % 5.28/5.47 ∀ (C : Iota), % 5.28/5.47 And % 5.28/5.47 (And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C) → % 5.28/5.47 And (relstr_set_smaller a C B) % 5.28/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D)) % 5.28/5.47 (And (relstr_set_smaller a C B) % 5.28/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D) → % 5.28/5.47 And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C))) % 5.28/5.47 True % 5.28/5.47 Clause #117 (by clausification #[116]): ∀ (a : Iota), % 5.28/5.47 Or (Eq (And (antisymmetric_relstr a) (rel_str a)) False) % 5.28/5.47 (Eq % 5.28/5.47 (∀ (B : Iota), % 5.28/5.47 element B (the_carrier a) → % 5.28/5.47 ∀ (C : Iota), % 5.28/5.47 And % 5.28/5.47 (And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C) → % 5.28/5.47 And (relstr_set_smaller a C B) % 5.28/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D)) % 5.28/5.47 (And (relstr_set_smaller a C B) % 5.28/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D) → % 5.28/5.47 And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C))) % 5.28/5.47 True) % 5.28/5.47 Clause #118 (by clausification #[117]): ∀ (a : Iota), % 5.28/5.47 Or % 5.28/5.47 (Eq % 5.28/5.47 (∀ (B : Iota), % 5.28/5.47 element B (the_carrier a) → % 5.28/5.47 ∀ (C : Iota), % 5.28/5.47 And % 5.28/5.47 (And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C) → % 5.28/5.47 And (relstr_set_smaller a C B) % 5.28/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D)) % 5.28/5.47 (And (relstr_set_smaller a C B) % 5.28/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D) → % 5.28/5.47 And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C))) % 5.28/5.47 True) % 5.28/5.47 (Or (Eq (antisymmetric_relstr a) False) (Eq (rel_str a) False)) % 5.28/5.47 Clause #119 (by clausification #[118]): ∀ (a a_1 : Iota), % 5.28/5.47 Or (Eq (antisymmetric_relstr a) False) % 5.28/5.47 (Or (Eq (rel_str a) False) % 5.28/5.47 (Eq % 5.28/5.47 (element a_1 (the_carrier a) → % 5.28/5.47 ∀ (C : Iota), % 5.28/5.47 And % 5.28/5.47 (And (Eq a_1 (join_on_relstr a C)) (ex_sup_of_relstr_set a C) → % 5.28/5.47 And (relstr_set_smaller a C a_1) % 5.28/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a a_1 D)) % 5.28/5.48 (And (relstr_set_smaller a C a_1) % 5.28/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a a_1 D) → % 5.28/5.48 And (Eq a_1 (join_on_relstr a C)) (ex_sup_of_relstr_set a C))) % 5.28/5.48 True)) % 5.28/5.48 Clause #120 (by clausification #[119]): ∀ (a a_1 : Iota), % 5.28/5.48 Or (Eq (antisymmetric_relstr a) False) % 5.28/5.48 (Or (Eq (rel_str a) False) % 5.28/5.48 (Or (Eq (element a_1 (the_carrier a)) False) % 5.28/5.48 (Eq % 5.28/5.48 (∀ (C : Iota), % 5.28/5.48 And % 5.28/5.48 (And (Eq a_1 (join_on_relstr a C)) (ex_sup_of_relstr_set a C) → % 5.28/5.48 And (relstr_set_smaller a C a_1) % 5.28/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a a_1 D)) % 5.28/5.48 (And (relstr_set_smaller a C a_1) % 5.28/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a a_1 D) → % 5.28/5.48 And (Eq a_1 (join_on_relstr a C)) (ex_sup_of_relstr_set a C))) % 5.28/5.48 True))) % 5.28/5.48 Clause #121 (by clausification #[120]): ∀ (a a_1 a_2 : Iota), % 5.28/5.48 Or (Eq (antisymmetric_relstr a) False) % 5.28/5.48 (Or (Eq (rel_str a) False) % 5.28/5.48 (Or (Eq (element a_1 (the_carrier a)) False) % 5.28/5.48 (Eq % 5.28/5.48 (And % 5.28/5.48 (And (Eq a_1 (join_on_relstr a a_2)) (ex_sup_of_relstr_set a a_2) → % 5.28/5.48 And (relstr_set_smaller a a_2 a_1) % 5.28/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D)) % 5.28/5.48 (And (relstr_set_smaller a a_2 a_1) % 5.28/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D) → % 5.28/5.48 And (Eq a_1 (join_on_relstr a a_2)) (ex_sup_of_relstr_set a a_2))) % 5.28/5.48 True))) % 5.28/5.48 Clause #123 (by clausification #[121]): ∀ (a a_1 a_2 : Iota), % 5.28/5.48 Or (Eq (antisymmetric_relstr a) False) % 5.28/5.48 (Or (Eq (rel_str a) False) % 5.28/5.48 (Or (Eq (element a_1 (the_carrier a)) False) % 5.28/5.48 (Eq % 5.28/5.48 (And (Eq a_1 (join_on_relstr a a_2)) (ex_sup_of_relstr_set a a_2) → % 5.28/5.48 And (relstr_set_smaller a a_2 a_1) % 5.28/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D)) % 5.28/5.48 True))) % 5.28/5.48 Clause #141 (by clausification #[22]): ∀ (a : Iota), % 5.28/5.48 Eq % 5.28/5.48 (rel_str a → % 5.28/5.48 ∀ (B : Iota), % 5.28/5.48 element B (the_carrier a) → And (relstr_set_smaller a empty_set B) (relstr_element_smaller a empty_set B)) % 5.28/5.48 True % 5.28/5.48 Clause #142 (by clausification #[141]): ∀ (a : Iota), % 5.28/5.48 Or (Eq (rel_str a) False) % 5.28/5.48 (Eq % 5.28/5.48 (∀ (B : Iota), % 5.28/5.48 element B (the_carrier a) → And (relstr_set_smaller a empty_set B) (relstr_element_smaller a empty_set B)) % 5.28/5.48 True) % 5.28/5.48 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota), % 5.28/5.48 Or (Eq (rel_str a) False) % 5.28/5.48 (Eq % 5.28/5.48 (element a_1 (the_carrier a) → And (relstr_set_smaller a empty_set a_1) (relstr_element_smaller a empty_set a_1)) % 5.28/5.48 True) % 5.28/5.48 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota), % 5.28/5.48 Or (Eq (rel_str a) False) % 5.28/5.48 (Or (Eq (element a_1 (the_carrier a)) False) % 5.28/5.48 (Eq (And (relstr_set_smaller a empty_set a_1) (relstr_element_smaller a empty_set a_1)) True)) % 5.28/5.48 Clause #146 (by clausification #[144]): ∀ (a a_1 : Iota), % 5.28/5.48 Or (Eq (rel_str a) False) (Or (Eq (element a_1 (the_carrier a)) False) (Eq (relstr_set_smaller a empty_set a_1) True)) % 5.28/5.48 Clause #150 (by superposition #[146, 109]): ∀ (a a_1 : Iota), % 5.28/5.48 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) % 5.28/5.48 (Or (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) True) (Eq False True)) % 5.28/5.48 Clause #159 (by clausification #[112]): ∀ (a : Iota), Eq (bottom_of_relstr (skS.0 7 a)) (join_on_relstr (skS.0 7 a) empty_set) % 5.28/5.48 Clause #161 (by clausification #[99]): ∀ (a : Iota), % 5.28/5.48 Or (Eq (rel_str a) False) % 5.28/5.48 (Or (Eq (ex_sup_of_relstr_set a empty_set) True) % 5.28/5.48 (Or (Eq (And (Not (empty_carrier a)) (antisymmetric_relstr a)) False) (Eq (lower_bounded_relstr a) False))) % 5.28/5.48 Clause #162 (by clausification #[161]): ∀ (a : Iota), % 5.28/5.48 Or (Eq (rel_str a) False) % 5.28/5.48 (Or (Eq (ex_sup_of_relstr_set a empty_set) True) % 5.28/5.48 (Or (Eq (lower_bounded_relstr a) False) % 5.28/5.48 (Or (Eq (Not (empty_carrier a)) False) (Eq (antisymmetric_relstr a) False)))) % 5.28/5.51 Clause #163 (by clausification #[162]): ∀ (a : Iota), % 5.28/5.51 Or (Eq (rel_str a) False) % 5.28/5.51 (Or (Eq (ex_sup_of_relstr_set a empty_set) True) % 5.28/5.51 (Or (Eq (lower_bounded_relstr a) False) (Or (Eq (antisymmetric_relstr a) False) (Eq (empty_carrier a) True)))) % 5.28/5.51 Clause #165 (by superposition #[163, 109]): ∀ (a : Iota), % 5.28/5.51 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) % 5.28/5.51 (Or (Eq (lower_bounded_relstr (skS.0 7 a)) False) % 5.28/5.51 (Or (Eq (antisymmetric_relstr (skS.0 7 a)) False) (Or (Eq (empty_carrier (skS.0 7 a)) True) (Eq False True)))) % 5.28/5.51 Clause #166 (by clausification #[108]): ∀ (a a_1 : Iota), % 5.28/5.51 Eq % 5.28/5.51 (Not % 5.28/5.51 (element (skS.0 9 a a_1) (the_carrier (skS.0 7 a)) → % 5.28/5.51 related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1))) % 5.28/5.51 True % 5.28/5.51 Clause #167 (by clausification #[166]): ∀ (a a_1 : Iota), % 5.28/5.51 Eq % 5.28/5.51 (element (skS.0 9 a a_1) (the_carrier (skS.0 7 a)) → % 5.28/5.51 related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) % 5.28/5.51 False % 5.28/5.51 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (element (skS.0 9 a a_1) (the_carrier (skS.0 7 a))) True % 5.28/5.51 Clause #169 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) False % 5.28/5.51 Clause #181 (by clausification #[114]): ∀ (a a_1 : Iota), Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) True % 5.28/5.51 Clause #199 (by clausification #[110]): ∀ (a : Iota), Eq (lower_bounded_relstr (skS.0 7 a)) True % 5.28/5.51 Clause #200 (by clausification #[110]): ∀ (a : Iota), Eq (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a))) True % 5.28/5.51 Clause #201 (by clausification #[200]): ∀ (a : Iota), Eq (antisymmetric_relstr (skS.0 7 a)) True % 5.28/5.51 Clause #202 (by clausification #[200]): ∀ (a : Iota), Eq (Not (empty_carrier (skS.0 7 a))) True % 5.28/5.51 Clause #204 (by clausification #[202]): ∀ (a : Iota), Eq (empty_carrier (skS.0 7 a)) False % 5.28/5.51 Clause #207 (by clausification #[150]): ∀ (a a_1 : Iota), % 5.28/5.51 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) True) % 5.28/5.51 Clause #208 (by superposition #[207, 168]): ∀ (a a_1 : Iota), Or (Eq (relstr_set_smaller (skS.0 7 a) empty_set (skS.0 9 a a_1)) True) (Eq False True) % 5.28/5.51 Clause #220 (by clausification #[208]): ∀ (a a_1 : Iota), Eq (relstr_set_smaller (skS.0 7 a) empty_set (skS.0 9 a a_1)) True % 5.28/5.51 Clause #228 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), % 5.28/5.51 Or (Eq (antisymmetric_relstr a) False) % 5.28/5.51 (Or (Eq (rel_str a) False) % 5.28/5.51 (Or (Eq (element a_1 (the_carrier a)) False) % 5.28/5.51 (Or (Eq (And (Eq a_1 (join_on_relstr a a_2)) (ex_sup_of_relstr_set a a_2)) False) % 5.28/5.51 (Eq % 5.28/5.51 (And (relstr_set_smaller a a_2 a_1) % 5.28/5.51 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D)) % 5.28/5.51 True)))) % 5.28/5.51 Clause #229 (by clausification #[228]): ∀ (a a_1 a_2 : Iota), % 5.28/5.51 Or (Eq (antisymmetric_relstr a) False) % 5.28/5.51 (Or (Eq (rel_str a) False) % 5.28/5.51 (Or (Eq (element a_1 (the_carrier a)) False) % 5.28/5.51 (Or % 5.28/5.51 (Eq % 5.28/5.51 (And (relstr_set_smaller a a_2 a_1) % 5.28/5.51 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D)) % 5.28/5.51 True) % 5.28/5.51 (Or (Eq (Eq a_1 (join_on_relstr a a_2)) False) (Eq (ex_sup_of_relstr_set a a_2) False))))) % 5.28/5.51 Clause #230 (by clausification #[229]): ∀ (a a_1 a_2 : Iota), % 5.28/5.51 Or (Eq (antisymmetric_relstr a) False) % 5.28/5.51 (Or (Eq (rel_str a) False) % 5.28/5.51 (Or (Eq (element a_1 (the_carrier a)) False) % 5.28/5.51 (Or (Eq (Eq a_1 (join_on_relstr a a_2)) False) % 5.28/5.51 (Or (Eq (ex_sup_of_relstr_set a a_2) False) % 5.28/5.51 (Eq (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D) True))))) % 5.28/5.51 Clause #232 (by clausification #[230]): ∀ (a a_1 a_2 : Iota), % 5.28/5.51 Or (Eq (antisymmetric_relstr a) False) % 5.28/5.51 (Or (Eq (rel_str a) False) % 5.28/5.51 (Or (Eq (element a_1 (the_carrier a)) False) % 5.28/5.51 (Or (Eq (ex_sup_of_relstr_set a a_2) False) % 5.28/5.51 (Or (Eq (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D) True) % 5.36/5.53 (Ne a_1 (join_on_relstr a a_2)))))) % 5.36/5.53 Clause #233 (by clausification #[232]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.53 Or (Eq (antisymmetric_relstr a) False) % 5.36/5.53 (Or (Eq (rel_str a) False) % 5.36/5.53 (Or (Eq (element a_1 (the_carrier a)) False) % 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set a a_2) False) % 5.36/5.53 (Or (Ne a_1 (join_on_relstr a a_2)) % 5.36/5.53 (Eq (element a_3 (the_carrier a) → relstr_set_smaller a a_2 a_3 → related a a_1 a_3) True))))) % 5.36/5.53 Clause #234 (by clausification #[233]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.53 Or (Eq (antisymmetric_relstr a) False) % 5.36/5.53 (Or (Eq (rel_str a) False) % 5.36/5.53 (Or (Eq (element a_1 (the_carrier a)) False) % 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set a a_2) False) % 5.36/5.53 (Or (Ne a_1 (join_on_relstr a a_2)) % 5.36/5.53 (Or (Eq (element a_3 (the_carrier a)) False) % 5.36/5.53 (Eq (relstr_set_smaller a a_2 a_3 → related a a_1 a_3) True)))))) % 5.36/5.53 Clause #235 (by clausification #[234]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.53 Or (Eq (antisymmetric_relstr a) False) % 5.36/5.53 (Or (Eq (rel_str a) False) % 5.36/5.53 (Or (Eq (element a_1 (the_carrier a)) False) % 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set a a_2) False) % 5.36/5.53 (Or (Ne a_1 (join_on_relstr a a_2)) % 5.36/5.53 (Or (Eq (element a_3 (the_carrier a)) False) % 5.36/5.53 (Or (Eq (relstr_set_smaller a a_2 a_3) False) (Eq (related a a_1 a_3) True))))))) % 5.36/5.53 Clause #236 (by destructive equality resolution #[235]): ∀ (a a_1 a_2 : Iota), % 5.36/5.53 Or (Eq (antisymmetric_relstr a) False) % 5.36/5.53 (Or (Eq (rel_str a) False) % 5.36/5.53 (Or (Eq (element (join_on_relstr a a_1) (the_carrier a)) False) % 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set a a_1) False) % 5.36/5.53 (Or (Eq (element a_2 (the_carrier a)) False) % 5.36/5.53 (Or (Eq (relstr_set_smaller a a_1 a_2) False) (Eq (related a (join_on_relstr a a_1) a_2) True)))))) % 5.36/5.53 Clause #237 (by superposition #[236, 201]): ∀ (a a_1 a_2 : Iota), % 5.36/5.53 Or (Eq (rel_str (skS.0 7 a)) False) % 5.36/5.53 (Or (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) False) % 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False) % 5.36/5.53 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False) % 5.36/5.53 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False) % 5.36/5.53 (Or (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True) (Eq False True)))))) % 5.36/5.53 Clause #283 (by clausification #[165]): ∀ (a : Iota), % 5.36/5.53 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) % 5.36/5.53 (Or (Eq (lower_bounded_relstr (skS.0 7 a)) False) % 5.36/5.53 (Or (Eq (antisymmetric_relstr (skS.0 7 a)) False) (Eq (empty_carrier (skS.0 7 a)) True))) % 5.36/5.53 Clause #284 (by forward demodulation #[283, 199]): ∀ (a : Iota), % 5.36/5.53 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) % 5.36/5.53 (Or (Eq True False) (Or (Eq (antisymmetric_relstr (skS.0 7 a)) False) (Eq (empty_carrier (skS.0 7 a)) True))) % 5.36/5.53 Clause #285 (by clausification #[284]): ∀ (a : Iota), % 5.36/5.53 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) % 5.36/5.53 (Or (Eq (antisymmetric_relstr (skS.0 7 a)) False) (Eq (empty_carrier (skS.0 7 a)) True)) % 5.36/5.53 Clause #286 (by forward demodulation #[285, 201]): ∀ (a : Iota), % 5.36/5.53 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) (Or (Eq True False) (Eq (empty_carrier (skS.0 7 a)) True)) % 5.36/5.53 Clause #287 (by clausification #[286]): ∀ (a : Iota), Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) (Eq (empty_carrier (skS.0 7 a)) True) % 5.36/5.53 Clause #288 (by forward demodulation #[287, 204]): ∀ (a : Iota), Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) (Eq False True) % 5.36/5.53 Clause #289 (by clausification #[288]): ∀ (a : Iota), Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True % 5.36/5.53 Clause #318 (by clausification #[237]): ∀ (a a_1 a_2 : Iota), % 5.36/5.53 Or (Eq (rel_str (skS.0 7 a)) False) % 5.36/5.53 (Or (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) False) % 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False) % 5.36/5.53 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False) % 5.36/5.53 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False) % 5.36/5.53 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True))))) % 5.36/5.53 Clause #319 (by forward demodulation #[318, 109]): ∀ (a a_1 a_2 : Iota), % 5.36/5.55 Or (Eq True False) % 5.36/5.55 (Or (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) False) % 5.36/5.55 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False) % 5.36/5.55 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False) % 5.36/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False) % 5.36/5.55 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True))))) % 5.36/5.55 Clause #320 (by clausification #[319]): ∀ (a a_1 a_2 : Iota), % 5.36/5.55 Or (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) False) % 5.36/5.55 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False) % 5.36/5.55 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False) % 5.36/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False) % 5.36/5.55 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True)))) % 5.36/5.55 Clause #321 (by forward demodulation #[320, 181]): ∀ (a a_1 a_2 : Iota), % 5.36/5.55 Or (Eq True False) % 5.36/5.55 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False) % 5.36/5.55 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False) % 5.36/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False) % 5.36/5.55 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True)))) % 5.36/5.55 Clause #322 (by clausification #[321]): ∀ (a a_1 a_2 : Iota), % 5.36/5.55 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False) % 5.36/5.55 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False) % 5.36/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False) % 5.36/5.55 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True))) % 5.36/5.55 Clause #323 (by superposition #[322, 289]): ∀ (a a_1 : Iota), % 5.36/5.55 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) % 5.36/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) False) % 5.36/5.55 (Or (Eq (related (skS.0 7 a_1) (join_on_relstr (skS.0 7 a_1) empty_set) a) True) (Eq False True))) % 5.36/5.55 Clause #324 (by clausification #[323]): ∀ (a a_1 : Iota), % 5.36/5.55 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) % 5.36/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) False) % 5.36/5.55 (Eq (related (skS.0 7 a_1) (join_on_relstr (skS.0 7 a_1) empty_set) a) True)) % 5.36/5.55 Clause #325 (by forward demodulation #[324, 159]): ∀ (a a_1 : Iota), % 5.36/5.55 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) % 5.36/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) False) % 5.36/5.55 (Eq (related (skS.0 7 a_1) (bottom_of_relstr (skS.0 7 a_1)) a) True)) % 5.36/5.55 Clause #326 (by superposition #[325, 168]): ∀ (a a_1 : Iota), % 5.36/5.55 Or (Eq (relstr_set_smaller (skS.0 7 a) empty_set (skS.0 9 a a_1)) False) % 5.36/5.55 (Or (Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) True) (Eq False True)) % 5.36/5.55 Clause #333 (by clausification #[326]): ∀ (a a_1 : Iota), % 5.36/5.55 Or (Eq (relstr_set_smaller (skS.0 7 a) empty_set (skS.0 9 a a_1)) False) % 5.36/5.55 (Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) True) % 5.36/5.55 Clause #334 (by forward demodulation #[333, 220]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) True) % 5.36/5.55 Clause #335 (by clausification #[334]): ∀ (a a_1 : Iota), Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) True % 5.36/5.55 Clause #336 (by superposition #[335, 169]): Eq True False % 5.36/5.55 Clause #337 (by clausification #[336]): False % 5.36/5.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------