%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWB031+2 : TPTP v9.2.0. Released v5.2.0. % 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 08:03:30 PM UTC 2025 % Result : Unsatisfiable 3.77s 3.95s % Output : Proof 3.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SWB031+2 : TPTP v9.2.0. Released v5.2.0. % 0.08/0.13 % Command : duper %s % 0.13/0.34 % Computer : n016.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 11:58:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.77/3.95 SZS status Theorem for theBenchmark.p % 3.77/3.95 SZS output start Proof for theBenchmark.p % 3.77/3.95 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), ir X) True % 3.77/3.95 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Iff (icext uri_owl_Thing X) (ir X)) True % 3.77/3.95 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), Not (icext uri_owl_Nothing X)) True % 3.77/3.95 Clause #3 (by assumption #[]): Eq % 3.77/3.95 (∀ (Z S1 A1 : Iota), % 3.77/3.95 And (iext uri_rdf_first S1 A1) (iext uri_rdf_rest S1 uri_rdf_nil) → % 3.77/3.95 Iff (iext uri_owl_oneOf Z S1) (And (ic Z) (∀ (X : Iota), Iff (icext Z X) (Eq X A1)))) % 3.77/3.95 True % 3.77/3.95 Clause #4 (by assumption #[]): Eq % 3.77/3.95 (∀ (C1 C2 : Iota), % 3.77/3.95 Iff (iext uri_owl_equivalentClass C1 C2) (And (And (ic C1) (ic C2)) (∀ (X : Iota), Iff (icext C1 X) (icext C2 X)))) % 3.77/3.95 True % 3.77/3.95 Clause #5 (by assumption #[]): Eq % 3.77/3.95 (Exists fun BNODE_x => % 3.77/3.95 Exists fun BNODE_l => % 3.77/3.95 And % 3.77/3.95 (And (And (iext uri_owl_equivalentClass uri_owl_Thing BNODE_x) (iext uri_owl_oneOf BNODE_x BNODE_l)) % 3.77/3.95 (iext uri_rdf_first BNODE_l uri_ex_w)) % 3.77/3.95 (iext uri_rdf_rest BNODE_l uri_rdf_nil)) % 3.77/3.96 True % 3.77/3.96 Clause #6 (by clausification #[0]): ∀ (a : Iota), Eq (ir a) True % 3.77/3.96 Clause #7 (by clausification #[2]): ∀ (a : Iota), Eq (Not (icext uri_owl_Nothing a)) True % 3.77/3.96 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (icext uri_owl_Nothing a) False % 3.77/3.96 Clause #9 (by clausification #[1]): ∀ (a : Iota), Eq (Iff (icext uri_owl_Thing a) (ir a)) True % 3.77/3.96 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq (icext uri_owl_Thing a) True) (Eq (ir a) False) % 3.77/3.96 Clause #12 (by forward demodulation #[10, 6]): ∀ (a : Iota), Or (Eq (icext uri_owl_Thing a) True) (Eq True False) % 3.77/3.96 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (icext uri_owl_Thing a) True % 3.77/3.96 Clause #15 (by clausification #[3]): ∀ (a : Iota), % 3.77/3.96 Eq % 3.77/3.96 (∀ (S1 A1 : Iota), % 3.77/3.96 And (iext uri_rdf_first S1 A1) (iext uri_rdf_rest S1 uri_rdf_nil) → % 3.77/3.96 Iff (iext uri_owl_oneOf a S1) (And (ic a) (∀ (X : Iota), Iff (icext a X) (Eq X A1)))) % 3.77/3.96 True % 3.77/3.96 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (∀ (A1 : Iota), % 3.77/3.96 And (iext uri_rdf_first a A1) (iext uri_rdf_rest a uri_rdf_nil) → % 3.77/3.96 Iff (iext uri_owl_oneOf a_1 a) (And (ic a_1) (∀ (X : Iota), Iff (icext a_1 X) (Eq X A1)))) % 3.77/3.96 True % 3.77/3.96 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a uri_rdf_nil) → % 3.77/3.96 Iff (iext uri_owl_oneOf a_2 a) (And (ic a_2) (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1)))) % 3.77/3.96 True % 3.77/3.96 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a uri_rdf_nil)) False) % 3.77/3.96 (Eq (Iff (iext uri_owl_oneOf a_2 a) (And (ic a_2) (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1)))) True) % 3.77/3.96 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (Iff (iext uri_owl_oneOf a a_1) (And (ic a) (∀ (X : Iota), Iff (icext a X) (Eq X a_2)))) True) % 3.77/3.96 (Or (Eq (iext uri_rdf_first a_1 a_2) False) (Eq (iext uri_rdf_rest a_1 uri_rdf_nil) False)) % 3.77/3.96 Clause #21 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (iext uri_rdf_first a a_1) False) % 3.77/3.96 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 3.77/3.96 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Eq (And (ic a_2) (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1))) True))) % 3.77/3.96 Clause #28 (by clausification #[4]): ∀ (a : Iota), % 3.77/3.96 Eq % 3.77/3.96 (∀ (C2 : Iota), % 3.77/3.96 Iff (iext uri_owl_equivalentClass a C2) (And (And (ic a) (ic C2)) (∀ (X : Iota), Iff (icext a X) (icext C2 X)))) % 3.77/3.96 True % 3.77/3.96 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (Iff (iext uri_owl_equivalentClass a a_1) (And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (icext a_1 X)))) % 3.77/3.96 True % 3.77/3.96 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), % 3.77/3.96 Or (Eq (iext uri_owl_equivalentClass a a_1) False) % 3.77/3.96 (Eq (And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (icext a_1 X))) True) % 3.77/3.96 Clause #38 (by clausification #[31]): ∀ (a a_1 : Iota), % 3.77/3.96 Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Eq (∀ (X : Iota), Iff (icext a X) (icext a_1 X)) True) % 3.77/3.96 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Eq (Iff (icext a a_2) (icext a_1 a_2)) True) % 3.77/3.98 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.77/3.98 Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Or (Eq (icext a a_2) False) (Eq (icext a_1 a_2) True)) % 3.77/3.98 Clause #45 (by clausification #[5]): ∀ (a : Iota), % 3.77/3.98 Eq % 3.77/3.98 (Exists fun BNODE_l => % 3.77/3.98 And % 3.77/3.98 (And (And (iext uri_owl_equivalentClass uri_owl_Thing (skS.0 2 a)) (iext uri_owl_oneOf (skS.0 2 a) BNODE_l)) % 3.77/3.98 (iext uri_rdf_first BNODE_l uri_ex_w)) % 3.77/3.98 (iext uri_rdf_rest BNODE_l uri_rdf_nil)) % 3.77/3.98 True % 3.77/3.98 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), % 3.77/3.98 Eq % 3.77/3.98 (And % 3.77/3.98 (And % 3.77/3.98 (And (iext uri_owl_equivalentClass uri_owl_Thing (skS.0 2 a)) (iext uri_owl_oneOf (skS.0 2 a) (skS.0 3 a a_1))) % 3.77/3.98 (iext uri_rdf_first (skS.0 3 a a_1) uri_ex_w)) % 3.77/3.98 (iext uri_rdf_rest (skS.0 3 a a_1) uri_rdf_nil)) % 3.77/3.98 True % 3.77/3.98 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (iext uri_rdf_rest (skS.0 3 a a_1) uri_rdf_nil) True % 3.77/3.98 Clause #48 (by clausification #[46]): ∀ (a a_1 : Iota), % 3.77/3.98 Eq % 3.77/3.98 (And (And (iext uri_owl_equivalentClass uri_owl_Thing (skS.0 2 a)) (iext uri_owl_oneOf (skS.0 2 a) (skS.0 3 a a_1))) % 3.77/3.98 (iext uri_rdf_first (skS.0 3 a a_1) uri_ex_w)) % 3.77/3.98 True % 3.77/3.98 Clause #49 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 3.77/3.98 Or (Eq (iext uri_rdf_first a a_1) False) % 3.77/3.98 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 3.77/3.98 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Eq (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1)) True))) % 3.77/3.98 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.98 Or (Eq (iext uri_rdf_first a a_1) False) % 3.77/3.98 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 3.77/3.98 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Eq (Iff (icext a_2 a_3) (Eq a_3 a_1)) True))) % 3.77/3.98 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.98 Or (Eq (iext uri_rdf_first a a_1) False) % 3.77/3.98 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 3.77/3.98 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Or (Eq (icext a_2 a_3) False) (Eq (Eq a_3 a_1) True)))) % 3.77/3.98 Clause #56 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.98 Or (Eq (iext uri_rdf_first a a_1) False) % 3.77/3.98 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 3.77/3.98 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Or (Eq (icext a_2 a_3) False) (Eq a_3 a_1)))) % 3.77/3.98 Clause #57 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (iext uri_rdf_first (skS.0 3 a a_1) uri_ex_w) True % 3.77/3.98 Clause #58 (by clausification #[48]): ∀ (a a_1 : Iota), % 3.77/3.98 Eq (And (iext uri_owl_equivalentClass uri_owl_Thing (skS.0 2 a)) (iext uri_owl_oneOf (skS.0 2 a) (skS.0 3 a a_1))) % 3.77/3.98 True % 3.77/3.98 Clause #62 (by superposition #[57, 56]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.98 Or (Eq True False) % 3.77/3.98 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1) uri_rdf_nil) False) % 3.77/3.98 (Or (Eq (iext uri_owl_oneOf a_2 (skS.0 3 a a_1)) False) (Or (Eq (icext a_2 a_3) False) (Eq a_3 uri_ex_w)))) % 3.77/3.98 Clause #63 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (iext uri_owl_oneOf (skS.0 2 a) (skS.0 3 a a_1)) True % 3.77/3.98 Clause #64 (by clausification #[58]): ∀ (a : Iota), Eq (iext uri_owl_equivalentClass uri_owl_Thing (skS.0 2 a)) True % 3.77/3.98 Clause #70 (by superposition #[64, 42]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (icext uri_owl_Thing a) False) (Eq (icext (skS.0 2 a_1) a) True)) % 3.77/3.98 Clause #79 (by clausification #[70]): ∀ (a a_1 : Iota), Or (Eq (icext uri_owl_Thing a) False) (Eq (icext (skS.0 2 a_1) a) True) % 3.77/3.98 Clause #80 (by forward demodulation #[79, 13]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (icext (skS.0 2 a) a_1) True) % 3.77/3.98 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (icext (skS.0 2 a) a_1) True % 3.77/3.98 Clause #96 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.98 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1) uri_rdf_nil) False) % 3.77/3.98 (Or (Eq (iext uri_owl_oneOf a_2 (skS.0 3 a a_1)) False) (Or (Eq (icext a_2 a_3) False) (Eq a_3 uri_ex_w))) % 3.77/3.98 Clause #97 (by forward demodulation #[96, 47]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.98 Or (Eq True False) % 3.77/3.98 (Or (Eq (iext uri_owl_oneOf a (skS.0 3 a_1 a_2)) False) (Or (Eq (icext a a_3) False) (Eq a_3 uri_ex_w))) % 3.77/3.98 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.98 Or (Eq (iext uri_owl_oneOf a (skS.0 3 a_1 a_2)) False) (Or (Eq (icext a a_3) False) (Eq a_3 uri_ex_w)) % 3.77/3.98 Clause #99 (by superposition #[98, 63]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 2 a) a_1) False) (Or (Eq a_1 uri_ex_w) (Eq False True)) % 3.77/3.98 Clause #105 (by clausification #[99]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 2 a) a_1) False) (Eq a_1 uri_ex_w) % 3.77/3.98 Clause #106 (by superposition #[105, 81]): ∀ (a : Iota), Or (Eq a uri_ex_w) (Eq False True) % 3.77/3.98 Clause #107 (by clausification #[106]): ∀ (a : Iota), Eq a uri_ex_w % 3.77/3.98 Clause #119 (by superposition #[107, 107]): ∀ (a a_1 : Iota), Eq a a_1 % 3.77/3.98 Clause #122 (by superposition #[119, 13]): ∀ (a a_1 : Iota), Eq (icext a a_1) True % 3.77/3.98 Clause #158 (by superposition #[122, 8]): Eq True False % 3.77/3.98 Clause #159 (by clausification #[158]): False % 3.77/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------