%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS141+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 07:52:41 PM UTC 2025 % Result : Theorem 3.71s 3.89s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : KRS141+1 : TPTP v9.2.0. Released v3.1.0. % 0.04/0.15 % Command : duper %s % 0.13/0.37 % Computer : n007.cluster.edu % 0.13/0.37 % Model : x86_64 x86_64 % 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.37 % Memory : 8042.1875MB % 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.37 % CPULimit : 300 % 0.13/0.37 % WCLimit : 300 % 0.13/0.37 % DateTime : Thu Oct 2 10:21:08 EDT 2025 % 0.13/0.37 % CPUTime : % 3.71/3.89 SZS status Theorem for theBenchmark.p % 3.71/3.89 SZS output start Proof for theBenchmark.p % 3.71/3.89 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 3.71/3.89 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) True % 3.71/3.89 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), cr X → ∀ (Y : Iota), rp X Y → cc Y) True % 3.71/3.89 Clause #3 (by assumption #[]): Eq (cr ii) True % 3.71/3.89 Clause #5 (by assumption #[]): Eq (rp ii io) True % 3.71/3.89 Clause #7 (by assumption #[]): Eq % 3.71/3.89 (Not % 3.71/3.89 (And % 3.71/3.89 (And % 3.71/3.89 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 3.71/3.89 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 3.71/3.89 (cc io)) % 3.71/3.89 (cowlThing io))) % 3.71/3.89 True % 3.71/3.89 Clause #8 (by clausification #[2]): ∀ (a : Iota), Eq (cr a → ∀ (Y : Iota), rp a Y → cc Y) True % 3.71/3.89 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (cr a) False) (Eq (∀ (Y : Iota), rp a Y → cc Y) True) % 3.71/3.89 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (cr a) False) (Eq (rp a a_1 → cc a_1) True) % 3.71/3.89 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (cr a) False) (Or (Eq (rp a a_1) False) (Eq (cc a_1) True)) % 3.71/3.89 Clause #12 (by superposition #[11, 3]): ∀ (a : Iota), Or (Eq (rp ii a) False) (Or (Eq (cc a) True) (Eq False True)) % 3.71/3.89 Clause #13 (by clausification #[0]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 3.71/3.89 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (Not (cowlNothing a)) True % 3.71/3.89 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (cowlThing a) True % 3.71/3.89 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (cowlNothing a) False % 3.71/3.89 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (Iff (xsd_string a) (Not (xsd_integer a))) True % 3.71/3.89 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (Not (xsd_integer a)) False) % 3.71/3.89 Clause #19 (by clausification #[17]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (Not (xsd_integer a)) True) % 3.71/3.89 Clause #20 (by clausification #[18]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (xsd_integer a) True) % 3.71/3.89 Clause #21 (by clausification #[19]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (xsd_integer a) False) % 3.71/3.89 Clause #22 (by clausification #[12]): ∀ (a : Iota), Or (Eq (rp ii a) False) (Eq (cc a) True) % 3.71/3.89 Clause #23 (by superposition #[22, 5]): Or (Eq (cc io) True) (Eq False True) % 3.71/3.89 Clause #24 (by clausification #[23]): Eq (cc io) True % 3.71/3.89 Clause #25 (by clausification #[7]): Eq % 3.71/3.89 (And % 3.71/3.89 (And % 3.71/3.89 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 3.71/3.89 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 3.71/3.89 (cc io)) % 3.71/3.89 (cowlThing io)) % 3.71/3.89 False % 3.71/3.89 Clause #26 (by clausification #[25]): Or % 3.71/3.89 (Eq % 3.71/3.89 (And % 3.71/3.89 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 3.71/3.89 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 3.71/3.89 (cc io)) % 3.71/3.89 False) % 3.71/3.89 (Eq (cowlThing io) False) % 3.71/3.89 Clause #27 (by clausification #[26]): Or (Eq (cowlThing io) False) % 3.71/3.89 (Or % 3.71/3.89 (Eq % 3.71/3.89 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 3.71/3.89 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 3.71/3.89 False) % 3.71/3.89 (Eq (cc io) False)) % 3.71/3.89 Clause #28 (by clausification #[27]): Or (Eq (cowlThing io) False) % 3.71/3.89 (Or (Eq (cc io) False) % 3.71/3.89 (Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 3.71/3.89 (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False))) % 3.71/3.89 Clause #29 (by clausification #[28]): ∀ (a : Iota), % 3.71/3.89 Or (Eq (cowlThing io) False) % 3.71/3.89 (Or (Eq (cc io) False) % 3.71/3.89 (Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 3.71/3.89 (Eq (Not (And (cowlThing (skS.0 0 a)) (Not (cowlNothing (skS.0 0 a))))) True))) % 3.71/3.89 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 3.71/3.89 Or (Eq (cowlThing io) False) % 3.71/3.89 (Or (Eq (cc io) False) % 3.71/3.89 (Or (Eq (Not (And (cowlThing (skS.0 0 a)) (Not (cowlNothing (skS.0 0 a))))) True) % 3.71/3.89 (Eq (Not (Iff (xsd_string (skS.0 1 a_1)) (Not (xsd_integer (skS.0 1 a_1))))) True))) % 3.71/3.89 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 3.71/3.89 Or (Eq (cowlThing io) False) % 3.71/3.89 (Or (Eq (cc io) False) % 3.71/3.89 (Or (Eq (Not (Iff (xsd_string (skS.0 1 a)) (Not (xsd_integer (skS.0 1 a))))) True) % 3.71/3.92 (Eq (And (cowlThing (skS.0 0 a_1)) (Not (cowlNothing (skS.0 0 a_1)))) False))) % 3.71/3.92 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing io) False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (And (cowlThing (skS.0 0 a)) (Not (cowlNothing (skS.0 0 a)))) False) % 3.71/3.92 (Eq (Iff (xsd_string (skS.0 1 a_1)) (Not (xsd_integer (skS.0 1 a_1)))) False))) % 3.71/3.92 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing io) False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (Iff (xsd_string (skS.0 1 a)) (Not (xsd_integer (skS.0 1 a)))) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a_1)) False) (Eq (Not (cowlNothing (skS.0 0 a_1))) False)))) % 3.71/3.92 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing io) False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (Not (cowlNothing (skS.0 0 a))) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) False) (Eq (Not (xsd_integer (skS.0 1 a_1))) False))))) % 3.71/3.92 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing io) False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (Not (cowlNothing (skS.0 0 a))) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) True) (Eq (Not (xsd_integer (skS.0 1 a_1))) True))))) % 3.71/3.92 Clause #36 (by clausification #[34]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing io) False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) False) % 3.71/3.92 (Or (Eq (Not (xsd_integer (skS.0 1 a_1))) False) (Eq (cowlNothing (skS.0 0 a)) True))))) % 3.71/3.92 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing io) False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) False) % 3.71/3.92 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) True))))) % 3.71/3.92 Clause #38 (by forward demodulation #[37, 15]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq True False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) False) % 3.71/3.92 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) True))))) % 3.71/3.92 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) False) % 3.71/3.92 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) True)))) % 3.71/3.92 Clause #40 (by forward demodulation #[39, 24]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq True False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) False) % 3.71/3.92 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) True)))) % 3.71/3.92 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) False) % 3.71/3.92 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) True))) % 3.71/3.92 Clause #42 (by forward demodulation #[41, 15]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq True False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a)) False) % 3.71/3.92 (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Eq (xsd_integer (skS.0 1 a)) True))) % 3.71/3.92 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (xsd_string (skS.0 1 a)) False) (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Eq (xsd_integer (skS.0 1 a)) True)) % 3.71/3.92 Clause #44 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing io) False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) True) % 3.71/3.92 (Or (Eq (Not (xsd_integer (skS.0 1 a_1))) True) (Eq (cowlNothing (skS.0 0 a)) True))))) % 3.71/3.92 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), % 3.71/3.92 Or (Eq (cowlThing io) False) % 3.71/3.92 (Or (Eq (cc io) False) % 3.71/3.92 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.71/3.92 (Or (Eq (xsd_string (skS.0 1 a_1)) True) % 3.71/3.92 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) False))))) % 3.71/3.92 Clause #46 (by forward demodulation #[45, 15]): ∀ (a a_1 : Iota), % 3.76/3.94 Or (Eq True False) % 3.76/3.94 (Or (Eq (cc io) False) % 3.76/3.94 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.76/3.94 (Or (Eq (xsd_string (skS.0 1 a_1)) True) % 3.76/3.94 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) False))))) % 3.76/3.94 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), % 3.76/3.94 Or (Eq (cc io) False) % 3.76/3.94 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.76/3.94 (Or (Eq (xsd_string (skS.0 1 a_1)) True) % 3.76/3.94 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) False)))) % 3.76/3.94 Clause #48 (by forward demodulation #[47, 24]): ∀ (a a_1 : Iota), % 3.76/3.94 Or (Eq True False) % 3.76/3.94 (Or (Eq (cowlThing (skS.0 0 a)) False) % 3.76/3.94 (Or (Eq (xsd_string (skS.0 1 a_1)) True) % 3.76/3.94 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) False)))) % 3.76/3.94 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 3.76/3.94 Or (Eq (cowlThing (skS.0 0 a)) False) % 3.76/3.94 (Or (Eq (xsd_string (skS.0 1 a_1)) True) % 3.76/3.94 (Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 1 a_1)) False))) % 3.76/3.94 Clause #50 (by forward demodulation #[49, 15]): ∀ (a a_1 : Iota), % 3.76/3.94 Or (Eq True False) % 3.76/3.94 (Or (Eq (xsd_string (skS.0 1 a)) True) % 3.76/3.94 (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Eq (xsd_integer (skS.0 1 a)) False))) % 3.76/3.94 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 3.76/3.94 Or (Eq (xsd_string (skS.0 1 a)) True) (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Eq (xsd_integer (skS.0 1 a)) False)) % 3.76/3.94 Clause #52 (by superposition #[51, 20]): ∀ (a a_1 : Iota), % 3.76/3.94 Or (Eq (xsd_string (skS.0 1 a)) True) % 3.76/3.94 (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Or (Eq (xsd_string (skS.0 1 a)) True) (Eq False True))) % 3.76/3.94 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 3.76/3.94 Or (Eq (xsd_string (skS.0 1 a)) True) (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Eq (xsd_string (skS.0 1 a)) True)) % 3.76/3.94 Clause #54 (by eliminate duplicate literals #[53]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 1 a)) True) (Eq (cowlNothing (skS.0 0 a_1)) True) % 3.76/3.94 Clause #55 (by superposition #[54, 43]): ∀ (a a_1 a_2 : Iota), % 3.76/3.94 Or (Eq (cowlNothing (skS.0 0 a)) True) % 3.76/3.94 (Or (Eq True False) (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Eq (xsd_integer (skS.0 1 a_2)) True))) % 3.76/3.94 Clause #57 (by superposition #[54, 16]): ∀ (a : Iota), Or (Eq (xsd_string (skS.0 1 a)) True) (Eq True False) % 3.76/3.94 Clause #58 (by clausification #[57]): ∀ (a : Iota), Eq (xsd_string (skS.0 1 a)) True % 3.76/3.94 Clause #60 (by superposition #[58, 21]): ∀ (a : Iota), Or (Eq True False) (Eq (xsd_integer (skS.0 1 a)) False) % 3.76/3.94 Clause #61 (by clausification #[60]): ∀ (a : Iota), Eq (xsd_integer (skS.0 1 a)) False % 3.76/3.94 Clause #63 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 3.76/3.94 Or (Eq (cowlNothing (skS.0 0 a)) True) % 3.76/3.94 (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Eq (xsd_integer (skS.0 1 a_2)) True)) % 3.76/3.94 Clause #65 (by superposition #[63, 61]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 0 a)) True) (Or (Eq (cowlNothing (skS.0 0 a_1)) True) (Eq True False)) % 3.76/3.94 Clause #68 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq (cowlNothing (skS.0 0 a_1)) True) % 3.76/3.94 Clause #69 (by superposition #[68, 16]): ∀ (a : Iota), Or (Eq (cowlNothing (skS.0 0 a)) True) (Eq True False) % 3.76/3.94 Clause #73 (by clausification #[69]): ∀ (a : Iota), Eq (cowlNothing (skS.0 0 a)) True % 3.76/3.94 Clause #74 (by superposition #[73, 16]): Eq True False % 3.76/3.94 Clause #75 (by clausification #[74]): False % 3.76/3.94 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------