%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS172+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 07:52:45 PM UTC 2025 % Result : Theorem 6.66s 6.84s % Output : Proof 6.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : KRS172+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.14 % Command : duper %s % 0.12/0.34 % Computer : n025.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 : Thu Oct 2 10:20:08 EDT 2025 % 0.19/0.34 % CPUTime : % 6.66/6.84 SZS status Theorem for theBenchmark.p % 6.66/6.84 SZS output start Proof for theBenchmark.p % 6.66/6.84 Clause #9 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 6.66/6.84 Clause #10 (by assumption #[]): Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) True % 6.66/6.84 Clause #11 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (rq X iv)) True % 6.66/6.84 Clause #12 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (rp X iv)) True % 6.66/6.84 Clause #13 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rp X Y) (rp X Z) → Eq Y Z) True % 6.66/6.84 Clause #14 (by assumption #[]): Eq (∀ (X Y : Iota), rp X Y → cd X) True % 6.66/6.84 Clause #15 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rq X Y) (rq X Z) → Eq Y Z) True % 6.66/6.84 Clause #16 (by assumption #[]): Eq (∀ (X Y : Iota), rq X Y → cd X) True % 6.66/6.84 Clause #18 (by assumption #[]): Eq % 6.66/6.84 (Not % 6.66/6.84 (And % 6.66/6.84 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 6.66/6.84 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 6.66/6.84 (∀ (X Y : Iota), Iff (rq X Y) (rp X Y)))) % 6.66/6.84 True % 6.66/6.84 Clause #19 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Y : Iota), rq a Y → cd a) True % 6.66/6.84 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (rq a a_1 → cd a) True % 6.66/6.84 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (rq a a_1) False) (Eq (cd a) True) % 6.66/6.84 Clause #22 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (Y : Iota), rp a Y → cd a) True % 6.66/6.84 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (rp a a_1 → cd a) True % 6.66/6.84 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (rp a a_1) False) (Eq (cd a) True) % 6.66/6.84 Clause #55 (by clausification #[9]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 6.66/6.84 Clause #56 (by clausification #[55]): ∀ (a : Iota), Eq (Not (cowlNothing a)) True % 6.66/6.84 Clause #57 (by clausification #[55]): ∀ (a : Iota), Eq (cowlThing a) True % 6.66/6.84 Clause #58 (by clausification #[56]): ∀ (a : Iota), Eq (cowlNothing a) False % 6.66/6.84 Clause #59 (by clausification #[11]): ∀ (a : Iota), Eq (Iff (cd a) (rq a iv)) True % 6.66/6.84 Clause #61 (by clausification #[59]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (rq a iv) True) % 6.66/6.84 Clause #69 (by clausification #[10]): ∀ (a : Iota), Eq (Iff (xsd_string a) (Not (xsd_integer a))) True % 6.66/6.84 Clause #70 (by clausification #[69]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (Not (xsd_integer a)) False) % 6.66/6.84 Clause #71 (by clausification #[69]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (Not (xsd_integer a)) True) % 6.66/6.84 Clause #72 (by clausification #[70]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (xsd_integer a) True) % 6.66/6.84 Clause #73 (by clausification #[71]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (xsd_integer a) False) % 6.66/6.84 Clause #74 (by clausification #[12]): ∀ (a : Iota), Eq (Iff (cd a) (rp a iv)) True % 6.66/6.84 Clause #76 (by clausification #[74]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (rp a iv) True) % 6.66/6.84 Clause #96 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rp a Y) (rp a Z) → Eq Y Z) True % 6.66/6.84 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rp a a_1) (rp a Z) → Eq a_1 Z) True % 6.66/6.84 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 : Iota), Eq (And (rp a a_1) (rp a a_2) → Eq a_1 a_2) True % 6.66/6.84 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rp a a_1) (rp a a_2)) False) (Eq (Eq a_1 a_2) True) % 6.66/6.84 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rp a_2 a) False) (Eq (rp a_2 a_1) False)) % 6.66/6.84 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (rp a a_1) False) (Or (Eq (rp a a_2) False) (Eq a_1 a_2)) % 6.66/6.84 Clause #102 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rq a Y) (rq a Z) → Eq Y Z) True % 6.66/6.84 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rq a a_1) (rq a Z) → Eq a_1 Z) True % 6.66/6.84 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), Eq (And (rq a a_1) (rq a a_2) → Eq a_1 a_2) True % 6.66/6.84 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rq a a_1) (rq a a_2)) False) (Eq (Eq a_1 a_2) True) % 6.66/6.84 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rq a_2 a) False) (Eq (rq a_2 a_1) False)) % 6.68/6.86 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), Or (Eq (rq a a_1) False) (Or (Eq (rq a a_2) False) (Eq a_1 a_2)) % 6.68/6.86 Clause #108 (by clausification #[18]): Eq % 6.68/6.86 (And % 6.68/6.86 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 6.68/6.86 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 6.68/6.86 (∀ (X Y : Iota), Iff (rq X Y) (rp X Y))) % 6.68/6.86 False % 6.68/6.86 Clause #109 (by clausification #[108]): Or % 6.68/6.86 (Eq % 6.68/6.86 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 6.68/6.86 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 6.68/6.86 False) % 6.68/6.86 (Eq (∀ (X Y : Iota), Iff (rq X Y) (rp X Y)) False) % 6.68/6.86 Clause #110 (by clausification #[109]): Or (Eq (∀ (X Y : Iota), Iff (rq X Y) (rp X Y)) False) % 6.68/6.86 (Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 6.68/6.86 (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False)) % 6.68/6.86 Clause #111 (by clausification #[110]): ∀ (a : Iota), % 6.68/6.86 Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 6.68/6.86 (Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 6.68/6.86 (Eq (Not (∀ (Y : Iota), Iff (rq (skS.0 0 a) Y) (rp (skS.0 0 a) Y))) True)) % 6.68/6.86 Clause #112 (by clausification #[111]): ∀ (a a_1 : Iota), % 6.68/6.86 Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 6.68/6.86 (Or (Eq (Not (∀ (Y : Iota), Iff (rq (skS.0 0 a) Y) (rp (skS.0 0 a) Y))) True) % 6.68/6.86 (Eq (Not (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1))))) True)) % 6.68/6.86 Clause #113 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), % 6.68/6.86 Or (Eq (Not (∀ (Y : Iota), Iff (rq (skS.0 0 a) Y) (rp (skS.0 0 a) Y))) True) % 6.68/6.86 (Or (Eq (Not (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1))))) True) % 6.68/6.86 (Eq (Not (Iff (xsd_string (skS.0 2 a_2)) (Not (xsd_integer (skS.0 2 a_2))))) True)) % 6.68/6.86 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), % 6.68/6.86 Or (Eq (Not (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a))))) True) % 6.68/6.86 (Or (Eq (Not (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1))))) True) % 6.68/6.86 (Eq (∀ (Y : Iota), Iff (rq (skS.0 0 a_2) Y) (rp (skS.0 0 a_2) Y)) False)) % 6.68/6.86 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), % 6.68/6.86 Or (Eq (Not (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a))))) True) % 6.68/6.86 (Or (Eq (∀ (Y : Iota), Iff (rq (skS.0 0 a_1) Y) (rp (skS.0 0 a_1) Y)) False) % 6.68/6.86 (Eq (And (cowlThing (skS.0 1 a_2)) (Not (cowlNothing (skS.0 1 a_2)))) False)) % 6.68/6.86 Clause #116 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), % 6.68/6.86 Or (Eq (∀ (Y : Iota), Iff (rq (skS.0 0 a) Y) (rp (skS.0 0 a) Y)) False) % 6.68/6.86 (Or (Eq (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1)))) False) % 6.68/6.86 (Eq (Iff (xsd_string (skS.0 2 a_2)) (Not (xsd_integer (skS.0 2 a_2)))) False)) % 6.68/6.86 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.86 Or (Eq (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a)))) False) % 6.68/6.86 (Or (Eq (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1)))) False) % 6.68/6.86 (Eq (Not (Iff (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)))) True)) % 6.68/6.86 Clause #118 (by clausification #[117]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.86 Or (Eq (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a)))) False) % 6.68/6.86 (Or (Eq (Not (Iff (rq (skS.0 0 a_1) (skS.0 3 a_1 a_2)) (rp (skS.0 0 a_1) (skS.0 3 a_1 a_2)))) True) % 6.68/6.86 (Or (Eq (cowlThing (skS.0 1 a_3)) False) (Eq (Not (cowlNothing (skS.0 1 a_3))) False))) % 6.68/6.86 Clause #119 (by clausification #[118]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.86 Or (Eq (Not (Iff (rq (skS.0 0 a) (skS.0 3 a a_1)) (rp (skS.0 0 a) (skS.0 3 a a_1)))) True) % 6.68/6.86 (Or (Eq (cowlThing (skS.0 1 a_2)) False) % 6.68/6.86 (Or (Eq (Not (cowlNothing (skS.0 1 a_2))) False) % 6.68/6.86 (Or (Eq (xsd_string (skS.0 2 a_3)) False) (Eq (Not (xsd_integer (skS.0 2 a_3))) False)))) % 6.68/6.86 Clause #120 (by clausification #[118]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.86 Or (Eq (Not (Iff (rq (skS.0 0 a) (skS.0 3 a a_1)) (rp (skS.0 0 a) (skS.0 3 a a_1)))) True) % 6.68/6.86 (Or (Eq (cowlThing (skS.0 1 a_2)) False) % 6.68/6.86 (Or (Eq (Not (cowlNothing (skS.0 1 a_2))) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Eq (Not (xsd_integer (skS.0 2 a_3))) True)))) % 6.68/6.89 Clause #121 (by clausification #[119]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (Not (cowlNothing (skS.0 1 a))) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 6.68/6.89 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) False) % 6.68/6.89 (Eq (Iff (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False)))) % 6.68/6.89 Clause #122 (by clausification #[121]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 6.68/6.89 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) False) % 6.68/6.89 (Or (Eq (Iff (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False) % 6.68/6.89 (Eq (cowlNothing (skS.0 1 a)) True)))) % 6.68/6.89 Clause #123 (by clausification #[122]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 6.68/6.89 (Or (Eq (Iff (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False) % 6.68/6.89 (Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) True)))) % 6.68/6.89 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 6.68/6.89 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.68/6.89 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.68/6.89 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))))) % 6.68/6.89 Clause #125 (by clausification #[123]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 6.68/6.89 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.68/6.89 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.68/6.89 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))))) % 6.68/6.89 Clause #126 (by forward demodulation #[124, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq True False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a)) False) % 6.68/6.89 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.68/6.89 (Or (Eq (xsd_integer (skS.0 2 a)) True) % 6.68/6.89 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))))) % 6.68/6.89 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (xsd_string (skS.0 2 a)) False) % 6.68/6.89 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.68/6.89 (Or (Eq (xsd_integer (skS.0 2 a)) True) % 6.68/6.89 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False)))) % 6.68/6.89 Clause #128 (by clausification #[120]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (Not (cowlNothing (skS.0 1 a))) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.68/6.89 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) True) % 6.68/6.89 (Eq (Iff (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False)))) % 6.68/6.89 Clause #129 (by clausification #[128]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.68/6.89 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) True) % 6.68/6.89 (Or (Eq (Iff (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False) % 6.68/6.89 (Eq (cowlNothing (skS.0 1 a)) True)))) % 6.68/6.89 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.68/6.89 (Or (Eq (Iff (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False) % 6.68/6.89 (Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) False)))) % 6.68/6.89 Clause #131 (by clausification #[130]): ∀ (a a_1 a_2 a_3 : Iota), % 6.68/6.89 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.68/6.89 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.68/6.89 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.68/6.89 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 6.68/6.89 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))))) % 6.68/6.89 Clause #132 (by clausification #[130]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (cowlThing (skS.0 1 a)) False) % 6.75/6.92 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.75/6.92 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))))) % 6.75/6.92 Clause #133 (by forward demodulation #[131, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq True False) % 6.75/6.92 (Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (xsd_integer (skS.0 2 a)) False) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))))) % 6.75/6.92 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (xsd_integer (skS.0 2 a)) False) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False)))) % 6.75/6.92 Clause #135 (by superposition #[134, 72]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) % 6.75/6.92 (Or (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Or (Eq (xsd_string (skS.0 2 a)) True) (Eq False True))))) % 6.75/6.92 Clause #136 (by clausification #[135]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) % 6.75/6.92 (Or (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (xsd_string (skS.0 2 a)) True)))) % 6.75/6.92 Clause #137 (by eliminate duplicate literals #[136]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))) % 6.75/6.92 Clause #138 (by forward demodulation #[132, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq True False) % 6.75/6.92 (Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (xsd_integer (skS.0 2 a)) False) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))))) % 6.75/6.92 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (xsd_integer (skS.0 2 a)) False) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)))) % 6.75/6.92 Clause #140 (by superposition #[139, 72]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 6.75/6.92 (Or (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Or (Eq (xsd_string (skS.0 2 a)) True) (Eq False True))))) % 6.75/6.92 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 6.75/6.92 (Or (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (xsd_string (skS.0 2 a)) True)))) % 6.75/6.92 Clause #142 (by eliminate duplicate literals #[141]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))) % 6.75/6.92 Clause #145 (by superposition #[142, 58]): ∀ (a a_1 a_2 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (rq (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 6.75/6.92 (Or (Eq (rp (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq True False))) % 6.75/6.92 Clause #147 (by superposition #[142, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.92 (Or (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Or (Eq True False) (Eq (cd (skS.0 0 a_2)) True)))) % 6.75/6.92 Clause #149 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.92 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.92 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.94 (Or (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (cd (skS.0 0 a_2)) True))) % 6.75/6.94 Clause #153 (by superposition #[149, 24]): ∀ (a a_1 a_2 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.94 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.94 (Or (Eq (cd (skS.0 0 a_2)) True) (Or (Eq True False) (Eq (cd (skS.0 0 a_2)) True)))) % 6.75/6.94 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.94 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Or (Eq (cd (skS.0 0 a_2)) True) (Eq (cd (skS.0 0 a_2)) True))) % 6.75/6.94 Clause #156 (by eliminate duplicate literals #[155]): ∀ (a a_1 a_2 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq (cd (skS.0 0 a_2)) True)) % 6.75/6.94 Clause #159 (by superposition #[156, 58]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq (cd (skS.0 0 a_1)) True) (Eq True False)) % 6.75/6.94 Clause #162 (by forward demodulation #[125, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.94 Or (Eq True False) % 6.75/6.94 (Or (Eq (xsd_string (skS.0 2 a)) False) % 6.75/6.94 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.94 (Or (Eq (xsd_integer (skS.0 2 a)) True) % 6.75/6.94 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))))) % 6.75/6.94 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) False) % 6.75/6.94 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.75/6.94 (Or (Eq (xsd_integer (skS.0 2 a)) True) % 6.75/6.94 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)))) % 6.75/6.94 Clause #166 (by clausification #[159]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (cd (skS.0 0 a_1)) True) % 6.75/6.94 Clause #170 (by superposition #[166, 61]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq True False) (Eq (rq (skS.0 0 a_1) iv) True)) % 6.75/6.94 Clause #171 (by superposition #[166, 76]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq True False) (Eq (rp (skS.0 0 a_1) iv) True)) % 6.75/6.94 Clause #175 (by clausification #[170]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (rq (skS.0 0 a_1) iv) True) % 6.75/6.94 Clause #180 (by superposition #[175, 107]): ∀ (a a_1 a_2 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq True False) (Or (Eq (rq (skS.0 0 a_1) a_2) False) (Eq iv a_2))) % 6.75/6.94 Clause #186 (by clausification #[171]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (rp (skS.0 0 a_1) iv) True) % 6.75/6.94 Clause #190 (by superposition #[186, 101]): ∀ (a a_1 a_2 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq True False) (Or (Eq (rp (skS.0 0 a_1) a_2) False) (Eq iv a_2))) % 6.75/6.94 Clause #196 (by clausification #[190]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq (rp (skS.0 0 a_1) a_2) False) (Eq iv a_2)) % 6.75/6.94 Clause #199 (by clausification #[180]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq (rq (skS.0 0 a_1) a_2) False) (Eq iv a_2)) % 6.75/6.94 Clause #203 (by clausification #[145]): ∀ (a a_1 a_2 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.94 (Or (Eq (rq (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq (rp (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True)) % 6.75/6.94 Clause #209 (by superposition #[203, 199]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.94 (Or (Eq (rp (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 6.75/6.94 (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Or (Eq True False) (Eq iv (skS.0 3 a_1 a_2))))) % 6.75/6.94 Clause #219 (by clausification #[209]): ∀ (a a_1 a_2 a_3 : Iota), % 6.75/6.94 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.75/6.94 (Or (Eq (rp (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 6.75/6.94 (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Eq iv (skS.0 3 a_1 a_2)))) % 6.75/6.94 Clause #229 (by equality factoring #[219]): ∀ (a a_1 a_2 : Iota), % 6.75/6.94 Or (Eq (rp (skS.0 0 a) (skS.0 3 a a_1)) True) % 6.75/6.94 (Or (Eq iv (skS.0 3 a a_1)) (Or (Ne True True) (Eq (xsd_string (skS.0 2 a_2)) True))) % 6.75/6.94 Clause #230 (by clausification #[229]): ∀ (a a_1 a_2 : Iota), % 6.75/6.94 Or (Eq (rp (skS.0 0 a) (skS.0 3 a a_1)) True) % 6.75/6.94 (Or (Eq iv (skS.0 3 a a_1)) (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Or (Eq True False) (Eq True False)))) % 6.75/6.94 Clause #232 (by clausification #[230]): ∀ (a a_1 a_2 : Iota), % 6.81/6.97 Or (Eq (rp (skS.0 0 a) (skS.0 3 a a_1)) True) % 6.81/6.97 (Or (Eq iv (skS.0 3 a a_1)) (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq True False))) % 6.81/6.97 Clause #233 (by clausification #[232]): ∀ (a a_1 a_2 : Iota), % 6.81/6.97 Or (Eq (rp (skS.0 0 a) (skS.0 3 a a_1)) True) (Or (Eq iv (skS.0 3 a a_1)) (Eq (xsd_string (skS.0 2 a_2)) True)) % 6.81/6.97 Clause #234 (by superposition #[233, 196]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/6.97 Or (Eq iv (skS.0 3 a a_1)) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_2)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Or (Eq True False) (Eq iv (skS.0 3 a a_1))))) % 6.81/6.97 Clause #247 (by clausification #[234]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/6.97 Or (Eq iv (skS.0 3 a a_1)) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Eq iv (skS.0 3 a a_1)))) % 6.81/6.97 Clause #248 (by eliminate duplicate literals #[247]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/6.97 Or (Eq iv (skS.0 3 a a_1)) (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq (xsd_string (skS.0 2 a_3)) True)) % 6.81/6.97 Clause #255 (by equality factoring #[248]): ∀ (a a_1 a_2 : Iota), Or (Eq iv (skS.0 3 a a_1)) (Or (Ne True True) (Eq (xsd_string (skS.0 2 a_2)) True)) % 6.81/6.97 Clause #256 (by clausification #[255]): ∀ (a a_1 a_2 : Iota), % 6.81/6.97 Or (Eq iv (skS.0 3 a a_1)) (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Or (Eq True False) (Eq True False))) % 6.81/6.97 Clause #258 (by clausification #[256]): ∀ (a a_1 a_2 : Iota), Or (Eq iv (skS.0 3 a a_1)) (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq True False)) % 6.81/6.97 Clause #259 (by clausification #[258]): ∀ (a a_1 a_2 : Iota), Or (Eq iv (skS.0 3 a a_1)) (Eq (xsd_string (skS.0 2 a_2)) True) % 6.81/6.97 Clause #260 (by superposition #[259, 137]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) (Or (Eq (rq (skS.0 0 a_3) iv) False) (Eq (rp (skS.0 0 a_3) iv) False)))) % 6.81/6.97 Clause #274 (by superposition #[260, 175]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) % 6.81/6.97 (Or (Eq (rp (skS.0 0 a_3) iv) False) (Or (Eq (xsd_string (skS.0 2 a_4)) True) (Eq False True))))) % 6.81/6.97 Clause #275 (by clausification #[274]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) % 6.81/6.97 (Or (Eq (rp (skS.0 0 a_3) iv) False) (Eq (xsd_string (skS.0 2 a_4)) True)))) % 6.81/6.97 Clause #276 (by superposition #[275, 186]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Or (Eq (xsd_string (skS.0 2 a_4)) True) (Eq False True))))) % 6.81/6.97 Clause #277 (by clausification #[276]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Eq (xsd_string (skS.0 2 a_4)) True)))) % 6.81/6.97 Clause #287 (by equality factoring #[277]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) (Or (Ne True True) (Eq (xsd_string (skS.0 2 a_3)) True)))) % 6.81/6.97 Clause #291 (by clausification #[287]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Or (Eq True False) (Eq True False))))) % 6.81/6.97 Clause #293 (by clausification #[291]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Eq True False)))) % 6.81/6.97 Clause #294 (by clausification #[293]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/6.97 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/6.97 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/6.97 (Or (Eq (cowlNothing (skS.0 1 a_2)) True) (Eq (xsd_string (skS.0 2 a_3)) True))) % 6.81/7.00 Clause #303 (by equality factoring #[294]): ∀ (a a_1 a_2 : Iota), % 6.81/7.00 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/7.00 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Or (Ne True True) (Eq (xsd_string (skS.0 2 a_2)) True))) % 6.81/7.00 Clause #304 (by clausification #[303]): ∀ (a a_1 a_2 : Iota), % 6.81/7.00 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/7.00 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 6.81/7.00 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Or (Eq True False) (Eq True False)))) % 6.81/7.00 Clause #306 (by clausification #[304]): ∀ (a a_1 a_2 : Iota), % 6.81/7.00 Or (Eq (xsd_string (skS.0 2 a)) True) % 6.81/7.00 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq True False))) % 6.81/7.00 Clause #307 (by clausification #[306]): ∀ (a a_1 a_2 : Iota), % 6.81/7.00 Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq (xsd_string (skS.0 2 a_2)) True)) % 6.81/7.00 Clause #315 (by equality factoring #[307]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Ne True True) (Eq (xsd_string (skS.0 2 a_1)) True)) % 6.81/7.00 Clause #316 (by clausification #[315]): ∀ (a a_1 : Iota), % 6.81/7.00 Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (xsd_string (skS.0 2 a_1)) True) (Or (Eq True False) (Eq True False))) % 6.81/7.00 Clause #318 (by clausification #[316]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (xsd_string (skS.0 2 a_1)) True) (Eq True False)) % 6.81/7.00 Clause #319 (by clausification #[318]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_string (skS.0 2 a_1)) True) % 6.81/7.00 Clause #320 (by superposition #[319, 58]): ∀ (a : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq True False) % 6.81/7.00 Clause #324 (by clausification #[320]): ∀ (a : Iota), Eq (xsd_string (skS.0 2 a)) True % 6.81/7.00 Clause #325 (by backward demodulation #[324, 127]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.00 Or (Eq True False) % 6.81/7.00 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.00 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.00 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False)))) % 6.81/7.00 Clause #326 (by backward demodulation #[324, 163]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.00 Or (Eq True False) % 6.81/7.00 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.00 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.00 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)))) % 6.81/7.00 Clause #327 (by superposition #[324, 73]): ∀ (a : Iota), Or (Eq True False) (Eq (xsd_integer (skS.0 2 a)) False) % 6.81/7.00 Clause #328 (by clausification #[327]): ∀ (a : Iota), Eq (xsd_integer (skS.0 2 a)) False % 6.81/7.00 Clause #411 (by clausification #[326]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.00 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.00 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.00 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))) % 6.81/7.00 Clause #413 (by superposition #[411, 328]): ∀ (a a_1 a_2 : Iota), % 6.81/7.00 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.00 (Or (Eq (rq (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 6.81/7.00 (Or (Eq (rp (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq True False))) % 6.81/7.00 Clause #416 (by superposition #[411, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.00 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.00 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.00 (Or (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Or (Eq True False) (Eq (cd (skS.0 0 a_2)) True)))) % 6.81/7.00 Clause #418 (by clausification #[416]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.00 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.00 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.00 (Or (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (cd (skS.0 0 a_2)) True))) % 6.81/7.00 Clause #421 (by superposition #[418, 24]): ∀ (a a_1 a_2 : Iota), % 6.81/7.00 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.00 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.00 (Or (Eq (cd (skS.0 0 a_2)) True) (Or (Eq True False) (Eq (cd (skS.0 0 a_2)) True)))) % 6.81/7.00 Clause #423 (by clausification #[421]): ∀ (a a_1 a_2 : Iota), % 6.81/7.00 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.00 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Or (Eq (cd (skS.0 0 a_2)) True) (Eq (cd (skS.0 0 a_2)) True))) % 6.81/7.00 Clause #424 (by eliminate duplicate literals #[423]): ∀ (a a_1 a_2 : Iota), % 6.81/7.00 Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (cd (skS.0 0 a_2)) True)) % 6.81/7.02 Clause #426 (by superposition #[424, 328]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (cd (skS.0 0 a_1)) True) (Eq True False)) % 6.81/7.02 Clause #430 (by clausification #[426]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (cd (skS.0 0 a_1)) True) % 6.81/7.02 Clause #431 (by superposition #[430, 58]): ∀ (a : Iota), Or (Eq (cd (skS.0 0 a)) True) (Eq True False) % 6.81/7.02 Clause #434 (by clausification #[431]): ∀ (a : Iota), Eq (cd (skS.0 0 a)) True % 6.81/7.02 Clause #435 (by superposition #[434, 61]): ∀ (a : Iota), Or (Eq True False) (Eq (rq (skS.0 0 a) iv) True) % 6.81/7.02 Clause #436 (by superposition #[434, 76]): ∀ (a : Iota), Or (Eq True False) (Eq (rp (skS.0 0 a) iv) True) % 6.81/7.02 Clause #437 (by clausification #[436]): ∀ (a : Iota), Eq (rp (skS.0 0 a) iv) True % 6.81/7.02 Clause #439 (by superposition #[437, 101]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (rp (skS.0 0 a) a_1) False) (Eq iv a_1)) % 6.81/7.02 Clause #440 (by clausification #[435]): ∀ (a : Iota), Eq (rq (skS.0 0 a) iv) True % 6.81/7.02 Clause #441 (by superposition #[440, 107]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (rq (skS.0 0 a) a_1) False) (Eq iv a_1)) % 6.81/7.02 Clause #443 (by clausification #[441]): ∀ (a a_1 : Iota), Or (Eq (rq (skS.0 0 a) a_1) False) (Eq iv a_1) % 6.81/7.02 Clause #447 (by clausification #[439]): ∀ (a a_1 : Iota), Or (Eq (rp (skS.0 0 a) a_1) False) (Eq iv a_1) % 6.81/7.02 Clause #459 (by clausification #[413]): ∀ (a a_1 a_2 : Iota), % 6.81/7.02 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.02 (Or (Eq (rq (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq (rp (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True)) % 6.81/7.02 Clause #460 (by superposition #[459, 58]): ∀ (a a_1 : Iota), % 6.81/7.02 Or (Eq (rq (skS.0 0 a) (skS.0 3 a a_1)) True) (Or (Eq (rp (skS.0 0 a) (skS.0 3 a a_1)) True) (Eq True False)) % 6.81/7.02 Clause #464 (by clausification #[460]): ∀ (a a_1 : Iota), Or (Eq (rq (skS.0 0 a) (skS.0 3 a a_1)) True) (Eq (rp (skS.0 0 a) (skS.0 3 a a_1)) True) % 6.81/7.02 Clause #465 (by superposition #[464, 443]): ∀ (a a_1 : Iota), Or (Eq (rp (skS.0 0 a) (skS.0 3 a a_1)) True) (Or (Eq True False) (Eq iv (skS.0 3 a a_1))) % 6.81/7.02 Clause #470 (by clausification #[465]): ∀ (a a_1 : Iota), Or (Eq (rp (skS.0 0 a) (skS.0 3 a a_1)) True) (Eq iv (skS.0 3 a a_1)) % 6.81/7.02 Clause #471 (by superposition #[470, 447]): ∀ (a a_1 : Iota), Or (Eq iv (skS.0 3 a a_1)) (Or (Eq True False) (Eq iv (skS.0 3 a a_1))) % 6.81/7.02 Clause #477 (by clausification #[471]): ∀ (a a_1 : Iota), Or (Eq iv (skS.0 3 a a_1)) (Eq iv (skS.0 3 a a_1)) % 6.81/7.02 Clause #478 (by eliminate duplicate literals #[477]): ∀ (a a_1 : Iota), Eq iv (skS.0 3 a a_1) % 6.81/7.02 Clause #505 (by clausification #[325]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.02 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.02 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.02 (Or (Eq (rq (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))) % 6.81/7.02 Clause #506 (by forward demodulation #[505, 478]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.02 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.02 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.02 (Or (Eq (rq (skS.0 0 a_2) iv) False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))) % 6.81/7.02 Clause #507 (by forward demodulation #[506, 440]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.02 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.02 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Or (Eq True False) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))) % 6.81/7.02 Clause #508 (by clausification #[507]): ∀ (a a_1 a_2 a_3 : Iota), % 6.81/7.02 Or (Eq (cowlNothing (skS.0 1 a)) True) % 6.81/7.02 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (rp (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False)) % 6.81/7.02 Clause #509 (by forward demodulation #[508, 478]): ∀ (a a_1 a_2 : Iota), % 6.81/7.02 Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (rp (skS.0 0 a_2) iv) False)) % 6.81/7.02 Clause #510 (by superposition #[509, 437]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq False True)) % 6.81/7.02 Clause #511 (by clausification #[510]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) True) % 6.81/7.02 Clause #513 (by superposition #[511, 328]): ∀ (a : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq True False) % 6.81/7.02 Clause #514 (by clausification #[513]): ∀ (a : Iota), Eq (cowlNothing (skS.0 1 a)) True % 6.81/7.02 Clause #515 (by superposition #[514, 58]): Eq True False % 6.81/7.02 Clause #516 (by clausification #[515]): False % 6.81/7.02 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------