%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS134+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 4.05s 4.29s % Output : Proof 4.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.18 % Problem : KRS134+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.19 % Command : duper %s % 0.13/0.41 % Computer : n001.cluster.edu % 0.13/0.41 % Model : x86_64 x86_64 % 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.41 % Memory : 8042.1875MB % 0.13/0.41 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.41 % CPULimit : 300 % 0.13/0.41 % WCLimit : 300 % 0.13/0.41 % DateTime : Thu Oct 2 10:24:08 EDT 2025 % 0.13/0.41 % CPUTime : % 4.05/4.29 SZS status Theorem for theBenchmark.p % 4.05/4.29 SZS output start Proof for theBenchmark.p % 4.05/4.29 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 4.05/4.29 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) True % 4.05/4.29 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), rprop X Y → cA Y) True % 4.05/4.29 Clause #3 (by assumption #[]): Eq % 4.05/4.29 (Not % 4.05/4.29 (And % 4.05/4.29 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.05/4.29 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.05/4.29 (∀ (X : Iota), cowlThing X → ∀ (Y : Iota), rprop X Y → cA Y))) % 4.05/4.29 True % 4.05/4.29 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), rprop a Y → cA Y) True % 4.05/4.29 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (rprop a a_1 → cA a_1) True % 4.05/4.29 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (rprop a a_1) False) (Eq (cA a_1) True) % 4.05/4.29 Clause #7 (by clausification #[1]): ∀ (a : Iota), Eq (Iff (xsd_string a) (Not (xsd_integer a))) True % 4.05/4.29 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (Not (xsd_integer a)) False) % 4.05/4.29 Clause #9 (by clausification #[7]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (Not (xsd_integer a)) True) % 4.05/4.29 Clause #10 (by clausification #[8]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (xsd_integer a) True) % 4.05/4.29 Clause #11 (by clausification #[9]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (xsd_integer a) False) % 4.05/4.29 Clause #13 (by clausification #[0]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 4.05/4.29 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (Not (cowlNothing a)) True % 4.05/4.29 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (cowlThing a) True % 4.05/4.29 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (cowlNothing a) False % 4.05/4.29 Clause #17 (by clausification #[3]): Eq % 4.05/4.29 (And % 4.05/4.29 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.05/4.29 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.05/4.29 (∀ (X : Iota), cowlThing X → ∀ (Y : Iota), rprop X Y → cA Y)) % 4.05/4.29 False % 4.05/4.29 Clause #18 (by clausification #[17]): Or % 4.05/4.29 (Eq % 4.05/4.29 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.05/4.29 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.05/4.29 False) % 4.05/4.29 (Eq (∀ (X : Iota), cowlThing X → ∀ (Y : Iota), rprop X Y → cA Y) False) % 4.05/4.29 Clause #19 (by clausification #[18]): Or (Eq (∀ (X : Iota), cowlThing X → ∀ (Y : Iota), rprop X Y → cA Y) False) % 4.05/4.29 (Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 4.05/4.29 (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False)) % 4.05/4.29 Clause #20 (by clausification #[19]): ∀ (a : Iota), % 4.05/4.29 Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 4.05/4.29 (Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 4.05/4.29 (Eq (Not (cowlThing (skS.0 0 a) → ∀ (Y : Iota), rprop (skS.0 0 a) Y → cA Y)) True)) % 4.05/4.29 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 4.05/4.29 Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 4.05/4.29 (Or (Eq (Not (cowlThing (skS.0 0 a) → ∀ (Y : Iota), rprop (skS.0 0 a) Y → cA Y)) True) % 4.05/4.29 (Eq (Not (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1))))) True)) % 4.05/4.29 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 4.05/4.29 Or (Eq (Not (cowlThing (skS.0 0 a) → ∀ (Y : Iota), rprop (skS.0 0 a) Y → cA Y)) True) % 4.05/4.29 (Or (Eq (Not (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1))))) True) % 4.05/4.29 (Eq (Not (Iff (xsd_string (skS.0 2 a_2)) (Not (xsd_integer (skS.0 2 a_2))))) True)) % 4.05/4.29 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 4.05/4.29 Or (Eq (Not (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a))))) True) % 4.05/4.29 (Or (Eq (Not (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1))))) True) % 4.05/4.29 (Eq (cowlThing (skS.0 0 a_2) → ∀ (Y : Iota), rprop (skS.0 0 a_2) Y → cA Y) False)) % 4.05/4.29 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 4.05/4.29 Or (Eq (Not (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a))))) True) % 4.05/4.29 (Or (Eq (cowlThing (skS.0 0 a_1) → ∀ (Y : Iota), rprop (skS.0 0 a_1) Y → cA Y) False) % 4.05/4.32 (Eq (And (cowlThing (skS.0 1 a_2)) (Not (cowlNothing (skS.0 1 a_2)))) False)) % 4.05/4.32 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 4.05/4.32 Or (Eq (cowlThing (skS.0 0 a) → ∀ (Y : Iota), rprop (skS.0 0 a) Y → cA Y) False) % 4.05/4.32 (Or (Eq (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1)))) False) % 4.05/4.32 (Eq (Iff (xsd_string (skS.0 2 a_2)) (Not (xsd_integer (skS.0 2 a_2)))) False)) % 4.05/4.32 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 4.05/4.32 Or (Eq (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a)))) False) % 4.05/4.32 (Or (Eq (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1)))) False) % 4.05/4.32 (Eq (∀ (Y : Iota), rprop (skS.0 0 a_2) Y → cA Y) False)) % 4.05/4.32 Clause #36 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 4.05/4.32 Or (Eq (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a)))) False) % 4.05/4.32 (Or (Eq (∀ (Y : Iota), rprop (skS.0 0 a_1) Y → cA Y) False) % 4.05/4.32 (Or (Eq (cowlThing (skS.0 1 a_2)) False) (Eq (Not (cowlNothing (skS.0 1 a_2))) False))) % 4.05/4.32 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 4.05/4.32 Or (Eq (∀ (Y : Iota), rprop (skS.0 0 a) Y → cA Y) False) % 4.05/4.32 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.05/4.32 (Or (Eq (Not (cowlNothing (skS.0 1 a_1))) False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Eq (Not (xsd_integer (skS.0 2 a_2))) False)))) % 4.05/4.32 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 4.05/4.32 Or (Eq (∀ (Y : Iota), rprop (skS.0 0 a) Y → cA Y) False) % 4.05/4.32 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.05/4.32 (Or (Eq (Not (cowlNothing (skS.0 1 a_1))) False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq (Not (xsd_integer (skS.0 2 a_2))) True)))) % 4.05/4.32 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.32 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.32 (Or (Eq (Not (cowlNothing (skS.0 1 a))) False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.05/4.32 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) False) % 4.05/4.32 (Eq (Not (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3) → cA (skS.0 3 a_2 a_3))) True)))) % 4.05/4.32 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.32 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.05/4.32 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) False) % 4.05/4.32 (Or (Eq (Not (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3) → cA (skS.0 3 a_2 a_3))) True) % 4.05/4.32 (Eq (cowlNothing (skS.0 1 a)) True)))) % 4.05/4.32 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.32 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.05/4.32 (Or (Eq (Not (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3) → cA (skS.0 3 a_2 a_3))) True) % 4.05/4.32 (Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) True)))) % 4.05/4.32 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.32 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.05/4.32 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.32 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.05/4.32 (Eq (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3) → cA (skS.0 3 a_2 a_3)) False)))) % 4.05/4.32 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.32 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.05/4.32 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.32 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)))) % 4.05/4.32 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.32 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.05/4.32 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.32 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (cA (skS.0 3 a_2 a_3)) False)))) % 4.05/4.32 Clause #45 (by forward demodulation #[43, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.32 Or (Eq True False) % 4.05/4.32 (Or (Eq (xsd_string (skS.0 2 a)) False) % 4.05/4.32 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.32 (Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)))) % 4.05/4.32 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.32 Or (Eq (xsd_string (skS.0 2 a)) False) % 4.05/4.32 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.32 (Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))) % 4.05/4.34 Clause #47 (by superposition #[46, 10]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.05/4.34 (Or (Eq (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a_1)) True)))) % 4.05/4.34 Clause #48 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.34 (Or (Eq (Not (cowlNothing (skS.0 1 a))) False) % 4.05/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.05/4.34 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) True) % 4.05/4.34 (Eq (Not (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3) → cA (skS.0 4 a_2 a_3))) True)))) % 4.05/4.34 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.05/4.34 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) True) % 4.05/4.34 (Or (Eq (Not (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3) → cA (skS.0 4 a_2 a_3))) True) % 4.05/4.34 (Eq (cowlNothing (skS.0 1 a)) True)))) % 4.05/4.34 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.05/4.34 (Or (Eq (Not (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3) → cA (skS.0 4 a_2 a_3))) True) % 4.05/4.34 (Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) False)))) % 4.05/4.34 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.05/4.34 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 4.05/4.34 (Eq (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3) → cA (skS.0 4 a_2 a_3)) False)))) % 4.05/4.34 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.05/4.34 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) (Eq (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3)) True)))) % 4.05/4.34 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.05/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.05/4.34 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) (Eq (cA (skS.0 4 a_2 a_3)) False)))) % 4.05/4.34 Clause #54 (by forward demodulation #[52, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq True False) % 4.05/4.34 (Or (Eq (xsd_string (skS.0 2 a)) True) % 4.05/4.34 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a)) False) (Eq (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3)) True)))) % 4.05/4.34 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.05/4.34 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a)) False) (Eq (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3)) True))) % 4.05/4.34 Clause #56 (by forward demodulation #[53, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq True False) % 4.05/4.34 (Or (Eq (xsd_string (skS.0 2 a)) True) % 4.05/4.34 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a)) False) (Eq (cA (skS.0 4 a_2 a_3)) False)))) % 4.05/4.34 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.05/4.34 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a)) False) (Eq (cA (skS.0 4 a_2 a_3)) False))) % 4.05/4.34 Clause #58 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.05/4.34 (Or (Eq (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (xsd_integer (skS.0 2 a_1)) True))) % 4.05/4.34 Clause #59 (by eliminate duplicate literals #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.34 Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.34 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (rprop (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)) % 4.05/4.34 Clause #60 (by superposition #[59, 16]): ∀ (a a_1 a_2 : Iota), % 4.05/4.34 Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Eq (rprop (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq True False)) % 4.05/4.34 Clause #68 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (rprop (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.05/4.37 Clause #71 (by superposition #[68, 6]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Eq True False) (Eq (cA (skS.0 3 a_1 a_2)) True)) % 4.05/4.37 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (cA (skS.0 3 a_1 a_2)) True) % 4.05/4.37 Clause #77 (by forward demodulation #[44, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq True False) % 4.05/4.37 (Or (Eq (xsd_string (skS.0 2 a)) False) % 4.05/4.37 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.37 (Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (cA (skS.0 3 a_2 a_3)) False)))) % 4.05/4.37 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq (xsd_string (skS.0 2 a)) False) % 4.05/4.37 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.37 (Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (cA (skS.0 3 a_2 a_3)) False))) % 4.05/4.37 Clause #79 (by superposition #[78, 10]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.37 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.05/4.37 (Or (Eq (cA (skS.0 3 a_2 a_3)) False) (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a_1)) True)))) % 4.05/4.37 Clause #88 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.37 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.05/4.37 (Or (Eq (cA (skS.0 3 a_2 a_3)) False) (Eq (xsd_integer (skS.0 2 a_1)) True))) % 4.05/4.37 Clause #89 (by eliminate duplicate literals #[88]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (cA (skS.0 3 a_2 a_3)) False)) % 4.05/4.37 Clause #90 (by superposition #[89, 72]): ∀ (a a_1 a_2 : Iota), % 4.05/4.37 Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.37 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Or (Eq (xsd_integer (skS.0 2 a_2)) True) (Eq False True))) % 4.05/4.37 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), % 4.05/4.37 Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.05/4.37 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) True)) % 4.05/4.37 Clause #95 (by equality factoring #[91]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Ne True True) (Eq (xsd_integer (skS.0 2 a_1)) True)) % 4.05/4.37 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), % 4.05/4.37 Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.05/4.37 Clause #98 (by clausification #[96]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq True False)) % 4.05/4.37 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.05/4.37 Clause #100 (by superposition #[99, 16]): ∀ (a : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq True False) % 4.05/4.37 Clause #103 (by clausification #[100]): ∀ (a : Iota), Eq (xsd_integer (skS.0 2 a)) True % 4.05/4.37 Clause #104 (by backward demodulation #[103, 55]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.05/4.37 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Or (Eq True False) (Eq (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3)) True))) % 4.05/4.37 Clause #105 (by backward demodulation #[103, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.05/4.37 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Or (Eq True False) (Eq (cA (skS.0 4 a_2 a_3)) False))) % 4.05/4.37 Clause #108 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq (cA (skS.0 4 a_2 a_3)) False)) % 4.05/4.37 Clause #109 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.37 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.05/4.37 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq (rprop (skS.0 0 a_2) (skS.0 4 a_2 a_3)) True)) % 4.05/4.37 Clause #111 (by superposition #[109, 16]): ∀ (a a_1 a_2 : Iota), % 4.05/4.37 Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq (rprop (skS.0 0 a_1) (skS.0 4 a_1 a_2)) True) (Eq True False)) % 4.05/4.37 Clause #113 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (rprop (skS.0 0 a_1) (skS.0 4 a_1 a_2)) True) % 4.05/4.37 Clause #115 (by superposition #[113, 6]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq True False) (Eq (cA (skS.0 4 a_1 a_2)) True)) % 4.05/4.38 Clause #116 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (cA (skS.0 4 a_1 a_2)) True) % 4.05/4.38 Clause #117 (by superposition #[116, 11]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 4 a a_1)) True) (Or (Eq True False) (Eq (xsd_integer (skS.0 2 a_2)) False)) % 4.05/4.38 Clause #120 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 4 a a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) False) % 4.05/4.38 Clause #121 (by superposition #[120, 103]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 4 a a_1)) True) (Eq False True) % 4.05/4.38 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota), Eq (cA (skS.0 4 a a_1)) True % 4.05/4.38 Clause #123 (by superposition #[122, 108]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq True False)) % 4.05/4.38 Clause #124 (by clausification #[123]): ∀ (a a_1 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (cowlNothing (skS.0 1 a_1)) True) % 4.05/4.38 Clause #126 (by superposition #[124, 16]): ∀ (a : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq True False) % 4.05/4.38 Clause #127 (by clausification #[126]): ∀ (a : Iota), Eq (xsd_string (skS.0 2 a)) True % 4.05/4.38 Clause #128 (by superposition #[127, 11]): ∀ (a : Iota), Or (Eq True False) (Eq (xsd_integer (skS.0 2 a)) False) % 4.05/4.38 Clause #129 (by clausification #[128]): ∀ (a : Iota), Eq (xsd_integer (skS.0 2 a)) False % 4.05/4.38 Clause #130 (by superposition #[129, 103]): Eq False True % 4.05/4.38 Clause #132 (by clausification #[130]): False % 4.05/4.38 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------