%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS166+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 07:52:44 PM UTC 2025 % Result : Theorem 4.53s 4.69s % Output : Proof 4.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : KRS166+1 : TPTP v9.2.0. Released v3.1.0. % 0.12/0.15 % Command : duper %s % 0.14/0.36 % Computer : n001.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 10:18:38 EDT 2025 % 0.14/0.37 % CPUTime : % 4.53/4.69 SZS status Theorem for theBenchmark.p % 4.53/4.69 SZS output start Proof for theBenchmark.p % 4.53/4.69 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 4.53/4.69 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) True % 4.53/4.69 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), cAutomobile X → cCar X) True % 4.53/4.69 Clause #3 (by assumption #[]): Eq (∀ (X : Iota), cCar X → cAutomobile X) True % 4.53/4.69 Clause #4 (by assumption #[]): Eq % 4.53/4.69 (Not % 4.53/4.69 (And % 4.53/4.69 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.53/4.69 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.53/4.69 (∀ (X : Iota), Iff (cCar X) (cAutomobile X)))) % 4.53/4.69 True % 4.53/4.69 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (cCar a → cAutomobile a) True % 4.53/4.69 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (cCar a) False) (Eq (cAutomobile a) True) % 4.53/4.69 Clause #7 (by clausification #[2]): ∀ (a : Iota), Eq (cAutomobile a → cCar a) True % 4.53/4.69 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (cAutomobile a) False) (Eq (cCar a) True) % 4.53/4.69 Clause #9 (by clausification #[1]): ∀ (a : Iota), Eq (Iff (xsd_string a) (Not (xsd_integer a))) True % 4.53/4.69 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (Not (xsd_integer a)) False) % 4.53/4.69 Clause #11 (by clausification #[9]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (Not (xsd_integer a)) True) % 4.53/4.69 Clause #12 (by clausification #[10]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (xsd_integer a) True) % 4.53/4.69 Clause #13 (by clausification #[11]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (xsd_integer a) False) % 4.53/4.69 Clause #15 (by clausification #[0]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 4.53/4.69 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (Not (cowlNothing a)) True % 4.53/4.69 Clause #17 (by clausification #[15]): ∀ (a : Iota), Eq (cowlThing a) True % 4.53/4.69 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (cowlNothing a) False % 4.53/4.69 Clause #19 (by clausification #[4]): Eq % 4.53/4.69 (And % 4.53/4.69 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.53/4.69 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.53/4.69 (∀ (X : Iota), Iff (cCar X) (cAutomobile X))) % 4.53/4.69 False % 4.53/4.69 Clause #20 (by clausification #[19]): Or % 4.53/4.69 (Eq % 4.53/4.69 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.53/4.69 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.53/4.69 False) % 4.53/4.69 (Eq (∀ (X : Iota), Iff (cCar X) (cAutomobile X)) False) % 4.53/4.69 Clause #21 (by clausification #[20]): Or (Eq (∀ (X : Iota), Iff (cCar X) (cAutomobile X)) False) % 4.53/4.69 (Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 4.53/4.69 (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False)) % 4.53/4.69 Clause #22 (by clausification #[21]): ∀ (a : Iota), % 4.53/4.69 Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 4.53/4.69 (Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 4.53/4.69 (Eq (Not (Iff (cCar (skS.0 0 a)) (cAutomobile (skS.0 0 a)))) True)) % 4.53/4.69 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 4.53/4.69 Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 4.53/4.69 (Or (Eq (Not (Iff (cCar (skS.0 0 a)) (cAutomobile (skS.0 0 a)))) True) % 4.53/4.69 (Eq (Not (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1))))) True)) % 4.53/4.69 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 4.53/4.69 Or (Eq (Not (Iff (cCar (skS.0 0 a)) (cAutomobile (skS.0 0 a)))) True) % 4.53/4.69 (Or (Eq (Not (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1))))) True) % 4.53/4.69 (Eq (Not (Iff (xsd_string (skS.0 2 a_2)) (Not (xsd_integer (skS.0 2 a_2))))) True)) % 4.53/4.69 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 4.53/4.69 Or (Eq (Not (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a))))) True) % 4.53/4.69 (Or (Eq (Not (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1))))) True) % 4.53/4.69 (Eq (Iff (cCar (skS.0 0 a_2)) (cAutomobile (skS.0 0 a_2))) False)) % 4.53/4.69 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 4.53/4.69 Or (Eq (Not (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a))))) True) % 4.53/4.69 (Or (Eq (Iff (cCar (skS.0 0 a_1)) (cAutomobile (skS.0 0 a_1))) False) % 4.55/4.72 (Eq (And (cowlThing (skS.0 1 a_2)) (Not (cowlNothing (skS.0 1 a_2)))) False)) % 4.55/4.72 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (Iff (cCar (skS.0 0 a)) (cAutomobile (skS.0 0 a))) False) % 4.55/4.72 (Or (Eq (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1)))) False) % 4.55/4.72 (Eq (Iff (xsd_string (skS.0 2 a_2)) (Not (xsd_integer (skS.0 2 a_2)))) False)) % 4.55/4.72 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a)))) False) % 4.55/4.72 (Or (Eq (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1)))) False) % 4.55/4.72 (Or (Eq (cCar (skS.0 0 a_2)) False) (Eq (cAutomobile (skS.0 0 a_2)) False))) % 4.55/4.72 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a)))) False) % 4.55/4.72 (Or (Eq (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1)))) False) % 4.55/4.72 (Or (Eq (cCar (skS.0 0 a_2)) True) (Eq (cAutomobile (skS.0 0 a_2)) True))) % 4.55/4.72 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a)))) False) % 4.55/4.72 (Or (Eq (cCar (skS.0 0 a_1)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a_1)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_2)) False) (Eq (Not (cowlNothing (skS.0 1 a_2))) False)))) % 4.55/4.72 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.55/4.72 (Or (Eq (Not (cowlNothing (skS.0 1 a_1))) False) % 4.55/4.72 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Eq (Not (xsd_integer (skS.0 2 a_2))) False))))) % 4.55/4.72 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.55/4.72 (Or (Eq (Not (cowlNothing (skS.0 1 a_1))) False) % 4.55/4.72 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq (Not (xsd_integer (skS.0 2 a_2))) True))))) % 4.55/4.72 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.55/4.72 (Or (Eq (xsd_string (skS.0 2 a_2)) False) % 4.55/4.72 (Or (Eq (Not (xsd_integer (skS.0 2 a_2))) False) (Eq (cowlNothing (skS.0 1 a_1)) True))))) % 4.55/4.72 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.55/4.72 (Or (Eq (xsd_string (skS.0 2 a_2)) False) % 4.55/4.72 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) True))))) % 4.55/4.72 Clause #35 (by forward demodulation #[34, 18]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.55/4.72 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a_2)) True))))) % 4.55/4.72 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.55/4.72 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Eq (xsd_integer (skS.0 2 a_2)) True)))) % 4.55/4.72 Clause #38 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.55/4.72 (Or (Eq (xsd_string (skS.0 2 a_2)) True) % 4.55/4.72 (Or (Eq (Not (xsd_integer (skS.0 2 a_2))) True) (Eq (cowlNothing (skS.0 1 a_1)) True))))) % 4.55/4.72 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.55/4.72 (Or (Eq (xsd_string (skS.0 2 a_2)) True) % 4.55/4.72 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) False))))) % 4.55/4.72 Clause #40 (by forward demodulation #[39, 18]): ∀ (a a_1 a_2 : Iota), % 4.55/4.72 Or (Eq (cCar (skS.0 0 a)) False) % 4.55/4.72 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a_2)) False))))) % 4.59/4.75 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) False) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq (xsd_integer (skS.0 2 a_2)) False)))) % 4.59/4.75 Clause #42 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a)))) False) % 4.59/4.75 (Or (Eq (cCar (skS.0 0 a_1)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a_1)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_2)) False) (Eq (Not (cowlNothing (skS.0 1 a_2))) False)))) % 4.59/4.75 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (Not (cowlNothing (skS.0 1 a_1))) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Eq (Not (xsd_integer (skS.0 2 a_2))) False))))) % 4.59/4.75 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (Not (cowlNothing (skS.0 1 a_1))) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq (Not (xsd_integer (skS.0 2 a_2))) True))))) % 4.59/4.75 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) False) % 4.59/4.75 (Or (Eq (Not (xsd_integer (skS.0 2 a_2))) False) (Eq (cowlNothing (skS.0 1 a_1)) True))))) % 4.59/4.75 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) False) % 4.59/4.75 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) True))))) % 4.59/4.75 Clause #47 (by forward demodulation #[46, 18]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a_2)) True))))) % 4.59/4.75 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Eq (xsd_integer (skS.0 2 a_2)) True)))) % 4.59/4.75 Clause #49 (by superposition #[48, 17]): ∀ (a a_1 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_1)) False) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq False True)))) % 4.59/4.75 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_1)) False) (Eq (xsd_integer (skS.0 2 a_1)) True))) % 4.59/4.75 Clause #51 (by superposition #[50, 12]): ∀ (a a_1 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a_1)) True)))) % 4.59/4.75 Clause #52 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) True) % 4.59/4.75 (Or (Eq (Not (xsd_integer (skS.0 2 a_2))) True) (Eq (cowlNothing (skS.0 1 a_1)) True))))) % 4.59/4.75 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 4.59/4.75 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.75 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.75 (Or (Eq (xsd_string (skS.0 2 a_2)) True) % 4.59/4.75 (Or (Eq (cowlNothing (skS.0 1 a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) False))))) % 4.59/4.78 Clause #54 (by forward demodulation #[53, 18]): ∀ (a a_1 a_2 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.78 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a_2)) False))))) % 4.59/4.78 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.59/4.78 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq (xsd_integer (skS.0 2 a_2)) False)))) % 4.59/4.78 Clause #56 (by superposition #[55, 17]): ∀ (a a_1 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (xsd_string (skS.0 2 a_1)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) False) (Eq False True)))) % 4.59/4.78 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (xsd_string (skS.0 2 a_1)) True) (Eq (xsd_integer (skS.0 2 a_1)) False))) % 4.59/4.78 Clause #58 (by clausification #[51]): ∀ (a a_1 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (xsd_integer (skS.0 2 a_1)) True))) % 4.59/4.78 Clause #59 (by eliminate duplicate literals #[58]): ∀ (a a_1 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) (Or (Eq (cAutomobile (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) True)) % 4.59/4.78 Clause #60 (by superposition #[59, 8]): ∀ (a a_1 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Or (Eq True False) (Eq (cCar (skS.0 0 a)) True))) % 4.59/4.78 Clause #62 (by clausification #[60]): ∀ (a a_1 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (cCar (skS.0 0 a)) True)) % 4.59/4.78 Clause #63 (by eliminate duplicate literals #[62]): ∀ (a a_1 : Iota), Or (Eq (cCar (skS.0 0 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.59/4.78 Clause #66 (by superposition #[63, 6]): ∀ (a a_1 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Eq True False) (Eq (cAutomobile (skS.0 0 a_1)) True)) % 4.59/4.78 Clause #67 (by superposition #[63, 57]): ∀ (a a_1 a_2 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cCar (skS.0 0 a_1)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a_1)) True) (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq True False)))) % 4.59/4.78 Clause #68 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (cAutomobile (skS.0 0 a_1)) True) % 4.59/4.78 Clause #77 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cCar (skS.0 0 a_1)) True) (Or (Eq (cAutomobile (skS.0 0 a_1)) True) (Eq (xsd_string (skS.0 2 a_2)) True))) % 4.59/4.78 Clause #82 (by superposition #[77, 13]): ∀ (a a_1 a_2 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cCar (skS.0 0 a_1)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a_1)) True) (Or (Eq True False) (Eq (xsd_integer (skS.0 2 a_2)) False)))) % 4.59/4.78 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cCar (skS.0 0 a_1)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) False))) % 4.59/4.78 Clause #85 (by superposition #[83, 68]): ∀ (a a_1 a_2 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cCar (skS.0 0 a_1)) True) % 4.59/4.78 (Or (Eq (cAutomobile (skS.0 0 a_1)) True) (Or (Eq False True) (Eq (cAutomobile (skS.0 0 a_2)) True)))) % 4.59/4.78 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cCar (skS.0 0 a_1)) True) (Or (Eq (cAutomobile (skS.0 0 a_1)) True) (Eq (cAutomobile (skS.0 0 a_2)) True))) % 4.59/4.78 Clause #92 (by equality factoring #[86]): ∀ (a a_1 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cCar (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (cAutomobile (skS.0 0 a_1)) True))) % 4.59/4.78 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), % 4.59/4.78 Or (Eq (cCar (skS.0 0 a)) True) % 4.59/4.78 (Or (Eq (cCar (skS.0 0 a_1)) True) (Or (Eq (cAutomobile (skS.0 0 a_1)) True) (Or (Eq True False) (Eq True False)))) % 4.59/4.78 Clause #95 (by clausification #[93]): ∀ (a a_1 : Iota), % 4.65/4.80 Or (Eq (cCar (skS.0 0 a)) True) % 4.65/4.80 (Or (Eq (cCar (skS.0 0 a_1)) True) (Or (Eq (cAutomobile (skS.0 0 a_1)) True) (Eq True False))) % 4.65/4.80 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), % 4.65/4.80 Or (Eq (cCar (skS.0 0 a)) True) (Or (Eq (cCar (skS.0 0 a_1)) True) (Eq (cAutomobile (skS.0 0 a_1)) True)) % 4.65/4.80 Clause #100 (by superposition #[96, 8]): ∀ (a a_1 : Iota), % 4.65/4.80 Or (Eq (cCar (skS.0 0 a)) True) % 4.65/4.80 (Or (Eq (cCar (skS.0 0 a_1)) True) (Or (Eq True False) (Eq (cCar (skS.0 0 a_1)) True))) % 4.65/4.80 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), Or (Eq (cCar (skS.0 0 a)) True) (Or (Eq (cCar (skS.0 0 a_1)) True) (Eq (cCar (skS.0 0 a_1)) True)) % 4.65/4.80 Clause #102 (by eliminate duplicate literals #[101]): ∀ (a a_1 : Iota), Or (Eq (cCar (skS.0 0 a)) True) (Eq (cCar (skS.0 0 a_1)) True) % 4.65/4.80 Clause #106 (by equality factoring #[102]): ∀ (a : Iota), Or (Ne True True) (Eq (cCar (skS.0 0 a)) True) % 4.65/4.80 Clause #109 (by clausification #[106]): ∀ (a : Iota), Or (Eq (cCar (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 4.65/4.80 Clause #111 (by clausification #[109]): ∀ (a : Iota), Or (Eq (cCar (skS.0 0 a)) True) (Eq True False) % 4.65/4.80 Clause #112 (by clausification #[111]): ∀ (a : Iota), Eq (cCar (skS.0 0 a)) True % 4.65/4.80 Clause #113 (by backward demodulation #[112, 36]): ∀ (a a_1 a_2 : Iota), % 4.65/4.80 Or (Eq True False) % 4.65/4.80 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.65/4.80 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.65/4.80 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Eq (xsd_integer (skS.0 2 a_2)) True)))) % 4.65/4.80 Clause #114 (by backward demodulation #[112, 41]): ∀ (a a_1 a_2 : Iota), % 4.65/4.80 Or (Eq True False) % 4.65/4.80 (Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.65/4.80 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.65/4.80 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq (xsd_integer (skS.0 2 a_2)) False)))) % 4.65/4.80 Clause #116 (by superposition #[112, 6]): ∀ (a : Iota), Or (Eq True False) (Eq (cAutomobile (skS.0 0 a)) True) % 4.65/4.80 Clause #117 (by clausification #[116]): ∀ (a : Iota), Eq (cAutomobile (skS.0 0 a)) True % 4.65/4.80 Clause #141 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), % 4.65/4.80 Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.65/4.80 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.65/4.80 (Or (Eq (xsd_string (skS.0 2 a_2)) False) (Eq (xsd_integer (skS.0 2 a_2)) True))) % 4.65/4.80 Clause #142 (by superposition #[141, 117]): ∀ (a a_1 : Iota), % 4.65/4.80 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.65/4.80 (Or (Eq (xsd_string (skS.0 2 a_1)) False) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq False True))) % 4.65/4.80 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota), % 4.65/4.80 Or (Eq (cowlThing (skS.0 1 a)) False) (Or (Eq (xsd_string (skS.0 2 a_1)) False) (Eq (xsd_integer (skS.0 2 a_1)) True)) % 4.65/4.80 Clause #144 (by superposition #[143, 17]): ∀ (a : Iota), Or (Eq (xsd_string (skS.0 2 a)) False) (Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq False True)) % 4.65/4.80 Clause #145 (by clausification #[144]): ∀ (a : Iota), Or (Eq (xsd_string (skS.0 2 a)) False) (Eq (xsd_integer (skS.0 2 a)) True) % 4.65/4.80 Clause #146 (by superposition #[145, 12]): ∀ (a : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a)) True)) % 4.65/4.80 Clause #147 (by clausification #[146]): ∀ (a : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (xsd_integer (skS.0 2 a)) True) % 4.65/4.80 Clause #148 (by eliminate duplicate literals #[147]): ∀ (a : Iota), Eq (xsd_integer (skS.0 2 a)) True % 4.65/4.80 Clause #155 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), % 4.65/4.80 Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.65/4.80 (Or (Eq (cowlThing (skS.0 1 a_1)) False) % 4.65/4.80 (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq (xsd_integer (skS.0 2 a_2)) False))) % 4.65/4.80 Clause #156 (by forward demodulation #[155, 148]): ∀ (a a_1 a_2 : Iota), % 4.65/4.80 Or (Eq (cAutomobile (skS.0 0 a)) False) % 4.65/4.80 (Or (Eq (cowlThing (skS.0 1 a_1)) False) (Or (Eq (xsd_string (skS.0 2 a_2)) True) (Eq True False))) % 4.65/4.80 Clause #157 (by clausification #[156]): ∀ (a a_1 a_2 : Iota), % 4.65/4.80 Or (Eq (cAutomobile (skS.0 0 a)) False) (Or (Eq (cowlThing (skS.0 1 a_1)) False) (Eq (xsd_string (skS.0 2 a_2)) True)) % 4.65/4.80 Clause #158 (by superposition #[157, 117]): ∀ (a a_1 : Iota), Or (Eq (cowlThing (skS.0 1 a)) False) (Or (Eq (xsd_string (skS.0 2 a_1)) True) (Eq False True)) % 4.65/4.81 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota), Or (Eq (cowlThing (skS.0 1 a)) False) (Eq (xsd_string (skS.0 2 a_1)) True) % 4.65/4.81 Clause #160 (by superposition #[159, 17]): ∀ (a : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq False True) % 4.65/4.81 Clause #161 (by clausification #[160]): ∀ (a : Iota), Eq (xsd_string (skS.0 2 a)) True % 4.65/4.81 Clause #162 (by superposition #[161, 13]): ∀ (a : Iota), Or (Eq True False) (Eq (xsd_integer (skS.0 2 a)) False) % 4.65/4.81 Clause #165 (by clausification #[162]): ∀ (a : Iota), Eq (xsd_integer (skS.0 2 a)) False % 4.65/4.81 Clause #166 (by superposition #[165, 148]): Eq False True % 4.65/4.81 Clause #167 (by clausification #[166]): False % 4.65/4.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------