%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS171+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 4.12s 4.32s % Output : Proof 4.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : KRS171+1 : TPTP v9.2.0. Released v3.1.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 10:11:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.12/4.32 SZS status Theorem for theBenchmark.p % 4.12/4.32 SZS output start Proof for theBenchmark.p % 4.12/4.32 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 4.12/4.32 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) True % 4.12/4.32 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), rhasHead X Y → rhasLeader X Y) True % 4.12/4.32 Clause #3 (by assumption #[]): Eq (∀ (X Y : Iota), rhasLeader X Y → rhasHead X Y) True % 4.12/4.32 Clause #4 (by assumption #[]): Eq % 4.12/4.32 (Not % 4.12/4.32 (And % 4.12/4.32 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.12/4.32 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.12/4.32 (∀ (X Y : Iota), Iff (rhasLeader X Y) (rhasHead X Y)))) % 4.12/4.32 True % 4.12/4.32 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Y : Iota), rhasLeader a Y → rhasHead a Y) True % 4.12/4.32 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (rhasLeader a a_1 → rhasHead a a_1) True % 4.12/4.32 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (rhasLeader a a_1) False) (Eq (rhasHead a a_1) True) % 4.12/4.32 Clause #8 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), rhasHead a Y → rhasLeader a Y) True % 4.12/4.32 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (rhasHead a a_1 → rhasLeader a a_1) True % 4.12/4.32 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (rhasHead a a_1) False) (Eq (rhasLeader a a_1) True) % 4.12/4.32 Clause #11 (by clausification #[1]): ∀ (a : Iota), Eq (Iff (xsd_string a) (Not (xsd_integer a))) True % 4.12/4.32 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (Not (xsd_integer a)) False) % 4.12/4.32 Clause #13 (by clausification #[11]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (Not (xsd_integer a)) True) % 4.12/4.32 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (xsd_string a) True) (Eq (xsd_integer a) True) % 4.12/4.32 Clause #15 (by clausification #[13]): ∀ (a : Iota), Or (Eq (xsd_string a) False) (Eq (xsd_integer a) False) % 4.12/4.32 Clause #17 (by clausification #[0]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 4.12/4.32 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (Not (cowlNothing a)) True % 4.12/4.32 Clause #19 (by clausification #[17]): ∀ (a : Iota), Eq (cowlThing a) True % 4.12/4.32 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (cowlNothing a) False % 4.12/4.32 Clause #21 (by clausification #[4]): Eq % 4.12/4.32 (And % 4.12/4.32 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.12/4.32 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.12/4.32 (∀ (X Y : Iota), Iff (rhasLeader X Y) (rhasHead X Y))) % 4.12/4.32 False % 4.12/4.32 Clause #22 (by clausification #[21]): Or % 4.12/4.32 (Eq % 4.12/4.32 (And (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) % 4.12/4.32 (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X)))) % 4.12/4.32 False) % 4.12/4.32 (Eq (∀ (X Y : Iota), Iff (rhasLeader X Y) (rhasHead X Y)) False) % 4.12/4.32 Clause #23 (by clausification #[22]): Or (Eq (∀ (X Y : Iota), Iff (rhasLeader X Y) (rhasHead X Y)) False) % 4.12/4.32 (Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 4.12/4.32 (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False)) % 4.12/4.32 Clause #24 (by clausification #[23]): ∀ (a : Iota), % 4.12/4.32 Or (Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) False) % 4.12/4.32 (Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 4.12/4.32 (Eq (Not (∀ (Y : Iota), Iff (rhasLeader (skS.0 0 a) Y) (rhasHead (skS.0 0 a) Y))) True)) % 4.12/4.32 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), % 4.12/4.32 Or (Eq (∀ (X : Iota), Iff (xsd_string X) (Not (xsd_integer X))) False) % 4.12/4.32 (Or (Eq (Not (∀ (Y : Iota), Iff (rhasLeader (skS.0 0 a) Y) (rhasHead (skS.0 0 a) Y))) True) % 4.12/4.32 (Eq (Not (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1))))) True)) % 4.12/4.32 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 4.12/4.32 Or (Eq (Not (∀ (Y : Iota), Iff (rhasLeader (skS.0 0 a) Y) (rhasHead (skS.0 0 a) Y))) True) % 4.12/4.32 (Or (Eq (Not (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1))))) True) % 4.12/4.32 (Eq (Not (Iff (xsd_string (skS.0 2 a_2)) (Not (xsd_integer (skS.0 2 a_2))))) True)) % 4.12/4.32 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 4.12/4.32 Or (Eq (Not (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a))))) True) % 4.12/4.34 (Or (Eq (Not (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1))))) True) % 4.12/4.34 (Eq (∀ (Y : Iota), Iff (rhasLeader (skS.0 0 a_2) Y) (rhasHead (skS.0 0 a_2) Y)) False)) % 4.12/4.34 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 4.12/4.34 Or (Eq (Not (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a))))) True) % 4.12/4.34 (Or (Eq (∀ (Y : Iota), Iff (rhasLeader (skS.0 0 a_1) Y) (rhasHead (skS.0 0 a_1) Y)) False) % 4.12/4.34 (Eq (And (cowlThing (skS.0 1 a_2)) (Not (cowlNothing (skS.0 1 a_2)))) False)) % 4.12/4.34 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 4.12/4.34 Or (Eq (∀ (Y : Iota), Iff (rhasLeader (skS.0 0 a) Y) (rhasHead (skS.0 0 a) Y)) False) % 4.12/4.34 (Or (Eq (And (cowlThing (skS.0 1 a_1)) (Not (cowlNothing (skS.0 1 a_1)))) False) % 4.12/4.34 (Eq (Iff (xsd_string (skS.0 2 a_2)) (Not (xsd_integer (skS.0 2 a_2)))) False)) % 4.12/4.34 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (And (cowlThing (skS.0 1 a)) (Not (cowlNothing (skS.0 1 a)))) False) % 4.12/4.34 (Or (Eq (Iff (xsd_string (skS.0 2 a_1)) (Not (xsd_integer (skS.0 2 a_1)))) False) % 4.12/4.34 (Eq (Not (Iff (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)))) True)) % 4.12/4.34 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (Iff (xsd_string (skS.0 2 a)) (Not (xsd_integer (skS.0 2 a)))) False) % 4.12/4.34 (Or (Eq (Not (Iff (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)))) True) % 4.12/4.34 (Or (Eq (cowlThing (skS.0 1 a_3)) False) (Eq (Not (cowlNothing (skS.0 1 a_3))) False))) % 4.12/4.34 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (Not (Iff (rhasLeader (skS.0 0 a) (skS.0 3 a a_1)) (rhasHead (skS.0 0 a) (skS.0 3 a a_1)))) True) % 4.12/4.34 (Or (Eq (cowlThing (skS.0 1 a_2)) False) % 4.12/4.34 (Or (Eq (Not (cowlNothing (skS.0 1 a_2))) False) % 4.12/4.34 (Or (Eq (xsd_string (skS.0 2 a_3)) False) (Eq (Not (xsd_integer (skS.0 2 a_3))) False)))) % 4.12/4.34 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (Not (Iff (rhasLeader (skS.0 0 a) (skS.0 3 a a_1)) (rhasHead (skS.0 0 a) (skS.0 3 a a_1)))) True) % 4.12/4.34 (Or (Eq (cowlThing (skS.0 1 a_2)) False) % 4.12/4.34 (Or (Eq (Not (cowlNothing (skS.0 1 a_2))) False) % 4.12/4.34 (Or (Eq (xsd_string (skS.0 2 a_3)) True) (Eq (Not (xsd_integer (skS.0 2 a_3))) True)))) % 4.12/4.34 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.12/4.34 (Or (Eq (Not (cowlNothing (skS.0 1 a))) False) % 4.12/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.12/4.34 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) False) % 4.12/4.34 (Eq (Iff (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False)))) % 4.12/4.34 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.12/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.12/4.34 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) False) % 4.12/4.34 (Or (Eq (Iff (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False) % 4.12/4.34 (Eq (cowlNothing (skS.0 1 a)) True)))) % 4.12/4.34 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.12/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.12/4.34 (Or (Eq (Iff (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False) % 4.12/4.34 (Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) True)))) % 4.12/4.34 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.12/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.12/4.34 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.12/4.34 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.12/4.34 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) % 4.12/4.34 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))))) % 4.12/4.34 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), % 4.12/4.34 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.12/4.34 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.12/4.34 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.12/4.34 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.12/4.34 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 4.22/4.37 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))))) % 4.22/4.37 Clause #39 (by forward demodulation #[37, 20]): ∀ (a a_1 a_2 a_3 : Iota), % 4.22/4.37 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.22/4.37 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.22/4.37 (Or (Eq False True) % 4.22/4.37 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) % 4.22/4.37 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))))) % 4.22/4.37 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 4.22/4.37 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.22/4.37 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.22/4.37 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) % 4.22/4.37 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False)))) % 4.22/4.37 Clause #41 (by superposition #[19, 40]): ∀ (a a_1 a_2 : Iota), % 4.22/4.37 Or (Eq (xsd_string (skS.0 2 a)) False) % 4.22/4.37 (Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.22/4.37 (Or (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) (Eq False True)))) % 4.22/4.37 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 4.22/4.37 Or (Eq (xsd_string (skS.0 2 a)) False) % 4.22/4.37 (Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.22/4.37 (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False))) % 4.22/4.37 Clause #44 (by superposition #[43, 14]): ∀ (a a_1 a_2 : Iota), % 4.22/4.37 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.22/4.37 (Or (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.22/4.37 (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a)) True)))) % 4.22/4.37 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 4.22/4.37 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.22/4.37 (Or (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) (Eq (xsd_integer (skS.0 2 a)) True))) % 4.22/4.37 Clause #46 (by eliminate duplicate literals #[45]): ∀ (a a_1 a_2 : Iota), % 4.22/4.37 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False)) % 4.22/4.37 Clause #47 (by forward demodulation #[38, 20]): ∀ (a a_1 a_2 a_3 : Iota), % 4.22/4.37 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.22/4.37 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.22/4.37 (Or (Eq False True) % 4.22/4.37 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 4.22/4.37 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))))) % 4.22/4.37 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 4.22/4.37 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.22/4.37 (Or (Eq (xsd_string (skS.0 2 a_1)) False) % 4.22/4.37 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 4.22/4.37 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)))) % 4.22/4.37 Clause #49 (by superposition #[48, 19]): ∀ (a a_1 a_2 : Iota), % 4.22/4.37 Or (Eq (xsd_string (skS.0 2 a)) False) % 4.22/4.37 (Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.22/4.37 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.22/4.37 (Or (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq False True)))) % 4.22/4.37 Clause #50 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 4.22/4.37 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.22/4.37 (Or (Eq (Not (cowlNothing (skS.0 1 a))) False) % 4.22/4.37 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.22/4.37 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) True) % 4.22/4.37 (Eq (Iff (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False)))) % 4.22/4.37 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), % 4.22/4.37 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.22/4.37 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.22/4.37 (Or (Eq (Not (xsd_integer (skS.0 2 a_1))) True) % 4.22/4.37 (Or (Eq (Iff (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False) % 4.22/4.37 (Eq (cowlNothing (skS.0 1 a)) True)))) % 4.22/4.37 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 4.22/4.37 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.22/4.37 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.24/4.40 (Or (Eq (Iff (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3))) False) % 4.24/4.40 (Or (Eq (cowlNothing (skS.0 1 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) False)))) % 4.24/4.40 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.40 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.24/4.40 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.24/4.40 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.24/4.40 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) % 4.24/4.40 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))))) % 4.24/4.40 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.40 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.24/4.40 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.24/4.40 (Or (Eq (cowlNothing (skS.0 1 a)) True) % 4.24/4.40 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 4.24/4.40 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))))) % 4.24/4.40 Clause #55 (by forward demodulation #[53, 20]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.40 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.24/4.40 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.24/4.40 (Or (Eq False True) % 4.24/4.40 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) % 4.24/4.40 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))))) % 4.24/4.40 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.40 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.24/4.40 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.24/4.40 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False) % 4.24/4.40 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False)))) % 4.24/4.40 Clause #57 (by superposition #[56, 19]): ∀ (a a_1 a_2 : Iota), % 4.24/4.40 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.24/4.40 (Or (Eq (xsd_integer (skS.0 2 a)) False) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.24/4.40 (Or (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) (Eq False True)))) % 4.24/4.40 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 4.24/4.40 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.24/4.40 (Or (Eq (xsd_integer (skS.0 2 a)) False) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.24/4.40 (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False))) % 4.24/4.40 Clause #59 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 4.24/4.40 Or (Eq (xsd_string (skS.0 2 a)) False) % 4.24/4.40 (Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True))) % 4.24/4.40 Clause #60 (by superposition #[59, 14]): ∀ (a a_1 a_2 : Iota), % 4.24/4.40 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.24/4.40 (Or (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.24/4.40 (Or (Eq False True) (Eq (xsd_integer (skS.0 2 a)) True)))) % 4.24/4.40 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 4.24/4.40 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.24/4.40 (Or (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq (xsd_integer (skS.0 2 a)) True))) % 4.24/4.40 Clause #62 (by eliminate duplicate literals #[61]): ∀ (a a_1 a_2 : Iota), % 4.24/4.40 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True)) % 4.24/4.40 Clause #64 (by superposition #[62, 10]): ∀ (a a_1 a_2 : Iota), % 4.24/4.40 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.24/4.40 (Or (Eq True False) (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True))) % 4.24/4.40 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 4.24/4.40 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.24/4.40 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True)) % 4.24/4.40 Clause #66 (by eliminate duplicate literals #[65]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.24/4.40 Clause #68 (by superposition #[66, 46]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.40 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.27/4.42 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.27/4.42 (Or (Eq True False) (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False))) % 4.27/4.42 Clause #69 (by superposition #[66, 7]): ∀ (a a_1 a_2 : Iota), % 4.27/4.42 Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Eq True False) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True)) % 4.27/4.42 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.27/4.42 Clause #73 (by forward demodulation #[54, 20]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.42 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.27/4.42 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.27/4.42 (Or (Eq False True) % 4.27/4.42 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 4.27/4.42 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 4.27/4.42 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))))) % 4.27/4.42 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.42 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.27/4.42 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.27/4.42 (Or (Eq (xsd_integer (skS.0 2 a_1)) False) % 4.27/4.42 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 4.27/4.42 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)))) % 4.27/4.42 Clause #76 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.42 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.27/4.42 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) False)) % 4.27/4.42 Clause #77 (by superposition #[76, 70]): ∀ (a a_1 a_2 : Iota), % 4.27/4.42 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.27/4.42 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Or (Eq (xsd_integer (skS.0 2 a_2)) True) (Eq False True))) % 4.27/4.42 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), % 4.27/4.42 Or (Eq (xsd_integer (skS.0 2 a)) True) % 4.27/4.42 (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) True)) % 4.27/4.42 Clause #80 (by equality factoring #[78]): ∀ (a a_1 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Ne True True) (Eq (xsd_integer (skS.0 2 a_1)) True)) % 4.27/4.42 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), % 4.27/4.42 Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.27/4.42 Clause #83 (by clausification #[81]): ∀ (a a_1 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Eq (xsd_integer (skS.0 2 a_1)) True) (Eq True False)) % 4.27/4.42 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq (xsd_integer (skS.0 2 a_1)) True) % 4.27/4.42 Clause #86 (by equality factoring #[84]): ∀ (a : Iota), Or (Ne True True) (Eq (xsd_integer (skS.0 2 a)) True) % 4.27/4.42 Clause #87 (by clausification #[86]): ∀ (a : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Or (Eq True False) (Eq True False)) % 4.27/4.42 Clause #89 (by clausification #[87]): ∀ (a : Iota), Or (Eq (xsd_integer (skS.0 2 a)) True) (Eq True False) % 4.27/4.42 Clause #90 (by clausification #[89]): ∀ (a : Iota), Eq (xsd_integer (skS.0 2 a)) True % 4.27/4.42 Clause #91 (by backward demodulation #[90, 58]): ∀ (a a_1 a_2 : Iota), % 4.27/4.42 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.27/4.42 (Or (Eq True False) % 4.27/4.42 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.27/4.42 (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False))) % 4.27/4.42 Clause #92 (by backward demodulation #[90, 74]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.42 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.27/4.42 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.27/4.42 (Or (Eq True False) % 4.27/4.42 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) % 4.27/4.42 (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True)))) % 4.27/4.42 Clause #94 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), % 4.27/4.42 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.27/4.42 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False)) % 4.27/4.42 Clause #95 (by clausification #[92]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.42 Or (Eq (cowlThing (skS.0 1 a)) False) % 4.27/4.42 (Or (Eq (xsd_string (skS.0 2 a_1)) True) % 4.27/4.42 (Or (Eq (rhasLeader (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True) (Eq (rhasHead (skS.0 0 a_2) (skS.0 3 a_2 a_3)) True))) % 4.27/4.42 Clause #96 (by superposition #[95, 19]): ∀ (a a_1 a_2 : Iota), % 4.27/4.42 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.27/4.42 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.27/4.44 (Or (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq False True))) % 4.27/4.44 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 4.27/4.44 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.27/4.44 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True)) % 4.27/4.44 Clause #99 (by superposition #[97, 10]): ∀ (a a_1 a_2 : Iota), % 4.27/4.44 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.27/4.44 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.27/4.44 (Or (Eq True False) (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True))) % 4.27/4.44 Clause #101 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), % 4.27/4.44 Or (Eq (xsd_string (skS.0 2 a)) True) % 4.27/4.44 (Or (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True)) % 4.27/4.44 Clause #102 (by eliminate duplicate literals #[101]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (rhasLeader (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.27/4.44 Clause #105 (by superposition #[102, 7]): ∀ (a a_1 a_2 : Iota), % 4.27/4.44 Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq True False) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True)) % 4.27/4.44 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) True) % 4.27/4.44 Clause #107 (by superposition #[106, 15]): ∀ (a a_1 a_2 : Iota), % 4.27/4.44 Or (Eq (rhasHead (skS.0 0 a) (skS.0 3 a a_1)) True) (Or (Eq True False) (Eq (xsd_integer (skS.0 2 a_2)) False)) % 4.27/4.44 Clause #109 (by clausification #[107]): ∀ (a a_1 a_2 : Iota), Or (Eq (rhasHead (skS.0 0 a) (skS.0 3 a a_1)) True) (Eq (xsd_integer (skS.0 2 a_2)) False) % 4.27/4.44 Clause #110 (by superposition #[109, 90]): ∀ (a a_1 : Iota), Or (Eq (rhasHead (skS.0 0 a) (skS.0 3 a a_1)) True) (Eq False True) % 4.27/4.44 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), Eq (rhasHead (skS.0 0 a) (skS.0 3 a a_1)) True % 4.27/4.44 Clause #112 (by superposition #[111, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (rhasLeader (skS.0 0 a) (skS.0 3 a a_1)) True) % 4.27/4.44 Clause #114 (by clausification #[112]): ∀ (a a_1 : Iota), Eq (rhasLeader (skS.0 0 a) (skS.0 3 a a_1)) True % 4.27/4.44 Clause #115 (by backward demodulation #[114, 94]): ∀ (a a_1 a_2 : Iota), % 4.27/4.44 Or (Eq (xsd_string (skS.0 2 a)) True) (Or (Eq True False) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False)) % 4.27/4.44 Clause #117 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq (rhasHead (skS.0 0 a_1) (skS.0 3 a_1 a_2)) False) % 4.27/4.44 Clause #118 (by superposition #[117, 111]): ∀ (a : Iota), Or (Eq (xsd_string (skS.0 2 a)) True) (Eq False True) % 4.27/4.44 Clause #119 (by clausification #[118]): ∀ (a : Iota), Eq (xsd_string (skS.0 2 a)) True % 4.27/4.44 Clause #120 (by superposition #[119, 15]): ∀ (a : Iota), Or (Eq True False) (Eq (xsd_integer (skS.0 2 a)) False) % 4.27/4.44 Clause #121 (by clausification #[120]): ∀ (a : Iota), Eq (xsd_integer (skS.0 2 a)) False % 4.27/4.44 Clause #122 (by superposition #[121, 90]): Eq False True % 4.27/4.44 Clause #125 (by clausification #[122]): False % 4.27/4.44 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------