TSTP Solution File: SYO113^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO113^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n024.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 Sep 1 04:21:33 EDT 2023
% Result : Theorem 4.79s 4.99s
% Output : Proof 4.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO113^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 06:36:54 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.79/4.99 SZS status Theorem for theBenchmark.p
% 4.79/4.99 SZS output start Proof for theBenchmark.p
% 4.79/4.99 Clause #0 (by assumption #[]): Eq
% 4.79/4.99 (Not
% 4.79/4.99 (And
% 4.79/4.99 (And
% 4.79/4.99 (And (And (And (cEVEN c0) (∀ (Xn : Iota), cEVEN Xn → cEVEN (cS (cS Xn)))) (cODD (cS c0)))
% 4.79/4.99 (∀ (Xn : Iota), cODD Xn → cODD (cS (cS Xn))))
% 4.79/4.99 (And (And (cNUMBER c0) (cNUMBER (cS c0)))
% 4.79/4.99 (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))) →
% 4.79/4.99 ∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx))))
% 4.79/4.99 (∀ (Xn : Iota), Iff (cNUMBER Xn) (Or (cEVEN Xn) (cODD Xn))) →
% 4.79/4.99 ∀ (Xn : Iota), cNUMBER Xn))
% 4.79/4.99 True
% 4.79/4.99 Clause #1 (by clausification #[0]): Eq
% 4.79/4.99 (And
% 4.79/4.99 (And
% 4.79/4.99 (And (And (And (cEVEN c0) (∀ (Xn : Iota), cEVEN Xn → cEVEN (cS (cS Xn)))) (cODD (cS c0)))
% 4.79/4.99 (∀ (Xn : Iota), cODD Xn → cODD (cS (cS Xn))))
% 4.79/4.99 (And (And (cNUMBER c0) (cNUMBER (cS c0)))
% 4.79/4.99 (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))) →
% 4.79/4.99 ∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx))))
% 4.79/4.99 (∀ (Xn : Iota), Iff (cNUMBER Xn) (Or (cEVEN Xn) (cODD Xn))) →
% 4.79/4.99 ∀ (Xn : Iota), cNUMBER Xn)
% 4.79/4.99 False
% 4.79/4.99 Clause #2 (by clausification #[1]): Eq
% 4.79/4.99 (And
% 4.79/4.99 (And
% 4.79/4.99 (And (And (And (cEVEN c0) (∀ (Xn : Iota), cEVEN Xn → cEVEN (cS (cS Xn)))) (cODD (cS c0)))
% 4.79/4.99 (∀ (Xn : Iota), cODD Xn → cODD (cS (cS Xn))))
% 4.79/4.99 (And (And (cNUMBER c0) (cNUMBER (cS c0)))
% 4.79/4.99 (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))) →
% 4.79/4.99 ∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx))))
% 4.79/4.99 (∀ (Xn : Iota), Iff (cNUMBER Xn) (Or (cEVEN Xn) (cODD Xn))))
% 4.79/4.99 True
% 4.79/4.99 Clause #3 (by clausification #[1]): Eq (∀ (Xn : Iota), cNUMBER Xn) False
% 4.79/4.99 Clause #4 (by clausification #[2]): Eq (∀ (Xn : Iota), Iff (cNUMBER Xn) (Or (cEVEN Xn) (cODD Xn))) True
% 4.79/4.99 Clause #5 (by clausification #[2]): Eq
% 4.79/4.99 (And
% 4.79/4.99 (And (And (And (cEVEN c0) (∀ (Xn : Iota), cEVEN Xn → cEVEN (cS (cS Xn)))) (cODD (cS c0)))
% 4.79/4.99 (∀ (Xn : Iota), cODD Xn → cODD (cS (cS Xn))))
% 4.79/4.99 (And (And (cNUMBER c0) (cNUMBER (cS c0)))
% 4.79/4.99 (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))) →
% 4.79/4.99 ∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx))))
% 4.79/4.99 True
% 4.79/4.99 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (Iff (cNUMBER a) (Or (cEVEN a) (cODD a))) True
% 4.79/4.99 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (cNUMBER a) True) (Eq (Or (cEVEN a) (cODD a)) False)
% 4.79/4.99 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq (cNUMBER a) False) (Eq (Or (cEVEN a) (cODD a)) True)
% 4.79/4.99 Clause #9 (by clausification #[7]): ∀ (a : Iota), Or (Eq (cNUMBER a) True) (Eq (cODD a) False)
% 4.79/4.99 Clause #10 (by clausification #[7]): ∀ (a : Iota), Or (Eq (cNUMBER a) True) (Eq (cEVEN a) False)
% 4.79/4.99 Clause #11 (by clausification #[3]): ∀ (a : Iota), Eq (Not (cNUMBER (skS.0 0 a))) True
% 4.79/4.99 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (cNUMBER (skS.0 0 a)) False
% 4.79/4.99 Clause #13 (by clausification #[8]): ∀ (a : Iota), Or (Eq (cNUMBER a) False) (Or (Eq (cEVEN a) True) (Eq (cODD a) True))
% 4.79/4.99 Clause #14 (by clausification #[5]): Eq
% 4.79/4.99 (And (And (cNUMBER c0) (cNUMBER (cS c0)))
% 4.79/4.99 (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))) →
% 4.79/4.99 ∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)))
% 4.79/4.99 True
% 4.79/4.99 Clause #15 (by clausification #[5]): Eq
% 4.79/4.99 (And (And (And (cEVEN c0) (∀ (Xn : Iota), cEVEN Xn → cEVEN (cS (cS Xn)))) (cODD (cS c0)))
% 4.79/4.99 (∀ (Xn : Iota), cODD Xn → cODD (cS (cS Xn))))
% 4.79/4.99 True
% 4.79/4.99 Clause #16 (by clausification #[14]): Or
% 4.79/4.99 (Eq
% 4.79/4.99 (And (And (cNUMBER c0) (cNUMBER (cS c0)))
% 4.79/4.99 (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))))
% 4.79/4.99 False)
% 4.79/4.99 (Eq (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx))) True)
% 4.79/4.99 Clause #17 (by clausification #[16]): Or (Eq (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx))) True)
% 4.79/4.99 (Or (Eq (And (cNUMBER c0) (cNUMBER (cS c0))) False)
% 4.79/4.99 (Eq (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))) False))
% 4.85/5.02 Clause #18 (by clausification #[17]): ∀ (a : Iota),
% 4.85/5.02 Or (Eq (And (cNUMBER c0) (cNUMBER (cS c0))) False)
% 4.85/5.02 (Or (Eq (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))) False)
% 4.85/5.02 (Eq (And (cNUMBER a) (cNUMBER (cS a))) True))
% 4.85/5.02 Clause #19 (by clausification #[18]): ∀ (a : Iota),
% 4.85/5.02 Or (Eq (∀ (Xx : Iota), And (cNUMBER Xx) (cNUMBER (cS Xx)) → And (cNUMBER (cS Xx)) (cNUMBER (cS (cS Xx)))) False)
% 4.85/5.02 (Or (Eq (And (cNUMBER a) (cNUMBER (cS a))) True) (Or (Eq (cNUMBER c0) False) (Eq (cNUMBER (cS c0)) False)))
% 4.85/5.02 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (And (cNUMBER a) (cNUMBER (cS a))) True)
% 4.85/5.02 (Or (Eq (cNUMBER c0) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.02 (Eq
% 4.85/5.02 (Not
% 4.85/5.02 (And (cNUMBER (skS.0 1 a_1)) (cNUMBER (cS (skS.0 1 a_1))) →
% 4.85/5.02 And (cNUMBER (cS (skS.0 1 a_1))) (cNUMBER (cS (cS (skS.0 1 a_1))))))
% 4.85/5.02 True)))
% 4.85/5.02 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (cNUMBER c0) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.02 (Or
% 4.85/5.02 (Eq
% 4.85/5.02 (Not
% 4.85/5.02 (And (cNUMBER (skS.0 1 a)) (cNUMBER (cS (skS.0 1 a))) →
% 4.85/5.02 And (cNUMBER (cS (skS.0 1 a))) (cNUMBER (cS (cS (skS.0 1 a))))))
% 4.85/5.02 True)
% 4.85/5.02 (Eq (cNUMBER (cS a_1)) True)))
% 4.85/5.02 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (cNUMBER c0) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.02 (Or
% 4.85/5.02 (Eq
% 4.85/5.02 (Not
% 4.85/5.02 (And (cNUMBER (skS.0 1 a)) (cNUMBER (cS (skS.0 1 a))) →
% 4.85/5.02 And (cNUMBER (cS (skS.0 1 a))) (cNUMBER (cS (cS (skS.0 1 a))))))
% 4.85/5.02 True)
% 4.85/5.02 (Eq (cNUMBER a_1) True)))
% 4.85/5.02 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (cNUMBER c0) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS a)) True)
% 4.85/5.02 (Eq
% 4.85/5.02 (And (cNUMBER (skS.0 1 a_1)) (cNUMBER (cS (skS.0 1 a_1))) →
% 4.85/5.02 And (cNUMBER (cS (skS.0 1 a_1))) (cNUMBER (cS (cS (skS.0 1 a_1)))))
% 4.85/5.02 False)))
% 4.85/5.02 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (cNUMBER c0) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS a)) True) (Eq (And (cNUMBER (skS.0 1 a_1)) (cNUMBER (cS (skS.0 1 a_1)))) True)))
% 4.85/5.02 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (cNUMBER c0) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS c0)) False) (Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (cS (skS.0 1 a_1))) True)))
% 4.85/5.02 Clause #27 (by clausification #[24]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (cNUMBER c0) False)
% 4.85/5.02 (Or (Eq (cNUMBER (cS c0)) False) (Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (skS.0 1 a_1)) True)))
% 4.85/5.02 Clause #28 (by clausification #[15]): Eq (∀ (Xn : Iota), cODD Xn → cODD (cS (cS Xn))) True
% 4.85/5.02 Clause #29 (by clausification #[15]): Eq (And (And (cEVEN c0) (∀ (Xn : Iota), cEVEN Xn → cEVEN (cS (cS Xn)))) (cODD (cS c0))) True
% 4.85/5.02 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (cODD a → cODD (cS (cS a))) True
% 4.85/5.02 Clause #31 (by clausification #[30]): ∀ (a : Iota), Or (Eq (cODD a) False) (Eq (cODD (cS (cS a))) True)
% 4.85/5.02 Clause #32 (by clausification #[29]): Eq (cODD (cS c0)) True
% 4.85/5.02 Clause #33 (by clausification #[29]): Eq (And (cEVEN c0) (∀ (Xn : Iota), cEVEN Xn → cEVEN (cS (cS Xn)))) True
% 4.85/5.02 Clause #34 (by superposition #[32, 9]): Or (Eq (cNUMBER (cS c0)) True) (Eq True False)
% 4.85/5.02 Clause #36 (by clausification #[34]): Eq (cNUMBER (cS c0)) True
% 4.85/5.02 Clause #37 (by backward demodulation #[36, 26]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (cNUMBER c0) False) (Or (Eq True False) (Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (cS (skS.0 1 a_1))) True)))
% 4.85/5.02 Clause #44 (by clausification #[33]): Eq (∀ (Xn : Iota), cEVEN Xn → cEVEN (cS (cS Xn))) True
% 4.85/5.02 Clause #45 (by clausification #[33]): Eq (cEVEN c0) True
% 4.85/5.02 Clause #46 (by clausification #[44]): ∀ (a : Iota), Eq (cEVEN a → cEVEN (cS (cS a))) True
% 4.85/5.02 Clause #47 (by clausification #[46]): ∀ (a : Iota), Or (Eq (cEVEN a) False) (Eq (cEVEN (cS (cS a))) True)
% 4.85/5.02 Clause #48 (by clausification #[22]): ∀ (a a_1 : Iota),
% 4.85/5.02 Or (Eq (cNUMBER c0) False)
% 4.85/5.04 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.04 (Or (Eq (cNUMBER a) True)
% 4.85/5.04 (Eq
% 4.85/5.04 (And (cNUMBER (skS.0 1 a_1)) (cNUMBER (cS (skS.0 1 a_1))) →
% 4.85/5.04 And (cNUMBER (cS (skS.0 1 a_1))) (cNUMBER (cS (cS (skS.0 1 a_1)))))
% 4.85/5.04 False)))
% 4.85/5.04 Clause #50 (by clausification #[48]): ∀ (a a_1 : Iota),
% 4.85/5.04 Or (Eq (cNUMBER c0) False)
% 4.85/5.04 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.04 (Or (Eq (cNUMBER a) True) (Eq (And (cNUMBER (cS (skS.0 1 a_1))) (cNUMBER (cS (cS (skS.0 1 a_1))))) False)))
% 4.85/5.04 Clause #55 (by superposition #[45, 10]): Or (Eq (cNUMBER c0) True) (Eq True False)
% 4.85/5.04 Clause #57 (by clausification #[55]): Eq (cNUMBER c0) True
% 4.85/5.04 Clause #83 (by forward demodulation #[27, 57]): ∀ (a a_1 : Iota),
% 4.85/5.04 Or (Eq True False) (Or (Eq (cNUMBER (cS c0)) False) (Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (skS.0 1 a_1)) True)))
% 4.85/5.04 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (cNUMBER (cS c0)) False) (Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (skS.0 1 a_1)) True))
% 4.85/5.04 Clause #85 (by forward demodulation #[84, 36]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (skS.0 1 a_1)) True))
% 4.85/5.04 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (skS.0 1 a_1)) True)
% 4.85/5.04 Clause #102 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (cNUMBER c0) False) (Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (cS (skS.0 1 a_1))) True))
% 4.85/5.04 Clause #103 (by forward demodulation #[102, 57]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (cS (skS.0 1 a_1))) True))
% 4.85/5.04 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota), Or (Eq (cNUMBER (cS a)) True) (Eq (cNUMBER (cS (skS.0 1 a_1))) True)
% 4.85/5.04 Clause #109 (by equality factoring #[104]): ∀ (a : Iota), Or (Ne True True) (Eq (cNUMBER (cS (skS.0 1 a))) True)
% 4.85/5.04 Clause #110 (by clausification #[109]): ∀ (a : Iota), Or (Eq (cNUMBER (cS (skS.0 1 a))) True) (Or (Eq True False) (Eq True False))
% 4.85/5.04 Clause #112 (by clausification #[110]): ∀ (a : Iota), Or (Eq (cNUMBER (cS (skS.0 1 a))) True) (Eq True False)
% 4.85/5.04 Clause #113 (by clausification #[112]): ∀ (a : Iota), Eq (cNUMBER (cS (skS.0 1 a))) True
% 4.85/5.04 Clause #135 (by clausification #[50]): ∀ (a a_1 : Iota),
% 4.85/5.04 Or (Eq (cNUMBER c0) False)
% 4.85/5.04 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.04 (Or (Eq (cNUMBER a) True)
% 4.85/5.04 (Or (Eq (cNUMBER (cS (skS.0 1 a_1))) False) (Eq (cNUMBER (cS (cS (skS.0 1 a_1)))) False))))
% 4.85/5.04 Clause #136 (by forward demodulation #[135, 57]): ∀ (a a_1 : Iota),
% 4.85/5.04 Or (Eq True False)
% 4.85/5.04 (Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.04 (Or (Eq (cNUMBER a) True)
% 4.85/5.04 (Or (Eq (cNUMBER (cS (skS.0 1 a_1))) False) (Eq (cNUMBER (cS (cS (skS.0 1 a_1)))) False))))
% 4.85/5.04 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota),
% 4.85/5.04 Or (Eq (cNUMBER (cS c0)) False)
% 4.85/5.04 (Or (Eq (cNUMBER a) True) (Or (Eq (cNUMBER (cS (skS.0 1 a_1))) False) (Eq (cNUMBER (cS (cS (skS.0 1 a_1)))) False)))
% 4.85/5.04 Clause #138 (by forward demodulation #[137, 36]): ∀ (a a_1 : Iota),
% 4.85/5.04 Or (Eq True False)
% 4.85/5.04 (Or (Eq (cNUMBER a) True) (Or (Eq (cNUMBER (cS (skS.0 1 a_1))) False) (Eq (cNUMBER (cS (cS (skS.0 1 a_1)))) False)))
% 4.85/5.04 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota),
% 4.85/5.04 Or (Eq (cNUMBER a) True) (Or (Eq (cNUMBER (cS (skS.0 1 a_1))) False) (Eq (cNUMBER (cS (cS (skS.0 1 a_1)))) False))
% 4.85/5.04 Clause #140 (by forward demodulation #[139, 113]): ∀ (a a_1 : Iota), Or (Eq (cNUMBER a) True) (Or (Eq True False) (Eq (cNUMBER (cS (cS (skS.0 1 a_1)))) False))
% 4.85/5.04 Clause #141 (by clausification #[140]): ∀ (a a_1 : Iota), Or (Eq (cNUMBER a) True) (Eq (cNUMBER (cS (cS (skS.0 1 a_1)))) False)
% 4.85/5.04 Clause #142 (by superposition #[141, 86]): ∀ (a a_1 : Iota), Or (Eq (cNUMBER a) True) (Or (Eq False True) (Eq (cNUMBER (skS.0 1 a_1)) True))
% 4.85/5.04 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota), Or (Eq (cNUMBER a) True) (Eq (cNUMBER (skS.0 1 a_1)) True)
% 4.85/5.04 Clause #144 (by superposition #[143, 12]): ∀ (a : Iota), Or (Eq (cNUMBER (skS.0 1 a)) True) (Eq True False)
% 4.85/5.04 Clause #151 (by clausification #[144]): ∀ (a : Iota), Eq (cNUMBER (skS.0 1 a)) True
% 4.85/5.04 Clause #152 (by superposition #[151, 13]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (cEVEN (skS.0 1 a)) True) (Eq (cODD (skS.0 1 a)) True))
% 4.90/5.06 Clause #170 (by clausification #[152]): ∀ (a : Iota), Or (Eq (cEVEN (skS.0 1 a)) True) (Eq (cODD (skS.0 1 a)) True)
% 4.90/5.06 Clause #172 (by superposition #[170, 31]): ∀ (a : Iota), Or (Eq (cEVEN (skS.0 1 a)) True) (Or (Eq True False) (Eq (cODD (cS (cS (skS.0 1 a)))) True))
% 4.90/5.06 Clause #202 (by clausification #[172]): ∀ (a : Iota), Or (Eq (cEVEN (skS.0 1 a)) True) (Eq (cODD (cS (cS (skS.0 1 a)))) True)
% 4.90/5.06 Clause #203 (by superposition #[202, 9]): ∀ (a : Iota), Or (Eq (cEVEN (skS.0 1 a)) True) (Or (Eq (cNUMBER (cS (cS (skS.0 1 a)))) True) (Eq True False))
% 4.90/5.06 Clause #206 (by clausification #[203]): ∀ (a : Iota), Or (Eq (cEVEN (skS.0 1 a)) True) (Eq (cNUMBER (cS (cS (skS.0 1 a)))) True)
% 4.90/5.06 Clause #207 (by superposition #[206, 141]): ∀ (a a_1 : Iota), Or (Eq (cEVEN (skS.0 1 a)) True) (Or (Eq (cNUMBER a_1) True) (Eq True False))
% 4.90/5.06 Clause #209 (by clausification #[207]): ∀ (a a_1 : Iota), Or (Eq (cEVEN (skS.0 1 a)) True) (Eq (cNUMBER a_1) True)
% 4.90/5.06 Clause #212 (by superposition #[209, 12]): ∀ (a : Iota), Or (Eq (cEVEN (skS.0 1 a)) True) (Eq True False)
% 4.90/5.06 Clause #214 (by clausification #[212]): ∀ (a : Iota), Eq (cEVEN (skS.0 1 a)) True
% 4.90/5.06 Clause #217 (by superposition #[214, 47]): ∀ (a : Iota), Or (Eq True False) (Eq (cEVEN (cS (cS (skS.0 1 a)))) True)
% 4.90/5.06 Clause #218 (by clausification #[217]): ∀ (a : Iota), Eq (cEVEN (cS (cS (skS.0 1 a)))) True
% 4.90/5.06 Clause #219 (by superposition #[218, 10]): ∀ (a : Iota), Or (Eq (cNUMBER (cS (cS (skS.0 1 a)))) True) (Eq True False)
% 4.90/5.06 Clause #222 (by clausification #[219]): ∀ (a : Iota), Eq (cNUMBER (cS (cS (skS.0 1 a)))) True
% 4.90/5.06 Clause #223 (by superposition #[222, 141]): ∀ (a : Iota), Or (Eq (cNUMBER a) True) (Eq True False)
% 4.90/5.06 Clause #225 (by clausification #[223]): ∀ (a : Iota), Eq (cNUMBER a) True
% 4.90/5.06 Clause #229 (by superposition #[225, 12]): Eq True False
% 4.90/5.06 Clause #230 (by clausification #[229]): False
% 4.90/5.06 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------