TSTP Solution File: SYN059^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN059^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n018.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 02:10:23 EDT 2023
% Result : Theorem 12.06s 12.26s
% Output : Proof 12.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN059^5 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n018.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 17:34:15 EDT 2023
% 0.14/0.35 % CPUTime :
% 12.06/12.26 SZS status Theorem for theBenchmark.p
% 12.06/12.26 SZS output start Proof for theBenchmark.p
% 12.06/12.26 Clause #0 (by assumption #[]): Eq
% 12.06/12.26 (Not
% 12.06/12.26 (And (Exists fun Xx => cF Xx) (Exists fun Xx => cG Xx) →
% 12.06/12.26 And
% 12.06/12.26 (And (∀ (Xx : Iota), cF Xx → cH Xx) (∀ (Xx : Iota), cG Xx → cJ Xx) →
% 12.06/12.26 ∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy))
% 12.06/12.26 ((∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) → ∀ (Xx : Iota), cG Xx → cJ Xx)))
% 12.06/12.26 True
% 12.06/12.26 Clause #1 (by betaEtaReduce #[0]): Eq
% 12.06/12.26 (Not
% 12.06/12.26 (And (Exists cF) (Exists cG) →
% 12.06/12.26 And
% 12.06/12.26 (And (∀ (Xx : Iota), cF Xx → cH Xx) (∀ (Xx : Iota), cG Xx → cJ Xx) →
% 12.06/12.26 ∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy))
% 12.06/12.26 ((∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) → ∀ (Xx : Iota), cG Xx → cJ Xx)))
% 12.06/12.26 True
% 12.06/12.26 Clause #2 (by clausification #[1]): Eq
% 12.06/12.26 (And (Exists cF) (Exists cG) →
% 12.06/12.26 And
% 12.06/12.26 (And (∀ (Xx : Iota), cF Xx → cH Xx) (∀ (Xx : Iota), cG Xx → cJ Xx) →
% 12.06/12.26 ∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy))
% 12.06/12.26 ((∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) → ∀ (Xx : Iota), cG Xx → cJ Xx))
% 12.06/12.26 False
% 12.06/12.26 Clause #3 (by clausification #[2]): Eq (And (Exists cF) (Exists cG)) True
% 12.06/12.26 Clause #4 (by clausification #[2]): Eq
% 12.06/12.26 (And
% 12.06/12.26 (And (∀ (Xx : Iota), cF Xx → cH Xx) (∀ (Xx : Iota), cG Xx → cJ Xx) →
% 12.06/12.26 ∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy))
% 12.06/12.26 ((∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) → ∀ (Xx : Iota), cG Xx → cJ Xx))
% 12.06/12.26 False
% 12.06/12.26 Clause #5 (by clausification #[3]): Eq (Exists cG) True
% 12.06/12.26 Clause #6 (by clausification #[3]): Eq (Exists cF) True
% 12.06/12.26 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (cG (skS.0 0 a)) True
% 12.06/12.26 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (cF (skS.0 1 a)) True
% 12.06/12.26 Clause #9 (by clausification #[4]): Or
% 12.06/12.26 (Eq
% 12.06/12.26 (And (∀ (Xx : Iota), cF Xx → cH Xx) (∀ (Xx : Iota), cG Xx → cJ Xx) →
% 12.06/12.26 ∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy))
% 12.06/12.26 False)
% 12.06/12.26 (Eq ((∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) → ∀ (Xx : Iota), cG Xx → cJ Xx) False)
% 12.06/12.26 Clause #10 (by clausification #[9]): Or (Eq ((∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) → ∀ (Xx : Iota), cG Xx → cJ Xx) False)
% 12.06/12.26 (Eq (And (∀ (Xx : Iota), cF Xx → cH Xx) (∀ (Xx : Iota), cG Xx → cJ Xx)) True)
% 12.06/12.26 Clause #11 (by clausification #[9]): Or (Eq ((∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) → ∀ (Xx : Iota), cG Xx → cJ Xx) False)
% 12.06/12.26 (Eq (∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) False)
% 12.06/12.26 Clause #12 (by clausification #[10]): Or (Eq (And (∀ (Xx : Iota), cF Xx → cH Xx) (∀ (Xx : Iota), cG Xx → cJ Xx)) True)
% 12.06/12.26 (Eq (∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) True)
% 12.06/12.26 Clause #14 (by clausification #[12]): Or (Eq (∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) True) (Eq (∀ (Xx : Iota), cG Xx → cJ Xx) True)
% 12.06/12.26 Clause #15 (by clausification #[12]): Or (Eq (∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) True) (Eq (∀ (Xx : Iota), cF Xx → cH Xx) True)
% 12.06/12.26 Clause #16 (by clausification #[14]): ∀ (a : Iota),
% 12.06/12.26 Or (Eq (∀ (Xx : Iota), cG Xx → cJ Xx) True) (Eq (∀ (Xy : Iota), And (cF a) (cG Xy) → And (cH a) (cJ Xy)) True)
% 12.06/12.26 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xy : Iota), And (cF a) (cG Xy) → And (cH a) (cJ Xy)) True) (Eq (cG a_1 → cJ a_1) True)
% 12.06/12.26 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG a → cJ a) True) (Eq (And (cF a_1) (cG a_2) → And (cH a_1) (cJ a_2)) True)
% 12.06/12.26 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.26 Or (Eq (And (cF a) (cG a_1) → And (cH a) (cJ a_1)) True) (Or (Eq (cG a_2) False) (Eq (cJ a_2) True))
% 12.06/12.26 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.26 Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Or (Eq (And (cF a_1) (cG a_2)) False) (Eq (And (cH a_1) (cJ a_2)) True)))
% 12.06/12.26 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.29 Or (Eq (cG a) False)
% 12.06/12.29 (Or (Eq (cJ a) True) (Or (Eq (And (cH a_1) (cJ a_2)) True) (Or (Eq (cF a_1) False) (Eq (cG a_2) False))))
% 12.06/12.29 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.29 Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Or (Eq (cF a_1) False) (Or (Eq (cG a_2) False) (Eq (cJ a_2) True))))
% 12.06/12.29 Clause #25 (by clausification #[15]): ∀ (a : Iota),
% 12.06/12.29 Or (Eq (∀ (Xx : Iota), cF Xx → cH Xx) True) (Eq (∀ (Xy : Iota), And (cF a) (cG Xy) → And (cH a) (cJ Xy)) True)
% 12.06/12.29 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xy : Iota), And (cF a) (cG Xy) → And (cH a) (cJ Xy)) True) (Eq (cF a_1 → cH a_1) True)
% 12.06/12.29 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a → cH a) True) (Eq (And (cF a_1) (cG a_2) → And (cH a_1) (cJ a_2)) True)
% 12.06/12.29 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.29 Or (Eq (And (cF a) (cG a_1) → And (cH a) (cJ a_1)) True) (Or (Eq (cF a_2) False) (Eq (cH a_2) True))
% 12.06/12.29 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.29 Or (Eq (cF a) False) (Or (Eq (cH a) True) (Or (Eq (And (cF a_1) (cG a_2)) False) (Eq (And (cH a_1) (cJ a_2)) True)))
% 12.06/12.29 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.29 Or (Eq (cF a) False)
% 12.06/12.29 (Or (Eq (cH a) True) (Or (Eq (And (cH a_1) (cJ a_2)) True) (Or (Eq (cF a_1) False) (Eq (cG a_2) False))))
% 12.06/12.29 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.29 Or (Eq (cF a) False) (Or (Eq (cH a) True) (Or (Eq (cF a_1) False) (Or (Eq (cG a_2) False) (Eq (cH a_1) True))))
% 12.06/12.29 Clause #43 (by clausification #[11]): Or (Eq (∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) False)
% 12.06/12.29 (Eq (∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) True)
% 12.06/12.29 Clause #44 (by clausification #[11]): Or (Eq (∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) False) (Eq (∀ (Xx : Iota), cG Xx → cJ Xx) False)
% 12.06/12.29 Clause #45 (by clausification #[43]): ∀ (a : Iota),
% 12.06/12.29 Or (Eq (∀ (Xx Xy : Iota), And (cF Xx) (cG Xy) → And (cH Xx) (cJ Xy)) True)
% 12.06/12.29 (Eq (Not (∀ (Xy : Iota), And (cF (skS.0 3 a)) (cG Xy) → And (cH (skS.0 3 a)) (cJ Xy))) True)
% 12.06/12.29 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota),
% 12.06/12.29 Or (Eq (Not (∀ (Xy : Iota), And (cF (skS.0 3 a)) (cG Xy) → And (cH (skS.0 3 a)) (cJ Xy))) True)
% 12.06/12.29 (Eq (∀ (Xy : Iota), And (cF a_1) (cG Xy) → And (cH a_1) (cJ Xy)) True)
% 12.06/12.29 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota),
% 12.06/12.29 Or (Eq (∀ (Xy : Iota), And (cF a) (cG Xy) → And (cH a) (cJ Xy)) True)
% 12.06/12.29 (Eq (∀ (Xy : Iota), And (cF (skS.0 3 a_1)) (cG Xy) → And (cH (skS.0 3 a_1)) (cJ Xy)) False)
% 12.06/12.29 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota),
% 12.06/12.29 Or (Eq (∀ (Xy : Iota), And (cF (skS.0 3 a)) (cG Xy) → And (cH (skS.0 3 a)) (cJ Xy)) False)
% 12.06/12.29 (Eq (And (cF a_1) (cG a_2) → And (cH a_1) (cJ a_2)) True)
% 12.06/12.29 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.06/12.29 Or (Eq (And (cF a) (cG a_1) → And (cH a) (cJ a_1)) True)
% 12.06/12.29 (Eq (Not (And (cF (skS.0 3 a_2)) (cG (skS.0 4 a_2 a_3)) → And (cH (skS.0 3 a_2)) (cJ (skS.0 4 a_2 a_3)))) True)
% 12.06/12.29 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.06/12.29 Or (Eq (Not (And (cF (skS.0 3 a)) (cG (skS.0 4 a a_1)) → And (cH (skS.0 3 a)) (cJ (skS.0 4 a a_1)))) True)
% 12.06/12.29 (Or (Eq (And (cF a_2) (cG a_3)) False) (Eq (And (cH a_2) (cJ a_3)) True))
% 12.06/12.29 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.06/12.29 Or (Eq (And (cF a) (cG a_1)) False)
% 12.06/12.29 (Or (Eq (And (cH a) (cJ a_1)) True)
% 12.06/12.29 (Eq (And (cF (skS.0 3 a_2)) (cG (skS.0 4 a_2 a_3)) → And (cH (skS.0 3 a_2)) (cJ (skS.0 4 a_2 a_3))) False))
% 12.06/12.29 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.06/12.29 Or (Eq (And (cH a) (cJ a_1)) True)
% 12.06/12.29 (Or (Eq (And (cF (skS.0 3 a_2)) (cG (skS.0 4 a_2 a_3)) → And (cH (skS.0 3 a_2)) (cJ (skS.0 4 a_2 a_3))) False)
% 12.06/12.29 (Or (Eq (cF a) False) (Eq (cG a_1) False)))
% 12.06/12.29 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.06/12.29 Or (Eq (And (cF (skS.0 3 a)) (cG (skS.0 4 a a_1)) → And (cH (skS.0 3 a)) (cJ (skS.0 4 a a_1))) False)
% 12.06/12.29 (Or (Eq (cF a_2) False) (Or (Eq (cG a_3) False) (Eq (cJ a_3) True)))
% 12.06/12.29 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq (And (cF (skS.0 3 a)) (cG (skS.0 4 a a_1)) → And (cH (skS.0 3 a)) (cJ (skS.0 4 a a_1))) False)
% 12.15/12.31 (Or (Eq (cF a_2) False) (Or (Eq (cG a_3) False) (Eq (cH a_2) True)))
% 12.15/12.31 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq (cF a) False)
% 12.15/12.31 (Or (Eq (cG a_1) False) (Or (Eq (cJ a_1) True) (Eq (And (cF (skS.0 3 a_2)) (cG (skS.0 4 a_2 a_3))) True)))
% 12.15/12.31 Clause #56 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq (cF a) False)
% 12.15/12.31 (Or (Eq (cG a_1) False) (Or (Eq (cJ a_1) True) (Eq (And (cH (skS.0 3 a_2)) (cJ (skS.0 4 a_2 a_3))) False)))
% 12.15/12.31 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq (cF a) False) (Or (Eq (cG a_1) False) (Or (Eq (cJ a_1) True) (Eq (cG (skS.0 4 a_2 a_3)) True)))
% 12.15/12.31 Clause #58 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a) False) (Or (Eq (cG a_1) False) (Or (Eq (cJ a_1) True) (Eq (cF (skS.0 3 a_2)) True)))
% 12.15/12.31 Clause #59 (by superposition #[57, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Or (Eq (cG (skS.0 4 a_1 a_2)) True) (Eq False True)))
% 12.15/12.31 Clause #68 (by clausification #[44]): ∀ (a : Iota),
% 12.15/12.31 Or (Eq (∀ (Xx : Iota), cG Xx → cJ Xx) False)
% 12.15/12.31 (Eq (Not (∀ (Xy : Iota), And (cF (skS.0 6 a)) (cG Xy) → And (cH (skS.0 6 a)) (cJ Xy))) True)
% 12.15/12.31 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota),
% 12.15/12.31 Or (Eq (Not (∀ (Xy : Iota), And (cF (skS.0 6 a)) (cG Xy) → And (cH (skS.0 6 a)) (cJ Xy))) True)
% 12.15/12.31 (Eq (Not (cG (skS.0 7 a_1) → cJ (skS.0 7 a_1))) True)
% 12.15/12.31 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota),
% 12.15/12.31 Or (Eq (Not (cG (skS.0 7 a) → cJ (skS.0 7 a))) True)
% 12.15/12.31 (Eq (∀ (Xy : Iota), And (cF (skS.0 6 a_1)) (cG Xy) → And (cH (skS.0 6 a_1)) (cJ Xy)) False)
% 12.15/12.31 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota),
% 12.15/12.31 Or (Eq (∀ (Xy : Iota), And (cF (skS.0 6 a)) (cG Xy) → And (cH (skS.0 6 a)) (cJ Xy)) False)
% 12.15/12.31 (Eq (cG (skS.0 7 a_1) → cJ (skS.0 7 a_1)) False)
% 12.15/12.31 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (cG (skS.0 7 a) → cJ (skS.0 7 a)) False)
% 12.15/12.31 (Eq (Not (And (cF (skS.0 6 a_1)) (cG (skS.0 8 a_1 a_2)) → And (cH (skS.0 6 a_1)) (cJ (skS.0 8 a_1 a_2)))) True)
% 12.15/12.31 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (Not (And (cF (skS.0 6 a)) (cG (skS.0 8 a a_1)) → And (cH (skS.0 6 a)) (cJ (skS.0 8 a a_1)))) True)
% 12.15/12.31 (Eq (cG (skS.0 7 a_2)) True)
% 12.15/12.31 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (Not (And (cF (skS.0 6 a)) (cG (skS.0 8 a a_1)) → And (cH (skS.0 6 a)) (cJ (skS.0 8 a a_1)))) True)
% 12.15/12.31 (Eq (cJ (skS.0 7 a_2)) False)
% 12.15/12.31 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (cG (skS.0 7 a)) True)
% 12.15/12.31 (Eq (And (cF (skS.0 6 a_1)) (cG (skS.0 8 a_1 a_2)) → And (cH (skS.0 6 a_1)) (cJ (skS.0 8 a_1 a_2))) False)
% 12.15/12.31 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 7 a)) True) (Eq (And (cF (skS.0 6 a_1)) (cG (skS.0 8 a_1 a_2))) True)
% 12.15/12.31 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 7 a)) True) (Eq (And (cH (skS.0 6 a_1)) (cJ (skS.0 8 a_1 a_2))) False)
% 12.15/12.31 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 7 a)) True) (Eq (cG (skS.0 8 a_1 a_2)) True)
% 12.15/12.31 Clause #79 (by clausification #[76]): ∀ (a a_1 : Iota), Or (Eq (cG (skS.0 7 a)) True) (Eq (cF (skS.0 6 a_1)) True)
% 12.15/12.31 Clause #80 (by superposition #[78, 22]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.15/12.31 Or (Eq (cG (skS.0 8 a a_1)) True)
% 12.15/12.31 (Or (Eq True False)
% 12.15/12.31 (Or (Eq (cJ (skS.0 7 a_2)) True) (Or (Eq (cF a_3) False) (Or (Eq (cG a_4) False) (Eq (cJ a_4) True)))))
% 12.15/12.31 Clause #100 (by superposition #[58, 8]): ∀ (a a_1 : Iota), Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Or (Eq (cF (skS.0 3 a_1)) True) (Eq False True)))
% 12.15/12.31 Clause #102 (by clausification #[100]): ∀ (a a_1 : Iota), Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Eq (cF (skS.0 3 a_1)) True))
% 12.15/12.31 Clause #106 (by superposition #[102, 79]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cF (skS.0 3 a_1)) True) (Or (Eq False True) (Eq (cF (skS.0 6 a_2)) True)))
% 12.15/12.31 Clause #107 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Eq (cG (skS.0 4 a_1 a_2)) True))
% 12.15/12.34 Clause #111 (by superposition #[107, 79]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.34 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cG (skS.0 4 a_1 a_2)) True) (Or (Eq False True) (Eq (cF (skS.0 6 a_3)) True)))
% 12.15/12.34 Clause #148 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.34 Or (Eq (cF a) False)
% 12.15/12.34 (Or (Eq (cG a_1) False) (Or (Eq (cH a) True) (Eq (And (cF (skS.0 3 a_2)) (cG (skS.0 4 a_2 a_3))) True)))
% 12.15/12.34 Clause #150 (by clausification #[148]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.34 Or (Eq (cF a) False) (Or (Eq (cG a_1) False) (Or (Eq (cH a) True) (Eq (cG (skS.0 4 a_2 a_3)) True)))
% 12.15/12.34 Clause #151 (by clausification #[148]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a) False) (Or (Eq (cG a_1) False) (Or (Eq (cH a) True) (Eq (cF (skS.0 3 a_2)) True)))
% 12.15/12.34 Clause #167 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.34 Or (Eq (cF a) False)
% 12.15/12.34 (Or (Eq (cG a_1) False)
% 12.15/12.34 (Or (Eq (cJ a_1) True) (Or (Eq (cH (skS.0 3 a_2)) False) (Eq (cJ (skS.0 4 a_2 a_3)) False))))
% 12.15/12.34 Clause #168 (by superposition #[167, 8]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.34 Or (Eq (cG a) False)
% 12.15/12.34 (Or (Eq (cJ a) True) (Or (Eq (cH (skS.0 3 a_1)) False) (Or (Eq (cJ (skS.0 4 a_1 a_2)) False) (Eq False True))))
% 12.15/12.34 Clause #178 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.34 Or (Eq (cJ (skS.0 7 a)) False)
% 12.15/12.34 (Eq (And (cF (skS.0 6 a_1)) (cG (skS.0 8 a_1 a_2)) → And (cH (skS.0 6 a_1)) (cJ (skS.0 8 a_1 a_2))) False)
% 12.15/12.34 Clause #179 (by clausification #[178]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) False) (Eq (And (cF (skS.0 6 a_1)) (cG (skS.0 8 a_1 a_2))) True)
% 12.15/12.34 Clause #180 (by clausification #[178]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) False) (Eq (And (cH (skS.0 6 a_1)) (cJ (skS.0 8 a_1 a_2))) False)
% 12.15/12.34 Clause #181 (by clausification #[179]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) False) (Eq (cG (skS.0 8 a_1 a_2)) True)
% 12.15/12.34 Clause #182 (by clausification #[179]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) False) (Eq (cF (skS.0 6 a_1)) True)
% 12.15/12.34 Clause #187 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 7 a)) True) (Or (Eq (cH (skS.0 6 a_1)) False) (Eq (cJ (skS.0 8 a_1 a_2)) False))
% 12.15/12.34 Clause #192 (by clausification #[180]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.34 Or (Eq (cJ (skS.0 7 a)) False) (Or (Eq (cH (skS.0 6 a_1)) False) (Eq (cJ (skS.0 8 a_1 a_2)) False))
% 12.15/12.34 Clause #193 (by clausification #[80]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.15/12.34 Or (Eq (cG (skS.0 8 a a_1)) True)
% 12.15/12.34 (Or (Eq (cJ (skS.0 7 a_2)) True) (Or (Eq (cF a_3) False) (Or (Eq (cG a_4) False) (Eq (cJ a_4) True))))
% 12.15/12.34 Clause #194 (by superposition #[193, 8]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.34 Or (Eq (cG (skS.0 8 a a_1)) True)
% 12.15/12.34 (Or (Eq (cJ (skS.0 7 a_2)) True) (Or (Eq (cG a_3) False) (Or (Eq (cJ a_3) True) (Eq False True))))
% 12.15/12.34 Clause #196 (by clausification #[194]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.34 Or (Eq (cG (skS.0 8 a a_1)) True) (Or (Eq (cJ (skS.0 7 a_2)) True) (Or (Eq (cG a_3) False) (Eq (cJ a_3) True)))
% 12.15/12.34 Clause #198 (by superposition #[196, 78]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.15/12.34 Or (Eq (cG (skS.0 8 a a_1)) True)
% 12.15/12.34 (Or (Eq (cJ (skS.0 7 a_2)) True)
% 12.15/12.34 (Or (Eq (cJ (skS.0 7 a_3)) True) (Or (Eq False True) (Eq (cG (skS.0 8 a_4 a_5)) True))))
% 12.15/12.34 Clause #223 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cF (skS.0 3 a_1)) True) (Eq (cF (skS.0 6 a_2)) True))
% 12.15/12.34 Clause #225 (by superposition #[223, 182]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.34 Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cF (skS.0 6 a_1)) True) (Or (Eq True False) (Eq (cF (skS.0 6 a_2)) True)))
% 12.15/12.34 Clause #241 (by clausification #[225]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cF (skS.0 6 a_1)) True) (Eq (cF (skS.0 6 a_2)) True))
% 12.15/12.34 Clause #256 (by equality factoring #[241]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Ne True True) (Eq (cF (skS.0 6 a_1)) True))
% 12.15/12.34 Clause #257 (by clausification #[256]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cF (skS.0 6 a_1)) True) (Or (Eq True False) (Eq True False)))
% 12.15/12.34 Clause #259 (by clausification #[257]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cF (skS.0 6 a_1)) True) (Eq True False))
% 12.15/12.37 Clause #260 (by clausification #[259]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Eq (cF (skS.0 6 a_1)) True)
% 12.15/12.37 Clause #273 (by superposition #[260, 151]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cF (skS.0 3 a)) True)
% 12.15/12.37 (Or (Eq True False) (Or (Eq (cG a_1) False) (Or (Eq (cH (skS.0 6 a_2)) True) (Eq (cF (skS.0 3 a_3)) True))))
% 12.15/12.37 Clause #428 (by clausification #[168]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.37 Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Or (Eq (cH (skS.0 3 a_1)) False) (Eq (cJ (skS.0 4 a_1 a_2)) False)))
% 12.15/12.37 Clause #793 (by clausification #[111]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cG (skS.0 4 a_1 a_2)) True) (Eq (cF (skS.0 6 a_3)) True))
% 12.15/12.37 Clause #795 (by superposition #[793, 182]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cF (skS.0 6 a_2)) True) (Or (Eq True False) (Eq (cF (skS.0 6 a_3)) True)))
% 12.15/12.37 Clause #824 (by clausification #[795]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cF (skS.0 6 a_2)) True) (Eq (cF (skS.0 6 a_3)) True))
% 12.15/12.37 Clause #852 (by equality factoring #[824]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Ne True True) (Eq (cF (skS.0 6 a_2)) True))
% 12.15/12.37 Clause #853 (by clausification #[852]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.37 Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cF (skS.0 6 a_2)) True) (Or (Eq True False) (Eq True False)))
% 12.15/12.37 Clause #855 (by clausification #[853]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cF (skS.0 6 a_2)) True) (Eq True False))
% 12.15/12.37 Clause #856 (by clausification #[855]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Eq (cF (skS.0 6 a_2)) True)
% 12.15/12.37 Clause #874 (by superposition #[856, 150]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.15/12.37 Or (Eq (cG (skS.0 4 a a_1)) True)
% 12.15/12.37 (Or (Eq True False) (Or (Eq (cG a_2) False) (Or (Eq (cH (skS.0 6 a_3)) True) (Eq (cG (skS.0 4 a_4 a_5)) True))))
% 12.15/12.37 Clause #1020 (by clausification #[273]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cG a_1) False) (Or (Eq (cH (skS.0 6 a_2)) True) (Eq (cF (skS.0 3 a_3)) True)))
% 12.15/12.37 Clause #1021 (by superposition #[1020, 7]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.37 Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cH (skS.0 6 a_1)) True) (Or (Eq (cF (skS.0 3 a_2)) True) (Eq False True)))
% 12.15/12.37 Clause #1044 (by clausification #[1021]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cH (skS.0 6 a_1)) True) (Eq (cF (skS.0 3 a_2)) True))
% 12.15/12.37 Clause #1074 (by equality factoring #[1044]): ∀ (a a_1 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Ne True True) (Eq (cF (skS.0 3 a_1)) True))
% 12.15/12.37 Clause #1076 (by clausification #[1074]): ∀ (a a_1 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cF (skS.0 3 a_1)) True) (Or (Eq True False) (Eq True False)))
% 12.15/12.37 Clause #1078 (by clausification #[1076]): ∀ (a a_1 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cF (skS.0 3 a_1)) True) (Eq True False))
% 12.15/12.37 Clause #1079 (by clausification #[1078]): ∀ (a a_1 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Eq (cF (skS.0 3 a_1)) True)
% 12.15/12.37 Clause #1080 (by superposition #[1079, 187]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cG (skS.0 7 a_1)) True) (Or (Eq True False) (Eq (cJ (skS.0 8 a_2 a_3)) False)))
% 12.15/12.37 Clause #1162 (by clausification #[1080]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cG (skS.0 7 a_1)) True) (Eq (cJ (skS.0 8 a_2 a_3)) False))
% 12.15/12.37 Clause #1167 (by clausification #[198]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.15/12.37 Or (Eq (cG (skS.0 8 a a_1)) True)
% 12.15/12.37 (Or (Eq (cJ (skS.0 7 a_2)) True) (Or (Eq (cJ (skS.0 7 a_3)) True) (Eq (cG (skS.0 8 a_4 a_5)) True)))
% 12.15/12.37 Clause #1199 (by equality factoring #[1167]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cJ (skS.0 7 a_1)) True) (Or (Ne True True) (Eq (cG (skS.0 8 a_2 a_3)) True)))
% 12.15/12.37 Clause #1201 (by clausification #[1199]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.37 Or (Eq (cJ (skS.0 7 a)) True)
% 12.15/12.37 (Or (Eq (cJ (skS.0 7 a_1)) True) (Or (Eq (cG (skS.0 8 a_2 a_3)) True) (Or (Eq True False) (Eq True False))))
% 12.15/12.37 Clause #1203 (by clausification #[1201]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.24/12.40 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cJ (skS.0 7 a_1)) True) (Or (Eq (cG (skS.0 8 a_2 a_3)) True) (Eq True False)))
% 12.24/12.40 Clause #1204 (by clausification #[1203]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.24/12.40 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cJ (skS.0 7 a_1)) True) (Eq (cG (skS.0 8 a_2 a_3)) True))
% 12.24/12.40 Clause #1222 (by equality factoring #[1204]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 8 a a_1)) True) (Or (Ne True True) (Eq (cJ (skS.0 7 a_2)) True))
% 12.24/12.40 Clause #1223 (by clausification #[1222]): ∀ (a a_1 a_2 : Iota),
% 12.24/12.40 Or (Eq (cG (skS.0 8 a a_1)) True) (Or (Eq (cJ (skS.0 7 a_2)) True) (Or (Eq True False) (Eq True False)))
% 12.24/12.40 Clause #1225 (by clausification #[1223]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 8 a a_1)) True) (Or (Eq (cJ (skS.0 7 a_2)) True) (Eq True False))
% 12.24/12.40 Clause #1226 (by clausification #[1225]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 8 a a_1)) True) (Eq (cJ (skS.0 7 a_2)) True)
% 12.24/12.40 Clause #1240 (by superposition #[1226, 181]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cG (skS.0 8 a a_1)) True) (Or (Eq True False) (Eq (cG (skS.0 8 a_2 a_3)) True))
% 12.24/12.40 Clause #1271 (by clausification #[1240]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cG (skS.0 8 a a_1)) True) (Eq (cG (skS.0 8 a_2 a_3)) True)
% 12.24/12.40 Clause #1285 (by equality factoring #[1271]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (cG (skS.0 8 a a_1)) True)
% 12.24/12.40 Clause #1287 (by clausification #[1285]): ∀ (a a_1 : Iota), Or (Eq (cG (skS.0 8 a a_1)) True) (Or (Eq True False) (Eq True False))
% 12.24/12.40 Clause #1289 (by clausification #[1287]): ∀ (a a_1 : Iota), Or (Eq (cG (skS.0 8 a a_1)) True) (Eq True False)
% 12.24/12.40 Clause #1290 (by clausification #[1289]): ∀ (a a_1 : Iota), Eq (cG (skS.0 8 a a_1)) True
% 12.24/12.40 Clause #1291 (by superposition #[1290, 22]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.24/12.40 Or (Eq True False)
% 12.24/12.40 (Or (Eq (cJ (skS.0 8 a a_1)) True) (Or (Eq (cF a_2) False) (Or (Eq (cG a_3) False) (Eq (cJ a_3) True))))
% 12.24/12.40 Clause #1337 (by clausification #[1291]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.24/12.40 Or (Eq (cJ (skS.0 8 a a_1)) True) (Or (Eq (cF a_2) False) (Or (Eq (cG a_3) False) (Eq (cJ a_3) True)))
% 12.24/12.40 Clause #1338 (by superposition #[1337, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 8 a a_1)) True) (Or (Eq (cG a_2) False) (Or (Eq (cJ a_2) True) (Eq False True)))
% 12.24/12.40 Clause #1347 (by clausification #[1338]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 8 a a_1)) True) (Or (Eq (cG a_2) False) (Eq (cJ a_2) True))
% 12.24/12.40 Clause #1364 (by superposition #[1347, 1290]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cJ (skS.0 8 a a_1)) True) (Or (Eq (cJ (skS.0 8 a_2 a_3)) True) (Eq False True))
% 12.24/12.40 Clause #1377 (by clausification #[1364]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cJ (skS.0 8 a a_1)) True) (Eq (cJ (skS.0 8 a_2 a_3)) True)
% 12.24/12.40 Clause #1379 (by equality factoring #[1377]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (cJ (skS.0 8 a a_1)) True)
% 12.24/12.40 Clause #1381 (by clausification #[1379]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 8 a a_1)) True) (Or (Eq True False) (Eq True False))
% 12.24/12.40 Clause #1383 (by clausification #[1381]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 8 a a_1)) True) (Eq True False)
% 12.24/12.40 Clause #1384 (by clausification #[1383]): ∀ (a a_1 : Iota), Eq (cJ (skS.0 8 a a_1)) True
% 12.24/12.40 Clause #1385 (by superposition #[1384, 1162]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cG (skS.0 7 a_1)) True) (Eq True False))
% 12.24/12.40 Clause #1386 (by clausification #[1385]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Eq (cG (skS.0 7 a_1)) True)
% 12.24/12.40 Clause #1404 (by superposition #[1386, 102]): ∀ (a a_1 a_2 : Iota),
% 12.24/12.40 Or (Eq (cF (skS.0 3 a)) True) (Or (Eq True False) (Or (Eq (cJ (skS.0 7 a_1)) True) (Eq (cF (skS.0 3 a_2)) True)))
% 12.24/12.40 Clause #1422 (by clausification #[1404]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cJ (skS.0 7 a_1)) True) (Eq (cF (skS.0 3 a_2)) True))
% 12.24/12.40 Clause #1451 (by equality factoring #[1422]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Ne True True) (Eq (cF (skS.0 3 a_1)) True))
% 12.24/12.40 Clause #1452 (by clausification #[1451]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cF (skS.0 3 a_1)) True) (Or (Eq True False) (Eq True False)))
% 12.24/12.40 Clause #1454 (by clausification #[1452]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cF (skS.0 3 a_1)) True) (Eq True False))
% 12.26/12.43 Clause #1455 (by clausification #[1454]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Eq (cF (skS.0 3 a_1)) True)
% 12.26/12.43 Clause #1457 (by superposition #[1455, 192]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.43 Or (Eq (cF (skS.0 3 a)) True)
% 12.26/12.43 (Or (Eq True False) (Or (Eq (cH (skS.0 6 a_1)) False) (Eq (cJ (skS.0 8 a_1 a_2)) False)))
% 12.26/12.43 Clause #1639 (by clausification #[1457]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cH (skS.0 6 a_1)) False) (Eq (cJ (skS.0 8 a_1 a_2)) False))
% 12.26/12.43 Clause #1644 (by superposition #[1639, 1079]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.43 Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cJ (skS.0 8 a_1 a_2)) False) (Or (Eq False True) (Eq (cF (skS.0 3 a_3)) True)))
% 12.26/12.43 Clause #1647 (by clausification #[1644]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.43 Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cJ (skS.0 8 a_1 a_2)) False) (Eq (cF (skS.0 3 a_3)) True))
% 12.26/12.43 Clause #1648 (by superposition #[1647, 1384]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq (cF (skS.0 3 a_1)) True) (Eq False True))
% 12.26/12.43 Clause #1649 (by clausification #[1648]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 3 a)) True) (Eq (cF (skS.0 3 a_1)) True)
% 12.26/12.43 Clause #1665 (by equality factoring #[1649]): ∀ (a : Iota), Or (Ne True True) (Eq (cF (skS.0 3 a)) True)
% 12.26/12.43 Clause #1666 (by clausification #[1665]): ∀ (a : Iota), Or (Eq (cF (skS.0 3 a)) True) (Or (Eq True False) (Eq True False))
% 12.26/12.43 Clause #1668 (by clausification #[1666]): ∀ (a : Iota), Or (Eq (cF (skS.0 3 a)) True) (Eq True False)
% 12.26/12.43 Clause #1669 (by clausification #[1668]): ∀ (a : Iota), Eq (cF (skS.0 3 a)) True
% 12.26/12.43 Clause #1673 (by superposition #[1669, 32]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.43 Or (Eq True False)
% 12.26/12.43 (Or (Eq (cH (skS.0 3 a)) True) (Or (Eq (cF a_1) False) (Or (Eq (cG a_2) False) (Eq (cH a_1) True))))
% 12.26/12.43 Clause #1700 (by clausification #[1673]): ∀ (a a_1 a_2 : Iota), Or (Eq (cH (skS.0 3 a)) True) (Or (Eq (cF a_1) False) (Or (Eq (cG a_2) False) (Eq (cH a_1) True)))
% 12.26/12.43 Clause #1705 (by superposition #[1700, 1669]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.43 Or (Eq (cH (skS.0 3 a)) True) (Or (Eq (cG a_1) False) (Or (Eq (cH (skS.0 3 a_2)) True) (Eq False True)))
% 12.26/12.43 Clause #1730 (by clausification #[1705]): ∀ (a a_1 a_2 : Iota), Or (Eq (cH (skS.0 3 a)) True) (Or (Eq (cG a_1) False) (Eq (cH (skS.0 3 a_2)) True))
% 12.26/12.43 Clause #1731 (by superposition #[1730, 7]): ∀ (a a_1 : Iota), Or (Eq (cH (skS.0 3 a)) True) (Or (Eq (cH (skS.0 3 a_1)) True) (Eq False True))
% 12.26/12.43 Clause #1740 (by clausification #[1731]): ∀ (a a_1 : Iota), Or (Eq (cH (skS.0 3 a)) True) (Eq (cH (skS.0 3 a_1)) True)
% 12.26/12.43 Clause #1741 (by equality factoring #[1740]): ∀ (a : Iota), Or (Ne True True) (Eq (cH (skS.0 3 a)) True)
% 12.26/12.43 Clause #1742 (by clausification #[1741]): ∀ (a : Iota), Or (Eq (cH (skS.0 3 a)) True) (Or (Eq True False) (Eq True False))
% 12.26/12.43 Clause #1744 (by clausification #[1742]): ∀ (a : Iota), Or (Eq (cH (skS.0 3 a)) True) (Eq True False)
% 12.26/12.43 Clause #1745 (by clausification #[1744]): ∀ (a : Iota), Eq (cH (skS.0 3 a)) True
% 12.26/12.43 Clause #1746 (by backward demodulation #[1745, 428]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Or (Eq True False) (Eq (cJ (skS.0 4 a_1 a_2)) False)))
% 12.26/12.43 Clause #1749 (by clausification #[1746]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG a) False) (Or (Eq (cJ a) True) (Eq (cJ (skS.0 4 a_1 a_2)) False))
% 12.26/12.43 Clause #1751 (by superposition #[1749, 79]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.43 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cJ (skS.0 4 a_1 a_2)) False) (Or (Eq False True) (Eq (cF (skS.0 6 a_3)) True)))
% 12.26/12.43 Clause #1796 (by clausification #[1751]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.43 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cJ (skS.0 4 a_1 a_2)) False) (Eq (cF (skS.0 6 a_3)) True))
% 12.26/12.43 Clause #2046 (by clausification #[874]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.26/12.43 Or (Eq (cG (skS.0 4 a a_1)) True)
% 12.26/12.43 (Or (Eq (cG a_2) False) (Or (Eq (cH (skS.0 6 a_3)) True) (Eq (cG (skS.0 4 a_4 a_5)) True)))
% 12.26/12.43 Clause #2047 (by superposition #[2046, 7]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.26/12.43 Or (Eq (cG (skS.0 4 a a_1)) True)
% 12.26/12.43 (Or (Eq (cH (skS.0 6 a_2)) True) (Or (Eq (cG (skS.0 4 a_3 a_4)) True) (Eq False True)))
% 12.26/12.43 Clause #2056 (by clausification #[2047]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cH (skS.0 6 a_2)) True) (Eq (cG (skS.0 4 a_3 a_4)) True))
% 12.26/12.45 Clause #2078 (by equality factoring #[2056]): ∀ (a a_1 a_2 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Ne True True) (Eq (cG (skS.0 4 a_1 a_2)) True))
% 12.26/12.45 Clause #2079 (by clausification #[2078]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.45 Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cG (skS.0 4 a_1 a_2)) True) (Or (Eq True False) (Eq True False)))
% 12.26/12.45 Clause #2081 (by clausification #[2079]): ∀ (a a_1 a_2 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cG (skS.0 4 a_1 a_2)) True) (Eq True False))
% 12.26/12.45 Clause #2082 (by clausification #[2081]): ∀ (a a_1 a_2 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Eq (cG (skS.0 4 a_1 a_2)) True)
% 12.26/12.45 Clause #2083 (by superposition #[2082, 187]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True)
% 12.26/12.45 (Or (Eq (cG (skS.0 7 a_2)) True) (Or (Eq True False) (Eq (cJ (skS.0 8 a_3 a_4)) False)))
% 12.26/12.45 Clause #2139 (by clausification #[2083]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cG (skS.0 7 a_2)) True) (Eq (cJ (skS.0 8 a_3 a_4)) False))
% 12.26/12.45 Clause #2140 (by superposition #[2139, 1384]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cG (skS.0 7 a_2)) True) (Eq False True))
% 12.26/12.45 Clause #2141 (by clausification #[2140]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Eq (cG (skS.0 7 a_2)) True)
% 12.26/12.45 Clause #2157 (by superposition #[2141, 107]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True)
% 12.26/12.45 (Or (Eq True False) (Or (Eq (cJ (skS.0 7 a_2)) True) (Eq (cG (skS.0 4 a_3 a_4)) True)))
% 12.26/12.45 Clause #2264 (by clausification #[2157]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cJ (skS.0 7 a_2)) True) (Eq (cG (skS.0 4 a_3 a_4)) True))
% 12.26/12.45 Clause #2291 (by equality factoring #[2264]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Ne True True) (Eq (cG (skS.0 4 a_1 a_2)) True))
% 12.26/12.45 Clause #2292 (by clausification #[2291]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.45 Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cG (skS.0 4 a_1 a_2)) True) (Or (Eq True False) (Eq True False)))
% 12.26/12.45 Clause #2294 (by clausification #[2292]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cG (skS.0 4 a_1 a_2)) True) (Eq True False))
% 12.26/12.45 Clause #2295 (by clausification #[2294]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Eq (cG (skS.0 4 a_1 a_2)) True)
% 12.26/12.45 Clause #2297 (by superposition #[2295, 192]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True)
% 12.26/12.45 (Or (Eq True False) (Or (Eq (cH (skS.0 6 a_2)) False) (Eq (cJ (skS.0 8 a_2 a_3)) False)))
% 12.26/12.45 Clause #2367 (by clausification #[2297]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cH (skS.0 6 a_2)) False) (Eq (cJ (skS.0 8 a_2 a_3)) False))
% 12.26/12.45 Clause #2370 (by superposition #[2367, 2082]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True)
% 12.26/12.45 (Or (Eq (cJ (skS.0 8 a_2 a_3)) False) (Or (Eq False True) (Eq (cG (skS.0 4 a_4 a_5)) True)))
% 12.26/12.45 Clause #2392 (by clausification #[2370]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.26/12.45 Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cJ (skS.0 8 a_2 a_3)) False) (Eq (cG (skS.0 4 a_4 a_5)) True))
% 12.26/12.45 Clause #2393 (by superposition #[2392, 1384]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq (cG (skS.0 4 a_2 a_3)) True) (Eq False True))
% 12.26/12.45 Clause #2395 (by clausification #[2393]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Eq (cG (skS.0 4 a_2 a_3)) True)
% 12.26/12.45 Clause #2409 (by equality factoring #[2395]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (cG (skS.0 4 a a_1)) True)
% 12.26/12.45 Clause #2410 (by clausification #[2409]): ∀ (a a_1 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Or (Eq True False) (Eq True False))
% 12.26/12.45 Clause #2412 (by clausification #[2410]): ∀ (a a_1 : Iota), Or (Eq (cG (skS.0 4 a a_1)) True) (Eq True False)
% 12.26/12.45 Clause #2413 (by clausification #[2412]): ∀ (a a_1 : Iota), Eq (cG (skS.0 4 a a_1)) True
% 12.26/12.45 Clause #2414 (by superposition #[2413, 22]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq True False)
% 12.26/12.45 (Or (Eq (cJ (skS.0 4 a a_1)) True) (Or (Eq (cF a_2) False) (Or (Eq (cG a_3) False) (Eq (cJ a_3) True))))
% 12.26/12.48 Clause #2449 (by clausification #[2414]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.48 Or (Eq (cJ (skS.0 4 a a_1)) True) (Or (Eq (cF a_2) False) (Or (Eq (cG a_3) False) (Eq (cJ a_3) True)))
% 12.26/12.48 Clause #2450 (by superposition #[2449, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 4 a a_1)) True) (Or (Eq (cG a_2) False) (Or (Eq (cJ a_2) True) (Eq False True)))
% 12.26/12.48 Clause #2453 (by clausification #[2450]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 4 a a_1)) True) (Or (Eq (cG a_2) False) (Eq (cJ a_2) True))
% 12.26/12.48 Clause #2462 (by superposition #[2453, 2413]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cJ (skS.0 4 a a_1)) True) (Or (Eq (cJ (skS.0 4 a_2 a_3)) True) (Eq False True))
% 12.26/12.48 Clause #2473 (by clausification #[2462]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cJ (skS.0 4 a a_1)) True) (Eq (cJ (skS.0 4 a_2 a_3)) True)
% 12.26/12.48 Clause #2479 (by equality factoring #[2473]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (cJ (skS.0 4 a a_1)) True)
% 12.26/12.48 Clause #2480 (by clausification #[2479]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 4 a a_1)) True) (Or (Eq True False) (Eq True False))
% 12.26/12.48 Clause #2482 (by clausification #[2480]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 4 a a_1)) True) (Eq True False)
% 12.26/12.48 Clause #2483 (by clausification #[2482]): ∀ (a a_1 : Iota), Eq (cJ (skS.0 4 a a_1)) True
% 12.26/12.48 Clause #2484 (by superposition #[2483, 1796]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq True False) (Eq (cF (skS.0 6 a_1)) True))
% 12.26/12.48 Clause #2515 (by clausification #[2484]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Eq (cF (skS.0 6 a_1)) True)
% 12.26/12.48 Clause #2516 (by superposition #[2515, 182]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 6 a)) True) (Or (Eq True False) (Eq (cF (skS.0 6 a_1)) True))
% 12.26/12.48 Clause #2523 (by clausification #[2516]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 6 a)) True) (Eq (cF (skS.0 6 a_1)) True)
% 12.26/12.48 Clause #2529 (by equality factoring #[2523]): ∀ (a : Iota), Or (Ne True True) (Eq (cF (skS.0 6 a)) True)
% 12.26/12.48 Clause #2530 (by clausification #[2529]): ∀ (a : Iota), Or (Eq (cF (skS.0 6 a)) True) (Or (Eq True False) (Eq True False))
% 12.26/12.48 Clause #2532 (by clausification #[2530]): ∀ (a : Iota), Or (Eq (cF (skS.0 6 a)) True) (Eq True False)
% 12.26/12.48 Clause #2533 (by clausification #[2532]): ∀ (a : Iota), Eq (cF (skS.0 6 a)) True
% 12.26/12.48 Clause #2537 (by superposition #[2533, 32]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.48 Or (Eq True False)
% 12.26/12.48 (Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cF a_1) False) (Or (Eq (cG a_2) False) (Eq (cH a_1) True))))
% 12.26/12.48 Clause #2559 (by clausification #[2537]): ∀ (a a_1 a_2 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cF a_1) False) (Or (Eq (cG a_2) False) (Eq (cH a_1) True)))
% 12.26/12.48 Clause #2562 (by superposition #[2559, 2533]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.48 Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cG a_1) False) (Or (Eq (cH (skS.0 6 a_2)) True) (Eq False True)))
% 12.26/12.48 Clause #2565 (by clausification #[2562]): ∀ (a a_1 a_2 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cG a_1) False) (Eq (cH (skS.0 6 a_2)) True))
% 12.26/12.48 Clause #2566 (by superposition #[2565, 7]): ∀ (a a_1 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Eq (cH (skS.0 6 a_1)) True) (Eq False True))
% 12.26/12.48 Clause #2569 (by clausification #[2566]): ∀ (a a_1 : Iota), Or (Eq (cH (skS.0 6 a)) True) (Eq (cH (skS.0 6 a_1)) True)
% 12.26/12.48 Clause #2571 (by equality factoring #[2569]): ∀ (a : Iota), Or (Ne True True) (Eq (cH (skS.0 6 a)) True)
% 12.26/12.48 Clause #2572 (by clausification #[2571]): ∀ (a : Iota), Or (Eq (cH (skS.0 6 a)) True) (Or (Eq True False) (Eq True False))
% 12.26/12.48 Clause #2574 (by clausification #[2572]): ∀ (a : Iota), Or (Eq (cH (skS.0 6 a)) True) (Eq True False)
% 12.26/12.48 Clause #2575 (by clausification #[2574]): ∀ (a : Iota), Eq (cH (skS.0 6 a)) True
% 12.26/12.48 Clause #2576 (by backward demodulation #[2575, 187]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 7 a)) True) (Or (Eq True False) (Eq (cJ (skS.0 8 a_1 a_2)) False))
% 12.26/12.48 Clause #2577 (by backward demodulation #[2575, 192]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) False) (Or (Eq True False) (Eq (cJ (skS.0 8 a_1 a_2)) False))
% 12.26/12.48 Clause #2578 (by clausification #[2577]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) False) (Eq (cJ (skS.0 8 a_1 a_2)) False)
% 12.26/12.48 Clause #2579 (by clausification #[2576]): ∀ (a a_1 a_2 : Iota), Or (Eq (cG (skS.0 7 a)) True) (Eq (cJ (skS.0 8 a_1 a_2)) False)
% 12.26/12.50 Clause #2580 (by superposition #[2579, 1384]): ∀ (a : Iota), Or (Eq (cG (skS.0 7 a)) True) (Eq False True)
% 12.26/12.50 Clause #2582 (by clausification #[2580]): ∀ (a : Iota), Eq (cG (skS.0 7 a)) True
% 12.26/12.50 Clause #2583 (by superposition #[2582, 22]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.50 Or (Eq True False)
% 12.26/12.50 (Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cF a_1) False) (Or (Eq (cG a_2) False) (Eq (cJ a_2) True))))
% 12.26/12.50 Clause #2596 (by clausification #[2583]): ∀ (a a_1 a_2 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cF a_1) False) (Or (Eq (cG a_2) False) (Eq (cJ a_2) True)))
% 12.26/12.50 Clause #2597 (by superposition #[2596, 8]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cG a_1) False) (Or (Eq (cJ a_1) True) (Eq False True)))
% 12.26/12.50 Clause #2598 (by clausification #[2597]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cG a_1) False) (Eq (cJ a_1) True))
% 12.26/12.50 Clause #2602 (by superposition #[2598, 2582]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq (cJ (skS.0 7 a_1)) True) (Eq False True))
% 12.26/12.50 Clause #2605 (by clausification #[2602]): ∀ (a a_1 : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Eq (cJ (skS.0 7 a_1)) True)
% 12.26/12.50 Clause #2607 (by equality factoring #[2605]): ∀ (a : Iota), Or (Ne True True) (Eq (cJ (skS.0 7 a)) True)
% 12.26/12.50 Clause #2608 (by clausification #[2607]): ∀ (a : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Or (Eq True False) (Eq True False))
% 12.26/12.50 Clause #2610 (by clausification #[2608]): ∀ (a : Iota), Or (Eq (cJ (skS.0 7 a)) True) (Eq True False)
% 12.26/12.50 Clause #2611 (by clausification #[2610]): ∀ (a : Iota), Eq (cJ (skS.0 7 a)) True
% 12.26/12.50 Clause #2612 (by superposition #[2611, 2578]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cJ (skS.0 8 a a_1)) False)
% 12.26/12.50 Clause #2613 (by clausification #[2612]): ∀ (a a_1 : Iota), Eq (cJ (skS.0 8 a a_1)) False
% 12.26/12.50 Clause #2614 (by superposition #[2613, 1384]): Eq False True
% 12.26/12.50 Clause #2615 (by clausification #[2614]): False
% 12.26/12.50 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------