TSTP Solution File: SYO105^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO105^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n011.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 04:21:31 EDT 2023
% Result : Theorem 7.76s 8.00s
% Output : Proof 8.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO105^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 00:14:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 7.76/8.00 SZS status Theorem for theBenchmark.p
% 7.76/8.00 SZS output start Proof for theBenchmark.p
% 7.76/8.00 Clause #0 (by assumption #[]): Eq
% 7.76/8.00 (Not
% 7.76/8.00 (Iff
% 7.76/8.00 (Not
% 7.76/8.00 ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists fun Xv => cR Xv))))
% 7.76/8.00 (Exists fun Xx => ∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ Xx y → Not (cP Xu y Xz → Not (cR Xv))))))
% 7.76/8.00 True
% 7.76/8.00 Clause #1 (by betaEtaReduce #[0]): Eq
% 7.76/8.00 (Not
% 7.76/8.00 (Iff (Not ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))))
% 7.76/8.00 (Exists fun Xx => ∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ Xx y → Not (cP Xu y Xz → Not (cR Xv))))))
% 7.76/8.00 True
% 7.76/8.00 Clause #2 (by clausification #[1]): Eq
% 7.76/8.00 (Iff (Not ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))))
% 7.76/8.00 (Exists fun Xx => ∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ Xx y → Not (cP Xu y Xz → Not (cR Xv)))))
% 7.76/8.00 False
% 7.76/8.00 Clause #3 (by clausification #[2]): Or (Eq (Not ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR)))) False)
% 7.76/8.00 (Eq (Exists fun Xx => ∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ Xx y → Not (cP Xu y Xz → Not (cR Xv))))
% 7.76/8.00 False)
% 7.76/8.00 Clause #4 (by clausification #[2]): Or (Eq (Not ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR)))) True)
% 7.76/8.00 (Eq (Exists fun Xx => ∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ Xx y → Not (cP Xu y Xz → Not (cR Xv))))
% 7.76/8.00 True)
% 7.76/8.00 Clause #5 (by clausification #[3]): Or
% 7.76/8.00 (Eq (Exists fun Xx => ∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ Xx y → Not (cP Xu y Xz → Not (cR Xv))))
% 7.76/8.00 False)
% 7.76/8.00 (Eq ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) True)
% 7.76/8.00 Clause #6 (by clausification #[5]): ∀ (a : Iota),
% 7.76/8.00 Or (Eq ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) True)
% 7.76/8.00 (Eq (∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ a y → Not (cP Xu y Xz → Not (cR Xv)))) False)
% 7.76/8.00 Clause #7 (by clausification #[6]): ∀ (a : Iota),
% 7.76/8.00 Or (Eq (∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ a y → Not (cP Xu y Xz → Not (cR Xv)))) False)
% 7.76/8.00 (Or (Eq (Exists fun Xx => cQ Xx y) False)
% 7.76/8.00 (Eq (Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) True))
% 7.76/8.00 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 7.76/8.00 Or (Eq (Exists fun Xx => cQ Xx y) False)
% 7.76/8.00 (Or (Eq (Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) True)
% 7.76/8.00 (Eq (Not (Exists fun Xu => ∀ (Xv : Iota), Not (cQ a y → Not (cP Xu y (skS.0 0 a a_1) → Not (cR Xv))))) True))
% 7.76/8.00 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 7.76/8.00 Or (Eq (Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) True)
% 7.76/8.00 (Or (Eq (Not (Exists fun Xu => ∀ (Xv : Iota), Not (cQ a y → Not (cP Xu y (skS.0 0 a a_1) → Not (cR Xv))))) True)
% 7.76/8.00 (Eq (cQ a_2 y) False))
% 7.76/8.00 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 7.76/8.00 Or (Eq (Not (Exists fun Xu => ∀ (Xv : Iota), Not (cQ a y → Not (cP Xu y (skS.0 0 a a_1) → Not (cR Xv))))) True)
% 7.76/8.00 (Or (Eq (cQ a_2 y) False) (Eq (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR)) False))
% 7.76/8.00 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 7.76/8.00 Or (Eq (cQ a y) False)
% 7.76/8.00 (Or (Eq (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR)) False)
% 7.76/8.00 (Eq (Exists fun Xu => ∀ (Xv : Iota), Not (cQ a_1 y → Not (cP Xu y (skS.0 0 a_1 a_2) → Not (cR Xv)))) False))
% 7.76/8.00 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.76/8.00 Or (Eq (cQ a y) False)
% 7.76/8.00 (Or (Eq (Exists fun Xu => ∀ (Xv : Iota), Not (cQ a_1 y → Not (cP Xu y (skS.0 0 a_1 a_2) → Not (cR Xv)))) False)
% 7.76/8.00 (Eq (Not ((∀ (Xu : Iota), cP Xu y (skS.0 1 a_3)) → Not (Exists cR))) True))
% 7.76/8.00 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.76/8.00 Or (Eq (cQ a y) False)
% 7.76/8.00 (Or (Eq (Not ((∀ (Xu : Iota), cP Xu y (skS.0 1 a_1)) → Not (Exists cR))) True)
% 7.88/8.02 (Eq (∀ (Xv : Iota), Not (cQ a_2 y → Not (cP a_3 y (skS.0 0 a_2 a_4) → Not (cR Xv)))) False))
% 7.88/8.02 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (∀ (Xv : Iota), Not (cQ a_1 y → Not (cP a_2 y (skS.0 0 a_1 a_3) → Not (cR Xv)))) False)
% 7.88/8.02 (Eq ((∀ (Xu : Iota), cP Xu y (skS.0 1 a_4)) → Not (Exists cR)) False))
% 7.88/8.02 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq ((∀ (Xu : Iota), cP Xu y (skS.0 1 a_1)) → Not (Exists cR)) False)
% 7.88/8.02 (Eq (Not (Not (cQ a_2 y → Not (cP a_3 y (skS.0 0 a_2 a_4) → Not (cR (skS.0 2 a_2 a_3 a_4 a_5)))))) True))
% 7.88/8.02 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (Not (Not (cQ a_1 y → Not (cP a_2 y (skS.0 0 a_1 a_3) → Not (cR (skS.0 2 a_1 a_2 a_3 a_4)))))) True)
% 7.88/8.02 (Eq (∀ (Xu : Iota), cP Xu y (skS.0 1 a_5)) True))
% 7.88/8.02 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (Not (Not (cQ a_1 y → Not (cP a_2 y (skS.0 0 a_1 a_3) → Not (cR (skS.0 2 a_1 a_2 a_3 a_4)))))) True)
% 7.88/8.02 (Eq (Not (Exists cR)) False))
% 7.88/8.02 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (∀ (Xu : Iota), cP Xu y (skS.0 1 a_1)) True)
% 7.88/8.02 (Eq (Not (cQ a_2 y → Not (cP a_3 y (skS.0 0 a_2 a_4) → Not (cR (skS.0 2 a_2 a_3 a_4 a_5))))) False))
% 7.88/8.02 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (Not (cQ a_1 y → Not (cP a_2 y (skS.0 0 a_1 a_3) → Not (cR (skS.0 2 a_1 a_2 a_3 a_4))))) False)
% 7.88/8.02 (Eq (cP a_5 y (skS.0 1 a_6)) True))
% 7.88/8.02 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (cP a_1 y (skS.0 1 a_2)) True)
% 7.88/8.02 (Eq (cQ a_3 y → Not (cP a_4 y (skS.0 0 a_3 a_5) → Not (cR (skS.0 2 a_3 a_4 a_5 a_6)))) True))
% 7.88/8.02 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (cP a_1 y (skS.0 1 a_2)) True)
% 7.88/8.02 (Or (Eq (cQ a_3 y) False) (Eq (Not (cP a_4 y (skS.0 0 a_3 a_5) → Not (cR (skS.0 2 a_3 a_4 a_5 a_6)))) True)))
% 7.88/8.02 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (cP a_1 y (skS.0 1 a_2)) True)
% 7.88/8.02 (Or (Eq (cQ a_3 y) False) (Eq (cP a_4 y (skS.0 0 a_3 a_5) → Not (cR (skS.0 2 a_3 a_4 a_5 a_6))) False)))
% 7.88/8.02 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.02 Or (Eq (cQ a y) False)
% 7.88/8.02 (Or (Eq (cP a_1 y (skS.0 1 a_2)) True) (Or (Eq (cQ a_3 y) False) (Eq (cP a_4 y (skS.0 0 a_3 a_5)) True)))
% 7.88/8.02 Clause #25 (by clausification #[4]): Or
% 7.88/8.02 (Eq (Exists fun Xx => ∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ Xx y → Not (cP Xu y Xz → Not (cR Xv))))
% 7.88/8.02 True)
% 7.88/8.02 (Eq ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) False)
% 7.88/8.02 Clause #26 (by clausification #[25]): ∀ (a : Iota),
% 7.88/8.02 Or (Eq ((Exists fun Xx => cQ Xx y) → Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) False)
% 7.88/8.02 (Eq (∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP Xu y Xz → Not (cR Xv)))) True)
% 7.88/8.02 Clause #27 (by clausification #[26]): ∀ (a : Iota),
% 7.88/8.02 Or (Eq (∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP Xu y Xz → Not (cR Xv)))) True)
% 7.88/8.02 (Eq (Exists fun Xx => cQ Xx y) True)
% 7.88/8.02 Clause #28 (by clausification #[26]): ∀ (a : Iota),
% 7.88/8.02 Or (Eq (∀ (Xz : Iota), Exists fun Xu => ∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP Xu y Xz → Not (cR Xv)))) True)
% 7.88/8.02 (Eq (Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) False)
% 7.88/8.02 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota),
% 7.88/8.02 Or (Eq (Exists fun Xx => cQ Xx y) True)
% 7.88/8.02 (Eq (Exists fun Xu => ∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP Xu y a_1 → Not (cR Xv)))) True)
% 7.88/8.05 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota),
% 7.88/8.05 Or (Eq (Exists fun Xu => ∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP Xu y a_1 → Not (cR Xv)))) True)
% 7.88/8.05 (Eq (cQ (skS.0 4 a_2) y) True)
% 7.88/8.05 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.88/8.05 Or (Eq (cQ (skS.0 4 a) y) True)
% 7.88/8.05 (Eq (∀ (Xv : Iota), Not (cQ (skS.0 3 a_1) y → Not (cP (skS.0 5 a_1 a_2 a_3) y a_2 → Not (cR Xv)))) True)
% 7.88/8.05 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.05 Or (Eq (cQ (skS.0 4 a) y) True)
% 7.88/8.05 (Eq (Not (cQ (skS.0 3 a_1) y → Not (cP (skS.0 5 a_1 a_2 a_3) y a_2 → Not (cR a_4)))) True)
% 7.88/8.05 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.05 Or (Eq (cQ (skS.0 4 a) y) True) (Eq (cQ (skS.0 3 a_1) y → Not (cP (skS.0 5 a_1 a_2 a_3) y a_2 → Not (cR a_4))) False)
% 7.88/8.05 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Eq (cQ (skS.0 3 a_1) y) True)
% 7.88/8.05 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.05 Or (Eq (cQ (skS.0 4 a) y) True) (Eq (Not (cP (skS.0 5 a_1 a_2 a_3) y a_2 → Not (cR a_4))) False)
% 7.88/8.05 Clause #37 (by superposition #[34, 23]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.05 Or (Eq (cQ (skS.0 4 a) y) True)
% 7.88/8.05 (Or (Eq True False)
% 7.88/8.05 (Or (Eq (cP a_1 y (skS.0 1 a_2)) True) (Or (Eq (cQ a_3 y) False) (Eq (cP a_4 y (skS.0 0 a_3 a_5)) True))))
% 7.88/8.05 Clause #38 (by clausification #[35]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Eq (cP (skS.0 5 a_1 a_2 a_3) y a_2 → Not (cR a_4)) True)
% 7.88/8.05 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.05 Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cP (skS.0 5 a_1 a_2 a_3) y a_2) False) (Eq (Not (cR a_4)) True))
% 7.88/8.05 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.05 Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cP (skS.0 5 a_1 a_2 a_3) y a_2) False) (Eq (cR a_4) False))
% 7.88/8.05 Clause #41 (by clausification #[28]): ∀ (a a_1 : Iota),
% 7.88/8.05 Or (Eq (Not (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR))) False)
% 7.88/8.05 (Eq (Exists fun Xu => ∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP Xu y a_1 → Not (cR Xv)))) True)
% 7.88/8.05 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 7.88/8.05 Or (Eq (Exists fun Xu => ∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP Xu y a_1 → Not (cR Xv)))) True)
% 7.88/8.05 (Eq (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR)) True)
% 7.88/8.05 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota),
% 7.88/8.05 Or (Eq (∀ (Xz : Iota), (∀ (Xu : Iota), cP Xu y Xz) → Not (Exists cR)) True)
% 7.88/8.05 (Eq (∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP (skS.0 6 a a_1 a_2) y a_1 → Not (cR Xv)))) True)
% 7.88/8.05 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.88/8.05 Or (Eq (∀ (Xv : Iota), Not (cQ (skS.0 3 a) y → Not (cP (skS.0 6 a a_1 a_2) y a_1 → Not (cR Xv)))) True)
% 7.88/8.05 (Eq ((∀ (Xu : Iota), cP Xu y a_3) → Not (Exists cR)) True)
% 7.88/8.05 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.05 Or (Eq ((∀ (Xu : Iota), cP Xu y a) → Not (Exists cR)) True)
% 7.88/8.05 (Eq (Not (cQ (skS.0 3 a_1) y → Not (cP (skS.0 6 a_1 a_2 a_3) y a_2 → Not (cR a_4)))) True)
% 7.88/8.05 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.05 Or (Eq (Not (cQ (skS.0 3 a) y → Not (cP (skS.0 6 a a_1 a_2) y a_1 → Not (cR a_3)))) True)
% 7.88/8.05 (Or (Eq (∀ (Xu : Iota), cP Xu y a_4) False) (Eq (Not (Exists cR)) True))
% 7.88/8.05 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.05 Or (Eq (∀ (Xu : Iota), cP Xu y a) False)
% 7.88/8.05 (Or (Eq (Not (Exists cR)) True)
% 7.88/8.05 (Eq (cQ (skS.0 3 a_1) y → Not (cP (skS.0 6 a_1 a_2 a_3) y a_2 → Not (cR a_4))) False))
% 7.88/8.05 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.05 Or (Eq (Not (Exists cR)) True)
% 7.88/8.05 (Or (Eq (cQ (skS.0 3 a) y → Not (cP (skS.0 6 a a_1 a_2) y a_1 → Not (cR a_3))) False)
% 7.88/8.05 (Eq (Not (cP (skS.0 7 a_4 a_5) y a_4)) True))
% 7.88/8.05 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.05 Or (Eq (cQ (skS.0 3 a) y → Not (cP (skS.0 6 a a_1 a_2) y a_1 → Not (cR a_3))) False)
% 7.88/8.05 (Or (Eq (Not (cP (skS.0 7 a_4 a_5) y a_4)) True) (Eq (Exists cR) False))
% 7.88/8.08 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.08 Or (Eq (Not (cP (skS.0 7 a a_1) y a)) True)
% 7.88/8.08 (Or (Eq (Exists cR) False) (Eq (Not (cP (skS.0 6 a_2 a_3 a_4) y a_3 → Not (cR a_5))) False))
% 7.88/8.08 Clause #54 (by clausification #[51]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.08 Or (Eq (Exists cR) False)
% 7.88/8.08 (Or (Eq (Not (cP (skS.0 6 a a_1 a_2) y a_1 → Not (cR a_3))) False) (Eq (cP (skS.0 7 a_4 a_5) y a_4) False))
% 7.88/8.08 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.88/8.08 Or (Eq (Not (cP (skS.0 6 a a_1 a_2) y a_1 → Not (cR a_3))) False)
% 7.88/8.08 (Or (Eq (cP (skS.0 7 a_4 a_5) y a_4) False) (Eq (cR a_6) False))
% 7.88/8.08 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.88/8.08 Or (Eq (cP (skS.0 7 a a_1) y a) False)
% 7.88/8.08 (Or (Eq (cR a_2) False) (Eq (cP (skS.0 6 a_3 a_4 a_5) y a_4 → Not (cR a_6)) True))
% 7.88/8.08 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.88/8.08 Or (Eq (cP (skS.0 7 a a_1) y a) False)
% 7.88/8.08 (Or (Eq (cR a_2) False) (Or (Eq (cP (skS.0 6 a_3 a_4 a_5) y a_4) False) (Eq (Not (cR a_6)) True)))
% 7.88/8.08 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.88/8.08 Or (Eq (cP (skS.0 7 a a_1) y a) False)
% 7.88/8.08 (Or (Eq (cR a_2) False) (Or (Eq (cP (skS.0 6 a_3 a_4 a_5) y a_4) False) (Eq (cR a_6) False)))
% 7.88/8.08 Clause #59 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.08 Or (Eq (cQ a y) False)
% 7.88/8.08 (Or (Eq (Not (Exists cR)) False)
% 7.88/8.08 (Eq (Not (cQ a_1 y → Not (cP a_2 y (skS.0 0 a_1 a_3) → Not (cR (skS.0 2 a_1 a_2 a_3 a_4))))) False))
% 7.88/8.08 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.08 Or (Eq (cQ a y) False)
% 7.88/8.08 (Or (Eq (Not (cQ a_1 y → Not (cP a_2 y (skS.0 0 a_1 a_3) → Not (cR (skS.0 2 a_1 a_2 a_3 a_4))))) False)
% 7.88/8.08 (Eq (Exists cR) True))
% 7.88/8.08 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.08 Or (Eq (cQ a y) False)
% 7.88/8.08 (Or (Eq (Exists cR) True)
% 7.88/8.08 (Eq (cQ a_1 y → Not (cP a_2 y (skS.0 0 a_1 a_3) → Not (cR (skS.0 2 a_1 a_2 a_3 a_4)))) True))
% 7.88/8.08 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.08 Or (Eq (cQ a y) False)
% 7.88/8.08 (Or (Eq (cQ a_1 y → Not (cP a_2 y (skS.0 0 a_1 a_3) → Not (cR (skS.0 2 a_1 a_2 a_3 a_4)))) True)
% 7.88/8.08 (Eq (cR (skS.0 8 a_5)) True))
% 7.88/8.08 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.08 Or (Eq (cQ a y) False)
% 7.88/8.08 (Or (Eq (cR (skS.0 8 a_1)) True)
% 7.88/8.08 (Or (Eq (cQ a_2 y) False) (Eq (Not (cP a_3 y (skS.0 0 a_2 a_4) → Not (cR (skS.0 2 a_2 a_3 a_4 a_5)))) True)))
% 7.88/8.08 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.08 Or (Eq (cQ a y) False)
% 7.88/8.08 (Or (Eq (cR (skS.0 8 a_1)) True)
% 7.88/8.08 (Or (Eq (cQ a_2 y) False) (Eq (cP a_3 y (skS.0 0 a_2 a_4) → Not (cR (skS.0 2 a_2 a_3 a_4 a_5))) False)))
% 7.88/8.08 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.08 Or (Eq (cQ a y) False)
% 7.88/8.08 (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq (cQ a_2 y) False) (Eq (cP a_3 y (skS.0 0 a_2 a_4)) True)))
% 7.88/8.08 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.08 Or (Eq (cQ a y) False)
% 7.88/8.08 (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq (cQ a_2 y) False) (Eq (Not (cR (skS.0 2 a_2 a_3 a_4 a_5))) False)))
% 7.88/8.09 Clause #68 (by superposition #[65, 34]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.09 Or (Eq (cR (skS.0 8 a)) True)
% 7.88/8.09 (Or (Eq (cQ a_1 y) False)
% 7.88/8.09 (Or (Eq (cP a_2 y (skS.0 0 a_1 a_3)) True) (Or (Eq (cQ (skS.0 4 a_4) y) True) (Eq False True))))
% 7.88/8.09 Clause #69 (by clausification #[66]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.09 Or (Eq (cQ a y) False)
% 7.88/8.09 (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq (cQ a_2 y) False) (Eq (cR (skS.0 2 a_2 a_3 a_4 a_5)) True)))
% 7.88/8.09 Clause #71 (by superposition #[69, 34]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.88/8.09 Or (Eq (cR (skS.0 8 a)) True)
% 7.88/8.09 (Or (Eq (cQ a_1 y) False)
% 7.88/8.09 (Or (Eq (cR (skS.0 2 a_1 a_2 a_3 a_4)) True) (Or (Eq (cQ (skS.0 4 a_5) y) True) (Eq False True))))
% 7.88/8.09 Clause #75 (by clausification #[68]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.88/8.09 Or (Eq (cR (skS.0 8 a)) True)
% 7.88/8.09 (Or (Eq (cQ a_1 y) False) (Or (Eq (cP a_2 y (skS.0 0 a_1 a_3)) True) (Eq (cQ (skS.0 4 a_4) y) True)))
% 7.88/8.09 Clause #77 (by superposition #[75, 34]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cP a_1 y (skS.0 0 (skS.0 3 a_2) a_3)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_4) y) True) (Or (Eq (cQ (skS.0 4 a_5) y) True) (Eq False True))))
% 7.97/8.11 Clause #81 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cQ a_1 y) False) (Or (Eq (cR (skS.0 2 a_1 a_2 a_3 a_4)) True) (Eq (cQ (skS.0 4 a_5) y) True)))
% 7.97/8.11 Clause #83 (by superposition #[81, 34]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cR (skS.0 2 (skS.0 3 a_1) a_2 a_3 a_4)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_5) y) True) (Or (Eq (cQ (skS.0 4 a_6) y) True) (Eq False True))))
% 7.97/8.11 Clause #90 (by clausification #[37]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.11 Or (Eq (cQ (skS.0 4 a) y) True)
% 7.97/8.11 (Or (Eq (cP a_1 y (skS.0 1 a_2)) True) (Or (Eq (cQ a_3 y) False) (Eq (cP a_4 y (skS.0 0 a_3 a_5)) True)))
% 7.97/8.11 Clause #92 (by superposition #[90, 34]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.97/8.11 Or (Eq (cQ (skS.0 4 a) y) True)
% 7.97/8.11 (Or (Eq (cP a_1 y (skS.0 1 a_2)) True)
% 7.97/8.11 (Or (Eq (cP a_3 y (skS.0 0 (skS.0 3 a_4) a_5)) True) (Or (Eq (cQ (skS.0 4 a_6) y) True) (Eq False True))))
% 7.97/8.11 Clause #99 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cP a_1 y (skS.0 0 (skS.0 3 a_2) a_3)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_4) y) True) (Eq (cQ (skS.0 4 a_5) y) True)))
% 7.97/8.11 Clause #115 (by equality factoring #[99]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cP a_1 y (skS.0 0 (skS.0 3 a_2) a_3)) True) (Or (Ne True True) (Eq (cQ (skS.0 4 a_4) y) True)))
% 7.97/8.11 Clause #117 (by clausification #[115]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cP a_1 y (skS.0 0 (skS.0 3 a_2) a_3)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_4) y) True) (Or (Eq True False) (Eq True False))))
% 7.97/8.11 Clause #119 (by clausification #[117]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cP a_1 y (skS.0 0 (skS.0 3 a_2) a_3)) True) (Or (Eq (cQ (skS.0 4 a_4) y) True) (Eq True False)))
% 7.97/8.11 Clause #120 (by clausification #[119]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cP a_1 y (skS.0 0 (skS.0 3 a_2) a_3)) True) (Eq (cQ (skS.0 4 a_4) y) True))
% 7.97/8.11 Clause #121 (by superposition #[120, 40]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_1) y) True) (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Eq True False) (Eq (cR a_3) False))))
% 7.97/8.11 Clause #137 (by clausification #[121]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_1) y) True) (Or (Eq (cQ (skS.0 4 a_2) y) True) (Eq (cR a_3) False)))
% 7.97/8.11 Clause #193 (by clausification #[83]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cR (skS.0 2 (skS.0 3 a_1) a_2 a_3 a_4)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_5) y) True) (Eq (cQ (skS.0 4 a_6) y) True)))
% 7.97/8.11 Clause #214 (by equality factoring #[193]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cR (skS.0 2 (skS.0 3 a_1) a_2 a_3 a_4)) True) (Or (Ne True True) (Eq (cQ (skS.0 4 a_5) y) True)))
% 7.97/8.11 Clause #216 (by clausification #[214]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cR (skS.0 2 (skS.0 3 a_1) a_2 a_3 a_4)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_5) y) True) (Or (Eq True False) (Eq True False))))
% 7.97/8.11 Clause #218 (by clausification #[216]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cR (skS.0 2 (skS.0 3 a_1) a_2 a_3 a_4)) True) (Or (Eq (cQ (skS.0 4 a_5) y) True) (Eq True False)))
% 7.97/8.11 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 2 (skS.0 3 a_1) a_2 a_3 a_4)) True) (Eq (cQ (skS.0 4 a_5) y) True))
% 7.97/8.11 Clause #224 (by superposition #[219, 137]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.11 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_1) y) True)
% 7.97/8.11 (Or (Eq (cR (skS.0 8 a_2)) True)
% 7.97/8.11 (Or (Eq (cQ (skS.0 4 a_3) y) True) (Or (Eq (cQ (skS.0 4 a_4) y) True) (Eq True False)))))
% 7.97/8.14 Clause #241 (by clausification #[224]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.14 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.14 (Or (Eq (cQ (skS.0 4 a_1) y) True)
% 7.97/8.14 (Or (Eq (cR (skS.0 8 a_2)) True) (Or (Eq (cQ (skS.0 4 a_3) y) True) (Eq (cQ (skS.0 4 a_4) y) True))))
% 7.97/8.14 Clause #276 (by equality factoring #[241]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.14 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.14 (Or (Eq (cQ (skS.0 4 a_1) y) True)
% 7.97/8.14 (Or (Eq (cR (skS.0 8 a_2)) True) (Or (Ne True True) (Eq (cQ (skS.0 4 a_3) y) True))))
% 7.97/8.14 Clause #277 (by clausification #[276]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.14 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.14 (Or (Eq (cQ (skS.0 4 a_1) y) True)
% 7.97/8.14 (Or (Eq (cR (skS.0 8 a_2)) True) (Or (Eq (cQ (skS.0 4 a_3) y) True) (Or (Eq True False) (Eq True False)))))
% 7.97/8.14 Clause #279 (by clausification #[277]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.14 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.14 (Or (Eq (cQ (skS.0 4 a_1) y) True)
% 7.97/8.14 (Or (Eq (cR (skS.0 8 a_2)) True) (Or (Eq (cQ (skS.0 4 a_3) y) True) (Eq True False))))
% 7.97/8.14 Clause #280 (by clausification #[279]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.14 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.14 (Or (Eq (cQ (skS.0 4 a_1) y) True) (Or (Eq (cR (skS.0 8 a_2)) True) (Eq (cQ (skS.0 4 a_3) y) True)))
% 7.97/8.14 Clause #310 (by equality factoring #[280]): ∀ (a a_1 a_2 : Iota),
% 7.97/8.14 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Ne True True) (Eq (cQ (skS.0 4 a_2) y) True)))
% 7.97/8.14 Clause #343 (by clausification #[310]): ∀ (a a_1 a_2 : Iota),
% 7.97/8.14 Or (Eq (cR (skS.0 8 a)) True)
% 7.97/8.14 (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Eq True False) (Eq True False))))
% 7.97/8.14 Clause #345 (by clausification #[343]): ∀ (a a_1 a_2 : Iota),
% 7.97/8.14 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq (cQ (skS.0 4 a_2) y) True) (Eq True False)))
% 7.97/8.14 Clause #346 (by clausification #[345]): ∀ (a a_1 a_2 : Iota), Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Eq (cQ (skS.0 4 a_2) y) True))
% 7.97/8.14 Clause #359 (by equality factoring #[346]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Or (Ne True True) (Eq (cR (skS.0 8 a_1)) True))
% 7.97/8.14 Clause #360 (by clausification #[359]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq True False) (Eq True False)))
% 7.97/8.14 Clause #362 (by clausification #[360]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Eq True False))
% 7.97/8.14 Clause #363 (by clausification #[362]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Eq (cR (skS.0 8 a_1)) True)
% 7.97/8.14 Clause #500 (by clausification #[92]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 7.97/8.14 Or (Eq (cQ (skS.0 4 a) y) True)
% 7.97/8.14 (Or (Eq (cP a_1 y (skS.0 1 a_2)) True)
% 7.97/8.14 (Or (Eq (cP a_3 y (skS.0 0 (skS.0 3 a_4) a_5)) True) (Eq (cQ (skS.0 4 a_6) y) True)))
% 7.97/8.14 Clause #535 (by equality factoring #[500]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.14 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.14 (Or (Eq (cP a_2 y (skS.0 0 (skS.0 3 a_3) a_4)) True) (Or (Ne True True) (Eq (cQ (skS.0 4 a_5) y) True)))
% 7.97/8.14 Clause #536 (by clausification #[535]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.14 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.14 (Or (Eq (cP a_2 y (skS.0 0 (skS.0 3 a_3) a_4)) True)
% 7.97/8.14 (Or (Eq (cQ (skS.0 4 a_5) y) True) (Or (Eq True False) (Eq True False))))
% 7.97/8.14 Clause #538 (by clausification #[536]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.14 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.14 (Or (Eq (cP a_2 y (skS.0 0 (skS.0 3 a_3) a_4)) True) (Or (Eq (cQ (skS.0 4 a_5) y) True) (Eq True False)))
% 7.97/8.14 Clause #539 (by clausification #[538]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 7.97/8.14 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.14 (Or (Eq (cP a_2 y (skS.0 0 (skS.0 3 a_3) a_4)) True) (Eq (cQ (skS.0 4 a_5) y) True))
% 7.97/8.14 Clause #543 (by superposition #[539, 40]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.14 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.14 (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Eq (cQ (skS.0 4 a_3) y) True) (Or (Eq True False) (Eq (cR a_4) False))))
% 7.97/8.14 Clause #561 (by clausification #[543]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.14 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.14 (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Eq (cQ (skS.0 4 a_3) y) True) (Eq (cR a_4) False)))
% 7.97/8.17 Clause #563 (by superposition #[561, 363]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.17 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.17 (Or (Eq (cQ (skS.0 4 a_2) y) True)
% 7.97/8.17 (Or (Eq (cQ (skS.0 4 a_3) y) True) (Or (Eq (cQ (skS.0 4 a_4) y) True) (Eq False True))))
% 7.97/8.17 Clause #566 (by clausification #[563]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.17 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.17 (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Eq (cQ (skS.0 4 a_3) y) True) (Eq (cQ (skS.0 4 a_4) y) True)))
% 7.97/8.17 Clause #584 (by equality factoring #[566]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.17 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.17 (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Ne True True) (Eq (cQ (skS.0 4 a_3) y) True)))
% 7.97/8.17 Clause #585 (by clausification #[584]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.17 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.17 (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Eq (cQ (skS.0 4 a_3) y) True) (Or (Eq True False) (Eq True False))))
% 7.97/8.17 Clause #587 (by clausification #[585]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.17 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 7.97/8.17 (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Eq (cQ (skS.0 4 a_3) y) True) (Eq True False)))
% 7.97/8.17 Clause #588 (by clausification #[587]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.17 Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cQ (skS.0 4 a_2) y) True) (Eq (cQ (skS.0 4 a_3) y) True))
% 7.97/8.17 Clause #606 (by equality factoring #[588]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Ne True True) (Eq (cQ (skS.0 4 a_2) y) True))
% 7.97/8.17 Clause #630 (by clausification #[606]): ∀ (a a_1 a_2 : Iota),
% 7.97/8.17 Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cQ (skS.0 4 a_2) y) True) (Or (Eq True False) (Eq True False)))
% 7.97/8.17 Clause #632 (by clausification #[630]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cQ (skS.0 4 a_2) y) True) (Eq True False))
% 7.97/8.17 Clause #633 (by clausification #[632]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a y (skS.0 1 a_1)) True) (Eq (cQ (skS.0 4 a_2) y) True)
% 7.97/8.17 Clause #634 (by superposition #[633, 40]): ∀ (a a_1 a_2 : Iota),
% 7.97/8.17 Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cQ (skS.0 4 a_1) y) True) (Or (Eq True False) (Eq (cR a_2) False)))
% 7.97/8.17 Clause #650 (by clausification #[634]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cQ (skS.0 4 a_1) y) True) (Eq (cR a_2) False))
% 7.97/8.17 Clause #652 (by superposition #[650, 363]): ∀ (a a_1 a_2 : Iota),
% 7.97/8.17 Or (Eq (cQ (skS.0 4 a) y) True)
% 7.97/8.17 (Or (Eq (cQ (skS.0 4 a_1) y) True) (Or (Eq (cQ (skS.0 4 a_2) y) True) (Eq False True)))
% 7.97/8.17 Clause #656 (by clausification #[652]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cQ (skS.0 4 a_1) y) True) (Eq (cQ (skS.0 4 a_2) y) True))
% 7.97/8.17 Clause #669 (by equality factoring #[656]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Or (Ne True True) (Eq (cQ (skS.0 4 a_1) y) True))
% 7.97/8.17 Clause #671 (by clausification #[669]): ∀ (a a_1 : Iota),
% 7.97/8.17 Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cQ (skS.0 4 a_1) y) True) (Or (Eq True False) (Eq True False)))
% 7.97/8.17 Clause #673 (by clausification #[671]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq (cQ (skS.0 4 a_1) y) True) (Eq True False))
% 7.97/8.17 Clause #674 (by clausification #[673]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Eq (cQ (skS.0 4 a_1) y) True)
% 7.97/8.17 Clause #686 (by equality factoring #[674]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ (skS.0 4 a) y) True)
% 7.97/8.17 Clause #687 (by clausification #[686]): ∀ (a : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Or (Eq True False) (Eq True False))
% 7.97/8.17 Clause #689 (by clausification #[687]): ∀ (a : Iota), Or (Eq (cQ (skS.0 4 a) y) True) (Eq True False)
% 7.97/8.17 Clause #690 (by clausification #[689]): ∀ (a : Iota), Eq (cQ (skS.0 4 a) y) True
% 7.97/8.17 Clause #691 (by superposition #[690, 23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.17 Or (Eq True False)
% 7.97/8.17 (Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cQ a_2 y) False) (Eq (cP a_3 y (skS.0 0 a_2 a_4)) True)))
% 7.97/8.17 Clause #692 (by superposition #[690, 65]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.97/8.17 Or (Eq True False) (Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cQ a_1 y) False) (Eq (cP a_2 y (skS.0 0 a_1 a_3)) True)))
% 7.97/8.17 Clause #693 (by superposition #[690, 69]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.97/8.17 Or (Eq True False) (Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cQ a_1 y) False) (Eq (cR (skS.0 2 a_1 a_2 a_3 a_4)) True)))
% 8.04/8.20 Clause #703 (by clausification #[692]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cQ a_1 y) False) (Eq (cP a_2 y (skS.0 0 a_1 a_3)) True))
% 8.04/8.20 Clause #709 (by superposition #[703, 690]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cP a_1 y (skS.0 0 (skS.0 4 a_2) a_3)) True) (Eq False True))
% 8.04/8.20 Clause #711 (by clausification #[709]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cR (skS.0 8 a)) True) (Eq (cP a_1 y (skS.0 0 (skS.0 4 a_2) a_3)) True)
% 8.04/8.20 Clause #717 (by superposition #[711, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True)
% 8.04/8.20 (Or (Eq True False) (Or (Eq (cR a_1) False) (Or (Eq (cP (skS.0 6 a_2 a_3 a_4) y a_3) False) (Eq (cR a_5) False))))
% 8.04/8.20 Clause #723 (by clausification #[693]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cQ a_1 y) False) (Eq (cR (skS.0 2 a_1 a_2 a_3 a_4)) True))
% 8.04/8.20 Clause #728 (by superposition #[723, 690]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 2 (skS.0 4 a_1) a_2 a_3 a_4)) True) (Eq False True))
% 8.04/8.20 Clause #729 (by clausification #[691]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.04/8.20 Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cQ a_2 y) False) (Eq (cP a_3 y (skS.0 0 a_2 a_4)) True))
% 8.04/8.20 Clause #734 (by superposition #[729, 690]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.04/8.20 Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cP a_2 y (skS.0 0 (skS.0 4 a_3) a_4)) True) (Eq False True))
% 8.04/8.20 Clause #735 (by clausification #[734]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (cP a y (skS.0 1 a_1)) True) (Eq (cP a_2 y (skS.0 0 (skS.0 4 a_3) a_4)) True)
% 8.04/8.20 Clause #739 (by superposition #[735, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 8.04/8.20 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 8.04/8.20 (Or (Eq True False) (Or (Eq (cR a_2) False) (Or (Eq (cP (skS.0 6 a_3 a_4 a_5) y a_4) False) (Eq (cR a_6) False))))
% 8.04/8.20 Clause #746 (by clausification #[728]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (cR (skS.0 8 a)) True) (Eq (cR (skS.0 2 (skS.0 4 a_1) a_2 a_3 a_4)) True)
% 8.04/8.20 Clause #774 (by clausification #[717]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True)
% 8.04/8.20 (Or (Eq (cR a_1) False) (Or (Eq (cP (skS.0 6 a_2 a_3 a_4) y a_3) False) (Eq (cR a_5) False)))
% 8.04/8.20 Clause #778 (by superposition #[774, 746]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True)
% 8.04/8.20 (Or (Eq (cP (skS.0 6 a_1 a_2 a_3) y a_2) False)
% 8.04/8.20 (Or (Eq (cR a_4) False) (Or (Eq (cR (skS.0 8 a_5)) True) (Eq False True))))
% 8.04/8.20 Clause #864 (by clausification #[739]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 8.04/8.20 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 8.04/8.20 (Or (Eq (cR a_2) False) (Or (Eq (cP (skS.0 6 a_3 a_4 a_5) y a_4) False) (Eq (cR a_6) False)))
% 8.04/8.20 Clause #875 (by clausification #[778]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True)
% 8.04/8.20 (Or (Eq (cP (skS.0 6 a_1 a_2 a_3) y a_2) False) (Or (Eq (cR a_4) False) (Eq (cR (skS.0 8 a_5)) True)))
% 8.04/8.20 Clause #876 (by superposition #[875, 711]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True)
% 8.04/8.20 (Or (Eq (cR a_1) False) (Or (Eq (cR (skS.0 8 a_2)) True) (Or (Eq (cR (skS.0 8 a_3)) True) (Eq False True))))
% 8.04/8.20 Clause #882 (by clausification #[876]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR a_1) False) (Or (Eq (cR (skS.0 8 a_2)) True) (Eq (cR (skS.0 8 a_3)) True)))
% 8.04/8.20 Clause #885 (by superposition #[882, 746]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True)
% 8.04/8.20 (Or (Eq (cR (skS.0 8 a_1)) True)
% 8.04/8.20 (Or (Eq (cR (skS.0 8 a_2)) True) (Or (Eq (cR (skS.0 8 a_3)) True) (Eq False True))))
% 8.04/8.20 Clause #896 (by clausification #[885]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True)
% 8.04/8.20 (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq (cR (skS.0 8 a_2)) True) (Eq (cR (skS.0 8 a_3)) True)))
% 8.04/8.20 Clause #901 (by equality factoring #[896]): ∀ (a a_1 a_2 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Ne True True) (Eq (cR (skS.0 8 a_2)) True)))
% 8.04/8.20 Clause #903 (by clausification #[901]): ∀ (a a_1 a_2 : Iota),
% 8.04/8.20 Or (Eq (cR (skS.0 8 a)) True)
% 8.04/8.20 (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq (cR (skS.0 8 a_2)) True) (Or (Eq True False) (Eq True False))))
% 8.04/8.24 Clause #905 (by clausification #[903]): ∀ (a a_1 a_2 : Iota),
% 8.04/8.24 Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq (cR (skS.0 8 a_2)) True) (Eq True False)))
% 8.04/8.24 Clause #906 (by clausification #[905]): ∀ (a a_1 a_2 : Iota), Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Eq (cR (skS.0 8 a_2)) True))
% 8.04/8.24 Clause #910 (by equality factoring #[906]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 8 a)) True) (Or (Ne True True) (Eq (cR (skS.0 8 a_1)) True))
% 8.04/8.24 Clause #911 (by clausification #[910]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Or (Eq True False) (Eq True False)))
% 8.04/8.24 Clause #913 (by clausification #[911]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 8 a)) True) (Or (Eq (cR (skS.0 8 a_1)) True) (Eq True False))
% 8.04/8.24 Clause #914 (by clausification #[913]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 8 a)) True) (Eq (cR (skS.0 8 a_1)) True)
% 8.04/8.24 Clause #916 (by equality factoring #[914]): ∀ (a : Iota), Or (Ne True True) (Eq (cR (skS.0 8 a)) True)
% 8.04/8.24 Clause #917 (by clausification #[916]): ∀ (a : Iota), Or (Eq (cR (skS.0 8 a)) True) (Or (Eq True False) (Eq True False))
% 8.04/8.24 Clause #919 (by clausification #[917]): ∀ (a : Iota), Or (Eq (cR (skS.0 8 a)) True) (Eq True False)
% 8.04/8.24 Clause #920 (by clausification #[919]): ∀ (a : Iota), Eq (cR (skS.0 8 a)) True
% 8.04/8.24 Clause #921 (by superposition #[920, 864]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.04/8.24 Or (Eq (cP a y (skS.0 1 a_1)) True)
% 8.04/8.24 (Or (Eq True False) (Or (Eq (cP (skS.0 6 a_2 a_3 a_4) y a_3) False) (Eq (cR a_5) False)))
% 8.04/8.24 Clause #923 (by clausification #[921]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.04/8.24 Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cP (skS.0 6 a_2 a_3 a_4) y a_3) False) (Eq (cR a_5) False))
% 8.04/8.24 Clause #925 (by superposition #[923, 735]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.04/8.24 Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cR a_2) False) (Or (Eq (cP a_3 y (skS.0 1 a_4)) True) (Eq False True)))
% 8.04/8.24 Clause #929 (by clausification #[925]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.04/8.24 Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cR a_2) False) (Eq (cP a_3 y (skS.0 1 a_4)) True))
% 8.04/8.24 Clause #931 (by superposition #[929, 920]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq (cP a_2 y (skS.0 1 a_3)) True) (Eq False True))
% 8.04/8.24 Clause #932 (by clausification #[931]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP a y (skS.0 1 a_1)) True) (Eq (cP a_2 y (skS.0 1 a_3)) True)
% 8.04/8.24 Clause #934 (by equality factoring #[932]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (cP a y (skS.0 1 a_1)) True)
% 8.04/8.24 Clause #935 (by clausification #[934]): ∀ (a a_1 : Iota), Or (Eq (cP a y (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False))
% 8.04/8.24 Clause #937 (by clausification #[935]): ∀ (a a_1 : Iota), Or (Eq (cP a y (skS.0 1 a_1)) True) (Eq True False)
% 8.04/8.24 Clause #938 (by clausification #[937]): ∀ (a a_1 : Iota), Eq (cP a y (skS.0 1 a_1)) True
% 8.04/8.24 Clause #939 (by superposition #[938, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.04/8.24 Or (Eq True False) (Or (Eq (cR a) False) (Or (Eq (cP (skS.0 6 a_1 a_2 a_3) y a_2) False) (Eq (cR a_4) False)))
% 8.04/8.24 Clause #941 (by clausification #[939]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (cR a) False) (Or (Eq (cP (skS.0 6 a_1 a_2 a_3) y a_2) False) (Eq (cR a_4) False))
% 8.04/8.24 Clause #942 (by superposition #[941, 920]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP (skS.0 6 a a_1 a_2) y a_1) False) (Or (Eq (cR a_3) False) (Eq False True))
% 8.04/8.24 Clause #943 (by clausification #[942]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP (skS.0 6 a a_1 a_2) y a_1) False) (Eq (cR a_3) False)
% 8.04/8.24 Clause #944 (by superposition #[943, 938]): ∀ (a : Iota), Or (Eq (cR a) False) (Eq False True)
% 8.04/8.24 Clause #945 (by clausification #[944]): ∀ (a : Iota), Eq (cR a) False
% 8.04/8.24 Clause #946 (by superposition #[945, 920]): Eq False True
% 8.04/8.24 Clause #947 (by clausification #[946]): False
% 8.04/8.24 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------