TSTP Solution File: SYO256^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO256^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 04:21:59 EDT 2023
% Result : Theorem 4.51s 4.79s
% Output : Proof 4.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO256^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 07:07:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.51/4.79 SZS status Theorem for theBenchmark.p
% 4.51/4.79 SZS output start Proof for theBenchmark.p
% 4.51/4.79 Clause #0 (by assumption #[]): Eq (Not (∀ (Xr : Prop → Prop) (Xp Xq : a → Prop), Exists fun Xh => Iff (Xr Xh) (Xr (∀ (Xx : a), Or (Xp Xx) (Xq Xx)))))
% 4.51/4.79 True
% 4.51/4.79 Clause #1 (by clausification #[0]): Eq (∀ (Xr : Prop → Prop) (Xp Xq : a → Prop), Exists fun Xh => Iff (Xr Xh) (Xr (∀ (Xx : a), Or (Xp Xx) (Xq Xx)))) False
% 4.51/4.79 Clause #2 (by clausification #[1]): ∀ (a_1 : Prop → Prop),
% 4.51/4.79 Eq (Not (∀ (Xp Xq : a → Prop), Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (Xp Xx) (Xq Xx)))))
% 4.51/4.79 True
% 4.51/4.79 Clause #3 (by clausification #[2]): ∀ (a_1 : Prop → Prop),
% 4.51/4.79 Eq (∀ (Xp Xq : a → Prop), Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (Xp Xx) (Xq Xx)))) False
% 4.51/4.79 Clause #4 (by clausification #[3]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop),
% 4.51/4.79 Eq
% 4.51/4.79 (Not
% 4.51/4.79 (∀ (Xq : a → Prop),
% 4.51/4.79 Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (Xq Xx)))))
% 4.51/4.79 True
% 4.51/4.79 Clause #5 (by clausification #[4]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop),
% 4.51/4.79 Eq
% 4.51/4.79 (∀ (Xq : a → Prop),
% 4.51/4.79 Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (Xq Xx))))
% 4.51/4.79 False
% 4.51/4.79 Clause #6 (by clausification #[5]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop),
% 4.51/4.79 Eq
% 4.51/4.79 (Not
% 4.51/4.79 (Exists fun Xh =>
% 4.51/4.79 Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)))))
% 4.51/4.79 True
% 4.51/4.79 Clause #7 (by clausification #[6]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop),
% 4.51/4.79 Eq
% 4.51/4.79 (Exists fun Xh => Iff (skS.0 0 a_1 Xh) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))))
% 4.51/4.79 False
% 4.51/4.79 Clause #8 (by clausification #[7]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop),
% 4.51/4.79 Eq (Iff (skS.0 0 a_1 a_2) (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)))) False
% 4.51/4.79 Clause #9 (by clausification #[8]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop),
% 4.51/4.79 Or (Eq (skS.0 0 a_1 a_2) False)
% 4.51/4.79 (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx))) False)
% 4.51/4.79 Clause #10 (by clausification #[8]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop),
% 4.51/4.79 Or (Eq (skS.0 0 a_1 a_2) True) (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx))) True)
% 4.51/4.79 Clause #11 (by identity loobHoist #[9]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : Prop),
% 4.51/4.79 Or (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) False)
% 4.51/4.79 (Or (Eq (skS.0 0 a_1 True) False) (Eq a_4 False))
% 4.51/4.79 Clause #12 (by identity boolHoist #[9]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : Prop),
% 4.51/4.79 Or (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) False)
% 4.51/4.79 (Or (Eq (skS.0 0 a_1 False) False) (Eq a_4 True))
% 4.51/4.79 Clause #13 (by identity loobHoist #[11]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop),
% 4.51/4.79 Or (Eq (skS.0 0 a_1 True) False)
% 4.51/4.79 (Or (Eq a_2 False)
% 4.51/4.79 (Or (Eq (skS.0 0 a_1 True) False) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) False)))
% 4.51/4.79 Clause #15 (by clausification #[13]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.79 Or (Eq (skS.0 0 a_1 True) False)
% 4.51/4.79 (Or (Eq a_2 False)
% 4.51/4.79 (Or (Eq (skS.0 0 a_1 True) False)
% 4.51/4.79 (Eq (Not (Or (skS.0 1 a_1 a_3 (skS.0 3 a_1 a_3 a_4 a_5)) (skS.0 2 a_1 a_3 a_4 (skS.0 3 a_1 a_3 a_4 a_5))))
% 4.51/4.79 True)))
% 4.51/4.79 Clause #16 (by clausification #[15]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.79 Or (Eq (skS.0 0 a_1 True) False)
% 4.51/4.79 (Or (Eq a_2 False)
% 4.51/4.79 (Or (Eq (skS.0 0 a_1 True) False)
% 4.51/4.79 (Eq (Or (skS.0 1 a_1 a_3 (skS.0 3 a_1 a_3 a_4 a_5)) (skS.0 2 a_1 a_3 a_4 (skS.0 3 a_1 a_3 a_4 a_5))) False)))
% 4.51/4.79 Clause #17 (by clausification #[16]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.79 Or (Eq (skS.0 0 a_1 True) False)
% 4.51/4.79 (Or (Eq a_2 False) (Or (Eq (skS.0 0 a_1 True) False) (Eq (skS.0 2 a_1 a_3 a_4 (skS.0 3 a_1 a_3 a_4 a_5)) False)))
% 4.51/4.82 Clause #18 (by clausification #[16]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) False)
% 4.51/4.82 (Or (Eq a_2 False) (Or (Eq (skS.0 0 a_1 True) False) (Eq (skS.0 1 a_1 a_3 (skS.0 3 a_1 a_3 a_4 a_5)) False)))
% 4.51/4.82 Clause #19 (by eliminate duplicate literals #[17]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) False) (Or (Eq a_2 False) (Eq (skS.0 2 a_1 a_3 a_4 (skS.0 3 a_1 a_3 a_4 a_5)) False))
% 4.51/4.82 Clause #20 (by identity loobHoist #[10]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : Prop),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) True)
% 4.51/4.82 (Or (Eq (skS.0 0 a_1 True) True) (Eq a_4 False))
% 4.51/4.82 Clause #21 (by identity boolHoist #[10]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : Prop),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 (∀ (Xx : a), Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) True)
% 4.51/4.82 (Or (Eq (skS.0 0 a_1 False) True) (Eq a_4 True))
% 4.51/4.82 Clause #22 (by identity loobHoist #[20]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True)
% 4.51/4.82 (Or (Eq a_2 False)
% 4.51/4.82 (Or (Eq (skS.0 0 a_1 True) True) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) False)))
% 4.51/4.82 Clause #23 (by identity boolHoist #[20]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True)
% 4.51/4.82 (Or (Eq a_2 False)
% 4.51/4.82 (Or (Eq (skS.0 0 a_1 False) True) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) True)))
% 4.51/4.82 Clause #24 (by clausification #[22]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True)
% 4.51/4.82 (Or (Eq a_2 False)
% 4.51/4.82 (Or (Eq (skS.0 0 a_1 True) True)
% 4.51/4.82 (Eq (Not (Or (skS.0 1 a_1 a_3 (skS.0 4 a_1 a_3 a_4 a_5)) (skS.0 2 a_1 a_3 a_4 (skS.0 4 a_1 a_3 a_4 a_5))))
% 4.51/4.82 True)))
% 4.51/4.82 Clause #25 (by clausification #[24]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True)
% 4.51/4.82 (Or (Eq a_2 False)
% 4.51/4.82 (Or (Eq (skS.0 0 a_1 True) True)
% 4.51/4.82 (Eq (Or (skS.0 1 a_1 a_3 (skS.0 4 a_1 a_3 a_4 a_5)) (skS.0 2 a_1 a_3 a_4 (skS.0 4 a_1 a_3 a_4 a_5))) False)))
% 4.51/4.82 Clause #26 (by clausification #[25]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True)
% 4.51/4.82 (Or (Eq a_2 False) (Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 2 a_1 a_3 a_4 (skS.0 4 a_1 a_3 a_4 a_5)) False)))
% 4.51/4.82 Clause #27 (by clausification #[25]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True)
% 4.51/4.82 (Or (Eq a_2 False) (Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 1 a_1 a_3 (skS.0 4 a_1 a_3 a_4 a_5)) False)))
% 4.51/4.82 Clause #28 (by eliminate duplicate literals #[26]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True) (Or (Eq a_2 False) (Eq (skS.0 2 a_1 a_3 a_4 (skS.0 4 a_1 a_3 a_4 a_5)) False))
% 4.51/4.82 Clause #29 (by falseElim #[28]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) False)
% 4.51/4.82 Clause #30 (by eliminate duplicate literals #[18]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) False) (Or (Eq a_2 False) (Eq (skS.0 1 a_1 a_3 (skS.0 3 a_1 a_3 a_4 a_5)) False))
% 4.51/4.82 Clause #31 (by eliminate duplicate literals #[27]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True) (Or (Eq a_2 False) (Eq (skS.0 1 a_1 a_3 (skS.0 4 a_1 a_3 a_4 a_5)) False))
% 4.51/4.82 Clause #32 (by falseElim #[31]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False)
% 4.51/4.82 Clause #34 (by identity boolHoist #[12]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop),
% 4.51/4.82 Or (Eq (skS.0 0 a_1 False) False)
% 4.51/4.82 (Or (Eq a_2 True)
% 4.51/4.82 (Or (Eq (skS.0 0 a_1 False) False) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) True)))
% 4.66/4.85 Clause #40 (by identity boolHoist #[21]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 a_4 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.85 (Or (Eq a_2 True)
% 4.66/4.85 (Or (Eq (skS.0 0 a_1 False) True) (Eq (∀ (Xx : a), Or (skS.0 1 a_1 a_3 Xx) (skS.0 2 a_1 a_3 a_4 Xx)) True)))
% 4.66/4.85 Clause #47 (by clausification #[23]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.85 (Or (Eq a_2 False)
% 4.66/4.85 (Or (Eq (skS.0 0 a_1 False) True) (Eq (Or (skS.0 1 a_1 a_3 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) True)))
% 4.66/4.85 Clause #48 (by clausification #[47]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.85 (Or (Eq a_2 False)
% 4.66/4.85 (Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True))))
% 4.66/4.85 Clause #49 (by falseElim #[48]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.85 (Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True)))
% 4.66/4.85 Clause #50 (by superposition #[49, 29]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.85 Or (Eq (skS.0 0 (fun x => a_1 x) True) True)
% 4.66/4.85 (Or (Eq (skS.0 0 (fun x => a_1 x) False) True)
% 4.66/4.85 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 4.66/4.85 (Or (Eq (skS.0 0 a_1 True) True) (Eq True False))))
% 4.66/4.85 Clause #52 (by clausification #[34]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) False)
% 4.66/4.85 (Or (Eq a_2 True)
% 4.66/4.85 (Or (Eq (skS.0 0 a_1 False) False) (Eq (Or (skS.0 1 a_1 a_3 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) True)))
% 4.66/4.85 Clause #53 (by clausification #[52]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) False)
% 4.66/4.85 (Or (Eq a_2 True)
% 4.66/4.85 (Or (Eq (skS.0 0 a_1 False) False) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True))))
% 4.66/4.85 Clause #54 (by eliminate duplicate literals #[53]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) False)
% 4.66/4.85 (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True)))
% 4.66/4.85 Clause #55 (by clausification #[40]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.85 (Or (Eq a_2 True) (Or (Eq (skS.0 0 a_1 False) True) (Eq (Or (skS.0 1 a_1 a_3 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) True)))
% 4.66/4.85 Clause #56 (by clausification #[55]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.85 (Or (Eq a_2 True)
% 4.66/4.85 (Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True))))
% 4.66/4.85 Clause #57 (by eliminate duplicate literals #[56]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.85 (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True)))
% 4.66/4.85 Clause #71 (by equality factoring #[57]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.85 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Ne True True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True)))
% 4.66/4.85 Clause #72 (by clausification #[71]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.85 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Or (Eq True False) (Eq True False))))
% 4.66/4.85 Clause #74 (by clausification #[72]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.85 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Eq True False)))
% 4.66/4.85 Clause #75 (by clausification #[74]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.85 Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True))
% 4.66/4.87 Clause #78 (by betaEtaReduce #[50]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.87 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Or (Eq (skS.0 0 a_1 True) True) (Eq True False))))
% 4.66/4.87 Clause #79 (by clausification #[78]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq (skS.0 0 a_1 False) True)
% 4.66/4.87 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 True) True)))
% 4.66/4.87 Clause #80 (by eliminate duplicate literals #[79]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq (skS.0 0 a_1 False) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True))
% 4.66/4.87 Clause #81 (by superposition #[80, 32]): ∀ (a : Prop → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 (fun x => a x) True) True)
% 4.66/4.87 (Or (Eq (skS.0 0 (fun x => a x) False) True) (Or (Eq (skS.0 0 a True) True) (Eq True False)))
% 4.66/4.87 Clause #82 (by betaEtaReduce #[81]): ∀ (a : Prop → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 a True) True) (Or (Eq (skS.0 0 a False) True) (Or (Eq (skS.0 0 a True) True) (Eq True False)))
% 4.66/4.87 Clause #83 (by clausification #[82]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Or (Eq (skS.0 0 a False) True) (Eq (skS.0 0 a True) True))
% 4.66/4.87 Clause #84 (by eliminate duplicate literals #[83]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq (skS.0 0 a False) True)
% 4.66/4.87 Clause #87 (by superposition #[84, 54]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 (fun x => a_1 x) True) True)
% 4.66/4.87 (Or (Eq True False) (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True))))
% 4.66/4.87 Clause #88 (by betaEtaReduce #[87]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq True False) (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True))))
% 4.66/4.87 Clause #89 (by clausification #[88]): ∀ (a_1 : Prop → Prop) (a_2 : Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq a_2 True) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 2 a_1 a_3 a_5 a_4) True)))
% 4.66/4.87 Clause #101 (by equality factoring #[89]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Ne True True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True)))
% 4.66/4.87 Clause #102 (by clausification #[101]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Or (Eq True False) (Eq True False))))
% 4.66/4.87 Clause #104 (by clausification #[102]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Eq True False)))
% 4.66/4.87 Clause #105 (by clausification #[104]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True) (Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True))
% 4.66/4.87 Clause #106 (by superposition #[105, 29]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.87 Or (Eq (skS.0 0 (fun x => a_1 x) True) True)
% 4.66/4.87 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 4.66/4.87 (Or (Eq (skS.0 0 a_1 True) True) (Eq True False)))
% 4.66/4.87 Clause #132 (by betaEtaReduce #[106]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Or (Eq (skS.0 0 a_1 True) True) (Eq True False)))
% 4.66/4.87 Clause #133 (by clausification #[132]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.87 Or (Eq (skS.0 0 a_1 True) True)
% 4.66/4.87 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 True) True))
% 4.66/4.90 Clause #134 (by eliminate duplicate literals #[133]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.90 Or (Eq (skS.0 0 a_1 True) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 4.66/4.90 Clause #135 (by superposition #[134, 32]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 (fun x => a x) True) True) (Or (Eq (skS.0 0 a True) True) (Eq True False))
% 4.66/4.90 Clause #136 (by betaEtaReduce #[135]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Or (Eq (skS.0 0 a True) True) (Eq True False))
% 4.66/4.90 Clause #137 (by clausification #[136]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq (skS.0 0 a True) True)
% 4.66/4.90 Clause #138 (by eliminate duplicate literals #[137]): ∀ (a : Prop → Prop), Eq (skS.0 0 a True) True
% 4.66/4.90 Clause #139 (by backward demodulation #[138, 19]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.66/4.90 Or (Eq True False) (Or (Eq a_1 False) (Eq (skS.0 2 a_2 a_3 a_4 (skS.0 3 a_2 a_3 a_4 a_5)) False))
% 4.66/4.90 Clause #141 (by backward demodulation #[138, 30]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.66/4.90 Or (Eq True False) (Or (Eq a_1 False) (Eq (skS.0 1 a_2 a_3 (skS.0 3 a_2 a_3 a_4 a_5)) False))
% 4.66/4.90 Clause #152 (by clausification #[141]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.66/4.90 Or (Eq a_1 False) (Eq (skS.0 1 a_2 a_3 (skS.0 3 a_2 a_3 a_4 a_5)) False)
% 4.66/4.90 Clause #155 (by falseElim #[152]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) False
% 4.66/4.90 Clause #159 (by clausification #[139]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 a_4 : a → Prop) (a_5 : a),
% 4.66/4.90 Or (Eq a_1 False) (Eq (skS.0 2 a_2 a_3 a_4 (skS.0 3 a_2 a_3 a_4 a_5)) False)
% 4.66/4.90 Clause #162 (by falseElim #[159]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False
% 4.66/4.90 Clause #163 (by superposition #[162, 75]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.90 Or (Eq (skS.0 0 a_1 False) True) (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq False True))
% 4.66/4.90 Clause #166 (by clausification #[163]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.90 Or (Eq (skS.0 0 a_1 False) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 4.66/4.90 Clause #167 (by superposition #[166, 155]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 (fun x => a x) False) True) (Eq True False)
% 4.66/4.90 Clause #168 (by betaEtaReduce #[167]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a False) True) (Eq True False)
% 4.66/4.90 Clause #169 (by clausification #[168]): ∀ (a : Prop → Prop), Eq (skS.0 0 a False) True
% 4.66/4.90 Clause #170 (by backward demodulation #[169, 54]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.90 Or (Eq True False) (Or (Eq a_1 True) (Or (Eq (skS.0 1 a_2 a_3 a_4) True) (Eq (skS.0 2 a_2 a_3 a_5 a_4) True)))
% 4.66/4.90 Clause #172 (by clausification #[170]): ∀ (a_1 : Prop) (a_2 : Prop → Prop) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 4.66/4.90 Or (Eq a_1 True) (Or (Eq (skS.0 1 a_2 a_3 a_4) True) (Eq (skS.0 2 a_2 a_3 a_5 a_4) True))
% 4.66/4.90 Clause #173 (by superposition #[172, 155]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.90 Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 2 a_1 a_2 a_4 a_3) True) (Eq True False))
% 4.66/4.90 Clause #180 (by clausification #[173]): ∀ (a_1 : Prop → Prop) (a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 4.66/4.90 Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True)
% 4.66/4.90 Clause #181 (by superposition #[180, 162]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.90 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq True False)
% 4.66/4.90 Clause #184 (by betaEtaReduce #[181]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a),
% 4.66/4.90 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq True False)
% 4.66/4.90 Clause #185 (by clausification #[184]): ∀ (a_1 : Prop → Prop) (a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True
% 4.66/4.90 Clause #186 (by superposition #[185, 155]): Eq True False
% 4.66/4.90 Clause #187 (by clausification #[186]): False
% 4.72/4.90 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------