TSTP Solution File: SYO266^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO266^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n006.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 04:22:00 EDT 2023
% Result : Theorem 3.92s 4.10s
% Output : Proof 3.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO266^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : duper %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 04:41:22 EDT 2023
% 0.12/0.33 % CPUTime :
% 3.92/4.10 SZS status Theorem for theBenchmark.p
% 3.92/4.10 SZS output start Proof for theBenchmark.p
% 3.92/4.10 Clause #0 (by assumption #[]): Eq
% 3.92/4.10 (Not
% 3.92/4.10 (Iff (Exists fun S => ∀ (X : Iota), And (Or (S X) (cP X)) (Or (Not (S X)) (cQ X)))
% 3.92/4.10 (∀ (Y : Iota), Or (cP Y) (cQ Y))))
% 3.92/4.10 True
% 3.92/4.10 Clause #1 (by clausification #[0]): Eq (Iff (Exists fun S => ∀ (X : Iota), And (Or (S X) (cP X)) (Or (Not (S X)) (cQ X))) (∀ (Y : Iota), Or (cP Y) (cQ Y)))
% 3.92/4.10 False
% 3.92/4.10 Clause #2 (by clausification #[1]): Or (Eq (Exists fun S => ∀ (X : Iota), And (Or (S X) (cP X)) (Or (Not (S X)) (cQ X))) False)
% 3.92/4.10 (Eq (∀ (Y : Iota), Or (cP Y) (cQ Y)) False)
% 3.92/4.10 Clause #3 (by clausification #[1]): Or (Eq (Exists fun S => ∀ (X : Iota), And (Or (S X) (cP X)) (Or (Not (S X)) (cQ X))) True)
% 3.92/4.10 (Eq (∀ (Y : Iota), Or (cP Y) (cQ Y)) True)
% 3.92/4.10 Clause #4 (by clausification #[2]): ∀ (a : Iota → Prop),
% 3.92/4.10 Or (Eq (∀ (Y : Iota), Or (cP Y) (cQ Y)) False)
% 3.92/4.10 (Eq (∀ (X : Iota), And (Or (a X) (cP X)) (Or (Not (a X)) (cQ X))) False)
% 3.92/4.10 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 3.92/4.10 Or (Eq (∀ (X : Iota), And (Or (a X) (cP X)) (Or (Not (a X)) (cQ X))) False)
% 3.92/4.10 (Eq (Not (Or (cP (skS.0 0 a_1)) (cQ (skS.0 0 a_1)))) True)
% 3.92/4.10 Clause #6 (by clausification #[5]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.10 Or (Eq (Not (Or (cP (skS.0 0 a)) (cQ (skS.0 0 a)))) True)
% 3.92/4.10 (Eq
% 3.92/4.10 (Not
% 3.92/4.10 (And (Or (a_1 (skS.0 1 a_1 a_2)) (cP (skS.0 1 a_1 a_2)))
% 3.92/4.10 (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2)))))
% 3.92/4.10 True)
% 3.92/4.10 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.92/4.10 Or
% 3.92/4.10 (Eq (Not (And (Or (a (skS.0 1 a a_1)) (cP (skS.0 1 a a_1))) (Or (Not (a (skS.0 1 a a_1))) (cQ (skS.0 1 a a_1)))))
% 3.92/4.10 True)
% 3.92/4.10 (Eq (Or (cP (skS.0 0 a_2)) (cQ (skS.0 0 a_2))) False)
% 3.92/4.10 Clause #8 (by clausification #[7]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.10 Or (Eq (Or (cP (skS.0 0 a)) (cQ (skS.0 0 a))) False)
% 3.92/4.10 (Eq
% 3.92/4.10 (And (Or (a_1 (skS.0 1 a_1 a_2)) (cP (skS.0 1 a_1 a_2)))
% 3.92/4.10 (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))))
% 3.92/4.10 False)
% 3.92/4.10 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.92/4.10 Or (Eq (And (Or (a (skS.0 1 a a_1)) (cP (skS.0 1 a a_1))) (Or (Not (a (skS.0 1 a a_1))) (cQ (skS.0 1 a a_1)))) False)
% 3.92/4.10 (Eq (cQ (skS.0 0 a_2)) False)
% 3.92/4.10 Clause #10 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.92/4.10 Or (Eq (And (Or (a (skS.0 1 a a_1)) (cP (skS.0 1 a a_1))) (Or (Not (a (skS.0 1 a a_1))) (cQ (skS.0 1 a a_1)))) False)
% 3.92/4.10 (Eq (cP (skS.0 0 a_2)) False)
% 3.92/4.10 Clause #11 (by clausification #[9]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.10 Or (Eq (cQ (skS.0 0 a)) False)
% 3.92/4.10 (Or (Eq (Or (a_1 (skS.0 1 a_1 a_2)) (cP (skS.0 1 a_1 a_2))) False)
% 3.92/4.10 (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False))
% 3.92/4.10 Clause #12 (by clausification #[11]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.10 Or (Eq (cQ (skS.0 0 a)) False)
% 3.92/4.10 (Or (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False) (Eq (cP (skS.0 1 a_1 a_2)) False))
% 3.92/4.10 Clause #13 (by clausification #[11]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.10 Or (Eq (cQ (skS.0 0 a)) False)
% 3.92/4.10 (Or (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False) (Eq (a_1 (skS.0 1 a_1 a_2)) False))
% 3.92/4.10 Clause #15 (by clausification #[12]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.10 Or (Eq (cQ (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1 a_2)) False) (Eq (Not (a_1 (skS.0 1 a_1 a_2))) False))
% 3.92/4.10 Clause #16 (by clausification #[3]): ∀ (a : Iota → Prop),
% 3.92/4.10 Or (Eq (∀ (Y : Iota), Or (cP Y) (cQ Y)) True)
% 3.92/4.10 (Eq (∀ (X : Iota), And (Or (skS.0 2 a X) (cP X)) (Or (Not (skS.0 2 a X)) (cQ X))) True)
% 3.92/4.10 Clause #17 (by clausification #[16]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 3.92/4.10 Or (Eq (∀ (X : Iota), And (Or (skS.0 2 a X) (cP X)) (Or (Not (skS.0 2 a X)) (cQ X))) True)
% 3.92/4.10 (Eq (Or (cP a_1) (cQ a_1)) True)
% 3.92/4.10 Clause #18 (by clausification #[17]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.10 Or (Eq (Or (cP a) (cQ a)) True) (Eq (And (Or (skS.0 2 a_1 a_2) (cP a_2)) (Or (Not (skS.0 2 a_1 a_2)) (cQ a_2))) True)
% 3.92/4.10 Clause #19 (by clausification #[18]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.92/4.13 Or (Eq (And (Or (skS.0 2 a a_1) (cP a_1)) (Or (Not (skS.0 2 a a_1)) (cQ a_1))) True)
% 3.92/4.13 (Or (Eq (cP a_2) True) (Eq (cQ a_2) True))
% 3.92/4.13 Clause #20 (by clausification #[19]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.13 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Eq (Or (Not (skS.0 2 a_1 a_2)) (cQ a_2)) True))
% 3.92/4.13 Clause #21 (by clausification #[19]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.13 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Eq (Or (skS.0 2 a_1 a_2) (cP a_2)) True))
% 3.92/4.13 Clause #22 (by clausification #[20]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.13 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (Not (skS.0 2 a_1 a_2)) True) (Eq (cQ a_2) True)))
% 3.92/4.13 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop),
% 3.92/4.13 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Eq (skS.0 2 a_2 a_1) False)))
% 3.92/4.13 Clause #24 (by clausification #[21]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.13 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (skS.0 2 a_1 a_2) True) (Eq (cP a_2) True)))
% 3.92/4.13 Clause #25 (by superposition #[24, 23]): ∀ (a a_1 a_2 : Iota),
% 3.92/4.13 Or (Eq (cP a) True)
% 3.92/4.13 (Or (Eq (cQ a) True)
% 3.92/4.13 (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq (cQ a_2) True) (Or (Eq (cQ a_1) True) (Eq True False))))))
% 3.92/4.13 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 3.92/4.13 Or (Eq (cP a) True)
% 3.92/4.13 (Or (Eq (cQ a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq (cQ a_2) True) (Eq (cQ a_1) True)))))
% 3.92/4.13 Clause #29 (by equality factoring #[26]): ∀ (a a_1 : Iota),
% 3.92/4.13 Or (Eq (cP a) True)
% 3.92/4.13 (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Or (Eq (cQ a_1) True) (Or (Ne True True) (Eq (cP a_1) True)))))
% 3.92/4.13 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota),
% 3.92/4.13 Or (Eq (cP a) True)
% 3.92/4.13 (Or (Eq (cQ a) True)
% 3.92/4.13 (Or (Eq (cQ a_1) True) (Or (Eq (cQ a_1) True) (Or (Eq (cP a_1) True) (Or (Eq True False) (Eq True False))))))
% 3.92/4.13 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota),
% 3.92/4.13 Or (Eq (cP a) True)
% 3.92/4.13 (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Or (Eq (cQ a_1) True) (Or (Eq (cP a_1) True) (Eq True False)))))
% 3.92/4.13 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota),
% 3.92/4.13 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Or (Eq (cQ a_1) True) (Eq (cP a_1) True))))
% 3.92/4.13 Clause #34 (by eliminate duplicate literals #[33]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Eq (cP a_1) True)))
% 3.92/4.13 Clause #35 (by equality factoring #[34]): ∀ (a : Iota), Or (Eq (cQ a) True) (Or (Eq (cQ a) True) (Or (Ne True True) (Eq (cP a) True)))
% 3.92/4.13 Clause #36 (by clausification #[10]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.13 Or (Eq (cP (skS.0 0 a)) False)
% 3.92/4.13 (Or (Eq (Or (a_1 (skS.0 1 a_1 a_2)) (cP (skS.0 1 a_1 a_2))) False)
% 3.92/4.13 (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False))
% 3.92/4.13 Clause #37 (by clausification #[36]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.13 Or (Eq (cP (skS.0 0 a)) False)
% 3.92/4.13 (Or (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False) (Eq (cP (skS.0 1 a_1 a_2)) False))
% 3.92/4.13 Clause #38 (by clausification #[36]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.13 Or (Eq (cP (skS.0 0 a)) False)
% 3.92/4.13 (Or (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False) (Eq (a_1 (skS.0 1 a_1 a_2)) False))
% 3.92/4.13 Clause #40 (by clausification #[37]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.92/4.13 Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1 a_2)) False) (Eq (Not (a_1 (skS.0 1 a_1 a_2))) False))
% 3.92/4.13 Clause #44 (by clausification #[35]): ∀ (a : Iota), Or (Eq (cQ a) True) (Or (Eq (cQ a) True) (Or (Eq (cP a) True) (Or (Eq True False) (Eq True False))))
% 3.92/4.13 Clause #46 (by clausification #[44]): ∀ (a : Iota), Or (Eq (cQ a) True) (Or (Eq (cQ a) True) (Or (Eq (cP a) True) (Eq True False)))
% 3.92/4.13 Clause #47 (by clausification #[46]): ∀ (a : Iota), Or (Eq (cQ a) True) (Or (Eq (cQ a) True) (Eq (cP a) True))
% 3.92/4.13 Clause #48 (by eliminate duplicate literals #[47]): ∀ (a : Iota), Or (Eq (cQ a) True) (Eq (cP a) True)
% 3.92/4.13 Clause #59 (by clausification #[13]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.99/4.16 Or (Eq (cQ (skS.0 0 a)) False) (Or (Eq (a_1 (skS.0 1 a_1 a_2)) False) (Eq (cQ (skS.0 1 a_1 a_2)) False))
% 3.99/4.16 Clause #61 (by clausification #[40]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.99/4.16 Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1 a_2)) False) (Eq (a_1 (skS.0 1 a_1 a_2)) True))
% 3.99/4.16 Clause #62 (by superposition #[61, 48]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.99/4.16 Or (Eq (cP (skS.0 1 a a_1)) False)
% 3.99/4.16 (Or (Eq (a (skS.0 1 a a_1)) True) (Or (Eq (cQ (skS.0 0 a_2)) True) (Eq False True)))
% 3.99/4.16 Clause #63 (by clausification #[15]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.99/4.16 Or (Eq (cQ (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1 a_2)) False) (Eq (a_1 (skS.0 1 a_1 a_2)) True))
% 3.99/4.16 Clause #65 (by clausification #[38]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota),
% 3.99/4.16 Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (a_1 (skS.0 1 a_1 a_2)) False) (Eq (cQ (skS.0 1 a_1 a_2)) False))
% 3.99/4.16 Clause #67 (by superposition #[65, 48]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.99/4.16 Or (Eq (a (skS.0 1 a a_1)) False)
% 3.99/4.16 (Or (Eq (cQ (skS.0 1 a a_1)) False) (Or (Eq (cQ (skS.0 0 a_2)) True) (Eq False True)))
% 3.99/4.16 Clause #69 (by clausification #[67]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.99/4.16 Or (Eq (a (skS.0 1 a a_1)) False) (Or (Eq (cQ (skS.0 1 a a_1)) False) (Eq (cQ (skS.0 0 a_2)) True))
% 3.99/4.16 Clause #78 (by fluidLoobHoist #[69]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.99/4.16 Or (Eq (cQ (skS.0 1 a a_1)) False)
% 3.99/4.16 (Or (Eq (cQ (skS.0 0 a_2)) True) (Or (Eq True False) (Eq (a (skS.0 1 a a_1)) False)))
% 3.99/4.16 Clause #80 (by clausification #[78]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.99/4.16 Or (Eq (cQ (skS.0 1 a a_1)) False) (Or (Eq (cQ (skS.0 0 a_2)) True) (Eq (a (skS.0 1 a a_1)) False))
% 3.99/4.16 Clause #87 (by clausification #[62]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.99/4.16 Or (Eq (cP (skS.0 1 a a_1)) False) (Or (Eq (a (skS.0 1 a a_1)) True) (Eq (cQ (skS.0 0 a_2)) True))
% 3.99/4.16 Clause #88 (by superposition #[87, 48]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.99/4.16 Or (Eq (a (skS.0 1 a a_1)) True) (Or (Eq (cQ (skS.0 0 a_2)) True) (Or (Eq (cQ (skS.0 1 a a_1)) True) (Eq False True)))
% 3.99/4.16 Clause #91 (by clausification #[88]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 3.99/4.16 Or (Eq (a (skS.0 1 a a_1)) True) (Or (Eq (cQ (skS.0 0 a_2)) True) (Eq (cQ (skS.0 1 a a_1)) True))
% 3.99/4.16 Clause #99 (by equality factoring #[91]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Ne True True) (Eq (cQ (skS.0 1 (fun x => cQ x) a_1)) True))
% 3.99/4.16 Clause #137 (by betaEtaReduce #[99]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Ne True True) (Eq (cQ (skS.0 1 cQ a_1)) True))
% 3.99/4.16 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota),
% 3.99/4.16 Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq (cQ (skS.0 1 cQ a_1)) True) (Or (Eq True False) (Eq True False)))
% 3.99/4.16 Clause #140 (by clausification #[138]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq (cQ (skS.0 1 cQ a_1)) True) (Eq True False))
% 3.99/4.16 Clause #141 (by clausification #[140]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cQ (skS.0 1 cQ a_1)) True)
% 3.99/4.16 Clause #145 (by superposition #[141, 80]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq True False) (Or (Eq (cQ (skS.0 0 a_1)) True) (Eq True False)))
% 3.99/4.16 Clause #164 (by clausification #[145]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq (cQ (skS.0 0 a_1)) True) (Eq True False))
% 3.99/4.16 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cQ (skS.0 0 a_1)) True)
% 3.99/4.16 Clause #168 (by equality factoring #[165]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ (skS.0 0 a)) True)
% 3.99/4.16 Clause #178 (by clausification #[168]): ∀ (a : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq True False) (Eq True False))
% 3.99/4.16 Clause #180 (by clausification #[178]): ∀ (a : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq True False)
% 3.99/4.16 Clause #181 (by clausification #[180]): ∀ (a : Iota), Eq (cQ (skS.0 0 a)) True
% 3.99/4.16 Clause #183 (by superposition #[181, 59]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq True False) (Or (Eq (a (skS.0 1 a a_1)) False) (Eq (cQ (skS.0 1 a a_1)) False))
% 3.99/4.16 Clause #184 (by superposition #[181, 63]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq True False) (Or (Eq (cP (skS.0 1 a a_1)) False) (Eq (a (skS.0 1 a a_1)) True))
% 3.99/4.17 Clause #185 (by clausification #[183]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a (skS.0 1 a a_1)) False) (Eq (cQ (skS.0 1 a a_1)) False)
% 3.99/4.17 Clause #196 (by fluidLoobHoist #[185]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cQ (skS.0 1 a a_1)) False) (Or (Eq True False) (Eq (a (skS.0 1 a a_1)) False))
% 3.99/4.17 Clause #198 (by clausification #[196]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cQ (skS.0 1 a a_1)) False) (Eq (a (skS.0 1 a a_1)) False)
% 3.99/4.17 Clause #208 (by clausification #[184]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cP (skS.0 1 a a_1)) False) (Eq (a (skS.0 1 a a_1)) True)
% 3.99/4.17 Clause #209 (by superposition #[208, 48]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a (skS.0 1 a a_1)) True) (Or (Eq (cQ (skS.0 1 a a_1)) True) (Eq False True))
% 3.99/4.17 Clause #214 (by clausification #[209]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a (skS.0 1 a a_1)) True) (Eq (cQ (skS.0 1 a a_1)) True)
% 3.99/4.17 Clause #218 (by equality factoring #[214]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ (skS.0 1 (fun x => cQ x) a)) True)
% 3.99/4.17 Clause #252 (by betaEtaReduce #[218]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ (skS.0 1 cQ a)) True)
% 3.99/4.17 Clause #253 (by clausification #[252]): ∀ (a : Iota), Or (Eq (cQ (skS.0 1 cQ a)) True) (Or (Eq True False) (Eq True False))
% 3.99/4.17 Clause #255 (by clausification #[253]): ∀ (a : Iota), Or (Eq (cQ (skS.0 1 cQ a)) True) (Eq True False)
% 3.99/4.17 Clause #256 (by clausification #[255]): ∀ (a : Iota), Eq (cQ (skS.0 1 cQ a)) True
% 3.99/4.17 Clause #257 (by superposition #[256, 198]): Or (Eq True False) (Eq True False)
% 3.99/4.17 Clause #267 (by clausification #[257]): Eq True False
% 3.99/4.17 Clause #268 (by clausification #[267]): False
% 3.99/4.17 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------