TSTP Solution File: SYN374+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN374+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n015.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 02:11:29 EDT 2023
% Result : Theorem 5.35s 5.55s
% Output : Proof 5.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN374+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n015.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 18:16:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.35/5.55 SZS status Theorem for theBenchmark.p
% 5.35/5.55 SZS output start Proof for theBenchmark.p
% 5.35/5.55 Clause #0 (by assumption #[]): Eq
% 5.35/5.55 (Not
% 5.35/5.55 (Iff (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y))
% 5.35/5.55 (Iff (Exists fun X => big_p X) (∀ (Y : Iota), big_p Y))))
% 5.35/5.55 True
% 5.35/5.55 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)))) True
% 5.35/5.55 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) (Iff (Exists big_p) (∀ (Y : Iota), big_p Y))) False
% 5.35/5.55 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) False)
% 5.35/5.55 (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) False)
% 5.35/5.55 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) True)
% 5.35/5.55 (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) True)
% 5.35/5.55 Clause #5 (by clausification #[3]): ∀ (a : Iota),
% 5.35/5.55 Or (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) False) (Eq (∀ (Y : Iota), Iff (big_p a) (big_p Y)) False)
% 5.35/5.55 Clause #6 (by clausification #[5]): ∀ (a : Iota),
% 5.35/5.55 Or (Eq (∀ (Y : Iota), Iff (big_p a) (big_p Y)) False)
% 5.35/5.55 (Or (Eq (Exists big_p) False) (Eq (∀ (Y : Iota), big_p Y) False))
% 5.35/5.55 Clause #7 (by clausification #[5]): ∀ (a : Iota),
% 5.35/5.55 Or (Eq (∀ (Y : Iota), Iff (big_p a) (big_p Y)) False) (Or (Eq (Exists big_p) True) (Eq (∀ (Y : Iota), big_p Y) True))
% 5.35/5.55 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota),
% 5.35/5.55 Or (Eq (Exists big_p) False)
% 5.35/5.55 (Or (Eq (∀ (Y : Iota), big_p Y) False) (Eq (Not (Iff (big_p a) (big_p (skS.0 0 a a_1)))) True))
% 5.35/5.55 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.55 Or (Eq (∀ (Y : Iota), big_p Y) False)
% 5.35/5.55 (Or (Eq (Not (Iff (big_p a) (big_p (skS.0 0 a a_1)))) True) (Eq (big_p a_2) False))
% 5.35/5.55 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.55 Or (Eq (Not (Iff (big_p a) (big_p (skS.0 0 a a_1)))) True)
% 5.35/5.55 (Or (Eq (big_p a_2) False) (Eq (Not (big_p (skS.0 1 a_3))) True))
% 5.35/5.55 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.55 Or (Eq (big_p a) False)
% 5.35/5.55 (Or (Eq (Not (big_p (skS.0 1 a_1))) True) (Eq (Iff (big_p a_2) (big_p (skS.0 0 a_2 a_3))) False))
% 5.35/5.55 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.55 Or (Eq (big_p a) False) (Or (Eq (Iff (big_p a_1) (big_p (skS.0 0 a_1 a_2))) False) (Eq (big_p (skS.0 1 a_3)) False))
% 5.35/5.55 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.55 Or (Eq (big_p a) False)
% 5.35/5.55 (Or (Eq (big_p (skS.0 1 a_1)) False) (Or (Eq (big_p a_2) False) (Eq (big_p (skS.0 0 a_2 a_3)) False)))
% 5.35/5.55 Clause #15 (by clausification #[7]): ∀ (a a_1 : Iota),
% 5.35/5.55 Or (Eq (Exists big_p) True)
% 5.35/5.55 (Or (Eq (∀ (Y : Iota), big_p Y) True) (Eq (Not (Iff (big_p a) (big_p (skS.0 2 a a_1)))) True))
% 5.35/5.55 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.55 Or (Eq (∀ (Y : Iota), big_p Y) True)
% 5.35/5.55 (Or (Eq (Not (Iff (big_p a) (big_p (skS.0 2 a a_1)))) True) (Eq (big_p (skS.0 3 a_2)) True))
% 5.35/5.55 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.55 Or (Eq (Not (Iff (big_p a) (big_p (skS.0 2 a a_1)))) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Eq (big_p a_3) True))
% 5.35/5.55 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.55 Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Eq (Iff (big_p a_2) (big_p (skS.0 2 a_2 a_3))) False))
% 5.35/5.55 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.55 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.55 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p (skS.0 2 a_2 a_3)) True)))
% 5.35/5.55 Clause #21 (by clausification #[4]): ∀ (a : Iota),
% 5.35/5.55 Or (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) True) (Eq (∀ (Y : Iota), Iff (big_p (skS.0 4 a)) (big_p Y)) True)
% 5.35/5.55 Clause #23 (by clausification #[21]): ∀ (a : Iota),
% 5.35/5.55 Or (Eq (∀ (Y : Iota), Iff (big_p (skS.0 4 a)) (big_p Y)) True)
% 5.35/5.55 (Or (Eq (Exists big_p) False) (Eq (∀ (Y : Iota), big_p Y) True))
% 5.35/5.55 Clause #30 (by clausification #[23]): ∀ (a a_1 : Iota),
% 5.35/5.55 Or (Eq (Exists big_p) False) (Or (Eq (∀ (Y : Iota), big_p Y) True) (Eq (Iff (big_p (skS.0 4 a)) (big_p a_1)) True))
% 5.35/5.55 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.58 Or (Eq (∀ (Y : Iota), big_p Y) True) (Or (Eq (Iff (big_p (skS.0 4 a)) (big_p a_1)) True) (Eq (big_p a_2) False))
% 5.35/5.58 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.58 Or (Eq (Iff (big_p (skS.0 4 a)) (big_p a_1)) True) (Or (Eq (big_p a_2) False) (Eq (big_p a_3) True))
% 5.35/5.58 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.58 Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) True) (Eq (big_p a_3) False)))
% 5.35/5.58 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.58 Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) False) (Eq (big_p a_3) True)))
% 5.35/5.58 Clause #51 (by equality factoring #[20]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.58 Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Or (Ne True True) (Eq (big_p (skS.0 2 a_1 a_2)) True)))
% 5.35/5.58 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.58 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 2 a_1 a_2)) True) (Or (Eq True False) (Eq True False))))
% 5.35/5.58 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.58 Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 2 a_1 a_2)) True) (Eq True False)))
% 5.35/5.58 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Eq (big_p (skS.0 2 a_1 a_2)) True))
% 5.35/5.58 Clause #63 (by superposition #[55, 33]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.35/5.58 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True)
% 5.35/5.58 (Or (Eq True False) (Or (Eq (big_p a_2) True) (Or (Eq (big_p (skS.0 4 a_3)) True) (Eq (big_p a_4) False)))))
% 5.35/5.58 Clause #74 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.35/5.58 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Or (Eq (big_p (skS.0 4 a_3)) True) (Eq (big_p a_4) False))))
% 5.35/5.58 Clause #78 (by superposition #[74, 55]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.35/5.58 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True)
% 5.35/5.58 (Or (Eq (big_p a_2) True)
% 5.35/5.58 (Or (Eq (big_p (skS.0 4 a_3)) True)
% 5.35/5.58 (Or (Eq (big_p (skS.0 3 a_4)) True) (Or (Eq (big_p a_5) True) (Eq False True))))))
% 5.35/5.58 Clause #110 (by clausification #[78]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.35/5.58 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True)
% 5.35/5.58 (Or (Eq (big_p a_2) True)
% 5.35/5.58 (Or (Eq (big_p (skS.0 4 a_3)) True) (Or (Eq (big_p (skS.0 3 a_4)) True) (Eq (big_p a_5) True)))))
% 5.35/5.58 Clause #175 (by equality factoring #[110]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.35/5.58 Or (Eq (big_p a) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True)
% 5.35/5.58 (Or (Eq (big_p (skS.0 4 a_2)) True)
% 5.35/5.58 (Or (Eq (big_p a_3) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_4)) True)))))
% 5.35/5.58 Clause #183 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.35/5.58 Or (Eq (big_p a) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True)
% 5.35/5.58 (Or (Eq (big_p (skS.0 4 a_2)) True)
% 5.35/5.58 (Or (Eq (big_p a_3) True) (Or (Eq (big_p (skS.0 3 a_4)) True) (Or (Eq True False) (Eq True False))))))
% 5.35/5.58 Clause #185 (by clausification #[183]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.35/5.58 Or (Eq (big_p a) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True)
% 5.35/5.58 (Or (Eq (big_p (skS.0 4 a_2)) True)
% 5.35/5.58 (Or (Eq (big_p a_3) True) (Or (Eq (big_p (skS.0 3 a_4)) True) (Eq True False)))))
% 5.35/5.58 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.35/5.58 Or (Eq (big_p a) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True)
% 5.35/5.58 (Or (Eq (big_p (skS.0 4 a_2)) True) (Or (Eq (big_p a_3) True) (Eq (big_p (skS.0 3 a_4)) True))))
% 5.35/5.58 Clause #245 (by equality factoring #[186]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.58 Or (Eq (big_p a) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_3)) True))))
% 5.35/5.58 Clause #246 (by clausification #[245]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.58 Or (Eq (big_p a) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True)
% 5.35/5.58 (Or (Eq (big_p (skS.0 4 a_2)) True) (Or (Eq (big_p (skS.0 3 a_3)) True) (Or (Eq True False) (Eq True False)))))
% 5.35/5.58 Clause #248 (by clausification #[246]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.58 Or (Eq (big_p a) True)
% 5.35/5.58 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) True) (Or (Eq (big_p (skS.0 3 a_3)) True) (Eq True False))))
% 5.35/5.62 Clause #249 (by clausification #[248]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.62 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) True) (Eq (big_p (skS.0 3 a_3)) True)))
% 5.35/5.62 Clause #290 (by equality factoring #[249]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.62 Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_2)) True)))
% 5.35/5.62 Clause #291 (by clausification #[290]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.62 Or (Eq (big_p a) True)
% 5.35/5.62 (Or (Eq (big_p (skS.0 4 a_1)) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Or (Eq True False) (Eq True False))))
% 5.35/5.62 Clause #293 (by clausification #[291]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.62 Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Eq True False)))
% 5.35/5.62 Clause #294 (by clausification #[293]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Eq (big_p (skS.0 3 a_2)) True))
% 5.35/5.62 Clause #331 (by equality factoring #[294]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_1)) True))
% 5.35/5.62 Clause #332 (by clausification #[331]): ∀ (a a_1 : Iota),
% 5.35/5.62 Or (Eq (big_p (skS.0 4 a)) True) (Or (Eq (big_p (skS.0 3 a_1)) True) (Or (Eq True False) (Eq True False)))
% 5.35/5.62 Clause #334 (by clausification #[332]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Or (Eq (big_p (skS.0 3 a_1)) True) (Eq True False))
% 5.35/5.62 Clause #335 (by clausification #[334]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Eq (big_p (skS.0 3 a_1)) True)
% 5.35/5.62 Clause #343 (by superposition #[335, 34]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.62 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.62 (Or (Eq True False) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) False) (Eq (big_p a_3) True))))
% 5.35/5.62 Clause #399 (by clausification #[343]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.62 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.62 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) False) (Eq (big_p a_3) True)))
% 5.35/5.62 Clause #400 (by superposition #[399, 335]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.62 Or (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.62 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Or (Eq False True) (Eq (big_p (skS.0 3 a_3)) True))))
% 5.35/5.62 Clause #402 (by clausification #[400]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.35/5.62 Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p (skS.0 3 a_3)) True)))
% 5.35/5.62 Clause #429 (by equality factoring #[402]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.62 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_2)) True)))
% 5.35/5.62 Clause #432 (by clausification #[429]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.62 Or (Eq (big_p a) True)
% 5.35/5.62 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Or (Eq True False) (Eq True False))))
% 5.35/5.62 Clause #434 (by clausification #[432]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.62 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Eq True False)))
% 5.35/5.62 Clause #435 (by clausification #[434]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Eq (big_p (skS.0 3 a_2)) True))
% 5.35/5.62 Clause #453 (by equality factoring #[435]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_1)) True))
% 5.35/5.62 Clause #454 (by clausification #[453]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 3 a_1)) True) (Or (Eq True False) (Eq True False)))
% 5.35/5.62 Clause #456 (by clausification #[454]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 3 a_1)) True) (Eq True False))
% 5.35/5.62 Clause #457 (by clausification #[456]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p (skS.0 3 a_1)) True)
% 5.35/5.62 Clause #474 (by equality factoring #[457]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 3 a)) True)
% 5.35/5.62 Clause #475 (by clausification #[474]): ∀ (a : Iota), Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq True False) (Eq True False))
% 5.35/5.62 Clause #477 (by clausification #[475]): ∀ (a : Iota), Or (Eq (big_p (skS.0 3 a)) True) (Eq True False)
% 5.35/5.62 Clause #478 (by clausification #[477]): ∀ (a : Iota), Eq (big_p (skS.0 3 a)) True
% 5.35/5.62 Clause #479 (by superposition #[478, 13]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.64 Or (Eq True False)
% 5.35/5.64 (Or (Eq (big_p (skS.0 1 a)) False) (Or (Eq (big_p a_1) False) (Eq (big_p (skS.0 0 a_1 a_2)) False)))
% 5.35/5.64 Clause #480 (by superposition #[478, 33]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.64 Or (Eq True False) (Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Eq (big_p a_2) False)))
% 5.35/5.64 Clause #481 (by superposition #[478, 34]): ∀ (a a_1 a_2 : Iota),
% 5.35/5.64 Or (Eq True False) (Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) False) (Eq (big_p a_2) True)))
% 5.35/5.64 Clause #491 (by clausification #[481]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) False) (Eq (big_p a_2) True))
% 5.35/5.64 Clause #493 (by clausification #[480]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Eq (big_p a_2) False))
% 5.35/5.64 Clause #494 (by superposition #[493, 478]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Eq False True))
% 5.35/5.64 Clause #495 (by clausification #[494]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p (skS.0 4 a_1)) True)
% 5.35/5.64 Clause #500 (by equality factoring #[495]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 4 a)) True)
% 5.35/5.64 Clause #501 (by clausification #[500]): ∀ (a : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Or (Eq True False) (Eq True False))
% 5.35/5.64 Clause #503 (by clausification #[501]): ∀ (a : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Eq True False)
% 5.35/5.64 Clause #504 (by clausification #[503]): ∀ (a : Iota), Eq (big_p (skS.0 4 a)) True
% 5.35/5.64 Clause #505 (by superposition #[504, 491]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq True False) (Eq (big_p a_1) True))
% 5.35/5.64 Clause #506 (by clausification #[505]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p a_1) True)
% 5.35/5.64 Clause #507 (by equality factoring #[506]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p a) True)
% 5.35/5.64 Clause #508 (by clausification #[507]): ∀ (a : Iota), Or (Eq (big_p a) True) (Or (Eq True False) (Eq True False))
% 5.35/5.64 Clause #510 (by clausification #[508]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq True False)
% 5.35/5.64 Clause #511 (by clausification #[510]): ∀ (a : Iota), Eq (big_p a) True
% 5.35/5.64 Clause #538 (by clausification #[479]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Or (Eq (big_p a_1) False) (Eq (big_p (skS.0 0 a_1 a_2)) False))
% 5.35/5.64 Clause #539 (by forward demodulation #[538, 511]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Or (Eq True False) (Eq (big_p (skS.0 0 a_1 a_2)) False))
% 5.35/5.64 Clause #540 (by clausification #[539]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Eq (big_p (skS.0 0 a_1 a_2)) False)
% 5.35/5.64 Clause #541 (by superposition #[540, 511]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a a_1)) False) (Eq False True)
% 5.35/5.64 Clause #542 (by clausification #[541]): ∀ (a a_1 : Iota), Eq (big_p (skS.0 0 a a_1)) False
% 5.35/5.64 Clause #543 (by superposition #[542, 511]): Eq False True
% 5.35/5.64 Clause #546 (by clausification #[543]): False
% 5.35/5.64 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------