TSTP Solution File: SYN347+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN347+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n032.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 02:11:19 EDT 2023
% Result : Theorem 4.19s 4.39s
% Output : Proof 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYN347+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.10 % Command : duper %s
% 0.12/0.30 % Computer : n032.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Sat Aug 26 19:03:14 EDT 2023
% 0.12/0.30 % CPUTime :
% 4.19/4.39 SZS status Theorem for theBenchmark.p
% 4.19/4.39 SZS output start Proof for theBenchmark.p
% 4.19/4.39 Clause #0 (by assumption #[]): Eq
% 4.19/4.39 (Not
% 4.19/4.39 (∀ (Z1 Z2 : Iota),
% 4.19/4.39 Exists fun X1 =>
% 4.19/4.39 Exists fun X2 =>
% 4.19/4.39 ∀ (Y : Iota), Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f Z1 Z2)) (Iff (big_f Z1 Y) (big_f Z2 Y))))
% 4.19/4.39 True
% 4.19/4.39 Clause #1 (by clausification #[0]): Eq
% 4.19/4.39 (∀ (Z1 Z2 : Iota),
% 4.19/4.39 Exists fun X1 =>
% 4.19/4.39 Exists fun X2 =>
% 4.19/4.39 ∀ (Y : Iota), Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f Z1 Z2)) (Iff (big_f Z1 Y) (big_f Z2 Y)))
% 4.19/4.39 False
% 4.19/4.39 Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (Not
% 4.19/4.39 (∀ (Z2 : Iota),
% 4.19/4.39 Exists fun X1 =>
% 4.19/4.39 Exists fun X2 =>
% 4.19/4.39 ∀ (Y : Iota),
% 4.19/4.39 Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f (skS.0 0 a) Z2)) (Iff (big_f (skS.0 0 a) Y) (big_f Z2 Y))))
% 4.19/4.39 True
% 4.19/4.39 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (∀ (Z2 : Iota),
% 4.19/4.39 Exists fun X1 =>
% 4.19/4.39 Exists fun X2 =>
% 4.19/4.39 ∀ (Y : Iota),
% 4.19/4.39 Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f (skS.0 0 a) Z2)) (Iff (big_f (skS.0 0 a) Y) (big_f Z2 Y)))
% 4.19/4.39 False
% 4.19/4.39 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (Not
% 4.19/4.39 (Exists fun X1 =>
% 4.19/4.39 Exists fun X2 =>
% 4.19/4.39 ∀ (Y : Iota),
% 4.19/4.39 Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f (skS.0 0 a) (skS.0 1 a a_1)))
% 4.19/4.39 (Iff (big_f (skS.0 0 a) Y) (big_f (skS.0 1 a a_1) Y))))
% 4.19/4.39 True
% 4.19/4.39 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (Exists fun X1 =>
% 4.19/4.39 Exists fun X2 =>
% 4.19/4.39 ∀ (Y : Iota),
% 4.19/4.39 Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f (skS.0 0 a) (skS.0 1 a a_1)))
% 4.19/4.39 (Iff (big_f (skS.0 0 a) Y) (big_f (skS.0 1 a a_1) Y)))
% 4.19/4.39 False
% 4.19/4.39 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (Exists fun X2 =>
% 4.19/4.39 ∀ (Y : Iota),
% 4.19/4.39 Or (Iff (Iff (big_f a Y) (big_f X2 Y)) (big_f (skS.0 0 a_1) (skS.0 1 a_1 a_2)))
% 4.19/4.39 (Iff (big_f (skS.0 0 a_1) Y) (big_f (skS.0 1 a_1 a_2) Y)))
% 4.19/4.39 False
% 4.19/4.39 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (∀ (Y : Iota),
% 4.19/4.39 Or (Iff (Iff (big_f a Y) (big_f a_1 Y)) (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3)))
% 4.19/4.39 (Iff (big_f (skS.0 0 a_2) Y) (big_f (skS.0 1 a_2 a_3) Y)))
% 4.19/4.39 False
% 4.19/4.39 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (Not
% 4.19/4.39 (Or
% 4.19/4.39 (Iff (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)))
% 4.19/4.39 (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3)))
% 4.19/4.39 (Iff (big_f (skS.0 0 a_2) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f (skS.0 1 a_2 a_3) (skS.0 2 a a_1 a_2 a_3 a_4)))))
% 4.19/4.39 True
% 4.19/4.39 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (Or
% 4.19/4.39 (Iff (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)))
% 4.19/4.39 (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3)))
% 4.19/4.39 (Iff (big_f (skS.0 0 a_2) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f (skS.0 1 a_2 a_3) (skS.0 2 a a_1 a_2 a_3 a_4))))
% 4.19/4.39 False
% 4.19/4.39 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.19/4.39 Eq (Iff (big_f (skS.0 0 a) (skS.0 2 a_1 a_2 a a_3 a_4)) (big_f (skS.0 1 a a_3) (skS.0 2 a_1 a_2 a a_3 a_4))) False
% 4.19/4.39 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.19/4.39 Eq
% 4.19/4.39 (Iff (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)))
% 4.19/4.39 (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3)))
% 4.19/4.39 False
% 4.19/4.39 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.19/4.39 Or (Eq (big_f (skS.0 0 a) (skS.0 2 a_1 a_2 a a_3 a_4)) False)
% 4.19/4.39 (Eq (big_f (skS.0 1 a a_3) (skS.0 2 a_1 a_2 a a_3 a_4)) False)
% 4.19/4.39 Clause #13 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.19/4.39 Or (Eq (big_f (skS.0 0 a) (skS.0 2 a_1 a_2 a a_3 a_4)) True)
% 4.19/4.39 (Eq (big_f (skS.0 1 a a_3) (skS.0 2 a_1 a_2 a a_3 a_4)) True)
% 4.19/4.39 Clause #14 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.19/4.39 Or (Eq (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4))) False)
% 4.19/4.39 (Eq (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3)) False)
% 4.19/4.39 Clause #15 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.19/4.39 Or (Eq (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4))) True)
% 4.22/4.41 (Eq (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3)) True)
% 4.22/4.41 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False)
% 4.22/4.41 (Or (Eq (big_f a_2 (skS.0 2 a_2 a_3 a a_1 a_4)) False) (Eq (big_f a_3 (skS.0 2 a_2 a_3 a a_1 a_4)) False))
% 4.22/4.41 Clause #17 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False)
% 4.22/4.41 (Or (Eq (big_f a_2 (skS.0 2 a_2 a_3 a a_1 a_4)) True) (Eq (big_f a_3 (skS.0 2 a_2 a_3 a a_1 a_4)) True))
% 4.22/4.41 Clause #18 (by clausification #[15]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f a_2 (skS.0 2 a_2 a_3 a a_1 a_4)) True) (Eq (big_f a_3 (skS.0 2 a_2 a_3 a a_1 a_4)) False))
% 4.22/4.41 Clause #19 (by clausification #[15]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f a_2 (skS.0 2 a_2 a_3 a a_1 a_4)) False) (Eq (big_f a_3 (skS.0 2 a_2 a_3 a a_1 a_4)) True))
% 4.22/4.41 Clause #21 (by superposition #[19, 13]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f a_2 (skS.0 2 (skS.0 1 a a_1) a_2 a a_1 a_3)) True)
% 4.22/4.41 (Or (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) a_2 a a_1 a_3)) True) (Eq False True)))
% 4.22/4.41 Clause #34 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f a_2 (skS.0 2 (skS.0 1 a a_1) a_2 a a_1 a_3)) True)
% 4.22/4.41 (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) a_2 a a_1 a_3)) True))
% 4.22/4.41 Clause #37 (by equality factoring #[34]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Ne True True) (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True))
% 4.22/4.41 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True)
% 4.22/4.41 (Or (Eq True False) (Eq True False)))
% 4.22/4.41 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True) (Eq True False))
% 4.22/4.41 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True)
% 4.22/4.41 Clause #42 (by superposition #[41, 12]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq True False) (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) False))
% 4.22/4.41 Clause #43 (by superposition #[41, 18]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True) (Eq True False)))
% 4.22/4.41 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) False)
% 4.22/4.41 Clause #46 (by clausification #[43]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True))
% 4.22/4.41 Clause #47 (by eliminate duplicate literals #[46]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True)
% 4.22/4.41 Clause #48 (by superposition #[47, 44]): ∀ (a a_1 : Iota),
% 4.22/4.41 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False))
% 4.22/4.41 Clause #52 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.22/4.41 Clause #53 (by eliminate duplicate literals #[52]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True
% 4.22/4.42 Clause #61 (by superposition #[53, 16]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.22/4.42 Or (Eq True False)
% 4.22/4.42 (Or (Eq (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) False) (Eq (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)) False))
% 4.22/4.42 Clause #62 (by superposition #[53, 17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.22/4.42 Or (Eq True False)
% 4.22/4.42 (Or (Eq (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) True) (Eq (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)) True))
% 4.22/4.42 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.22/4.42 Or (Eq (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) True) (Eq (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)) True)
% 4.22/4.42 Clause #66 (by equality factoring #[63]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne True True) (Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) True)
% 4.22/4.42 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) True) (Or (Eq True False) (Eq True False))
% 4.22/4.42 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) True) (Eq True False)
% 4.22/4.42 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) True
% 4.22/4.42 Clause #77 (by clausification #[61]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.22/4.42 Or (Eq (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) False) (Eq (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)) False)
% 4.22/4.42 Clause #80 (by superposition #[77, 70]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) False) (Eq False True)
% 4.22/4.42 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) False
% 4.22/4.42 Clause #83 (by superposition #[81, 70]): Eq False True
% 4.22/4.42 Clause #87 (by clausification #[83]): False
% 4.22/4.42 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------