TSTP Solution File: SYN074+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN074+1 : TPTP v8.1.2. Released v2.0.0.
% 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 02:10:29 EDT 2023
% Result : Theorem 8.04s 8.21s
% Output : Proof 8.07s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN074+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 18:38:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 8.04/8.21 SZS status Theorem for theBenchmark.p
% 8.04/8.21 SZS output start Proof for theBenchmark.p
% 8.04/8.21 Clause #0 (by assumption #[]): Eq (Exists fun Z => Exists fun W => ∀ (X Y : Iota), Iff (big_f X Y) (And (Eq X Z) (Eq Y W))) True
% 8.04/8.21 Clause #1 (by assumption #[]): Eq (Not (Exists fun Z => ∀ (X : Iota), Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f X Y) (Eq Y W)) (Eq X Z))) True
% 8.04/8.21 Clause #2 (by clausification #[0]): ∀ (a : Iota), Eq (Exists fun W => ∀ (X Y : Iota), Iff (big_f X Y) (And (Eq X (skS.0 0 a)) (Eq Y W))) True
% 8.04/8.21 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), Eq (∀ (X Y : Iota), Iff (big_f X Y) (And (Eq X (skS.0 0 a)) (Eq Y (skS.0 1 a a_1)))) True
% 8.04/8.21 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Y : Iota), Iff (big_f a Y) (And (Eq a (skS.0 0 a_1)) (Eq Y (skS.0 1 a_1 a_2)))) True
% 8.04/8.21 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Iff (big_f a a_1) (And (Eq a (skS.0 0 a_2)) (Eq a_1 (skS.0 1 a_2 a_3)))) True
% 8.04/8.21 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) True) (Eq (And (Eq a (skS.0 0 a_2)) (Eq a_1 (skS.0 1 a_2 a_3))) False)
% 8.04/8.21 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) False) (Eq (And (Eq a (skS.0 0 a_2)) (Eq a_1 (skS.0 1 a_2 a_3))) True)
% 8.04/8.21 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.21 Or (Eq (big_f a a_1) True) (Or (Eq (Eq a (skS.0 0 a_2)) False) (Eq (Eq a_1 (skS.0 1 a_2 a_3)) False))
% 8.04/8.21 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq (Eq a_1 (skS.0 1 a_2 a_3)) False) (Ne a (skS.0 0 a_2)))
% 8.04/8.21 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) True) (Or (Ne a (skS.0 0 a_2)) (Ne a_1 (skS.0 1 a_2 a_3)))
% 8.04/8.21 Clause #11 (by destructive equality resolution #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a) a_1) True) (Ne a_1 (skS.0 1 a a_2))
% 8.04/8.21 Clause #12 (by destructive equality resolution #[11]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True
% 8.04/8.21 Clause #13 (by clausification #[1]): Eq (Exists fun Z => ∀ (X : Iota), Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f X Y) (Eq Y W)) (Eq X Z)) False
% 8.04/8.21 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (X : Iota), Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f X Y) (Eq Y W)) (Eq X a)) False
% 8.04/8.21 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota),
% 8.04/8.21 Eq (Not (Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y W)) (Eq (skS.0 2 a a_1) a))) True
% 8.04/8.21 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota),
% 8.04/8.21 Eq (Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y W)) (Eq (skS.0 2 a a_1) a)) False
% 8.04/8.21 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota),
% 8.04/8.21 Or (Eq (Exists fun W => ∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y W)) False) (Eq (Eq (skS.0 2 a a_1) a) False)
% 8.04/8.21 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota),
% 8.04/8.21 Or (Eq (Exists fun W => ∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y W)) True) (Eq (Eq (skS.0 2 a a_1) a) True)
% 8.04/8.21 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota),
% 8.04/8.21 Or (Eq (Eq (skS.0 2 a a_1) a) False) (Eq (∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y a_2)) False)
% 8.04/8.21 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y a_2)) False) (Ne (skS.0 2 a a_1) a)
% 8.04/8.21 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.21 Or (Ne (skS.0 2 a a_1) a)
% 8.04/8.21 (Eq (Not (Iff (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) (Eq (skS.0 3 a a_1 a_2 a_3) a_2))) True)
% 8.04/8.21 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.21 Or (Ne (skS.0 2 a a_1) a)
% 8.04/8.21 (Eq (Iff (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) (Eq (skS.0 3 a a_1 a_2 a_3) a_2)) False)
% 8.04/8.21 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.21 Or (Ne (skS.0 2 a a_1) a)
% 8.04/8.21 (Or (Eq (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) False) (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) False))
% 8.04/8.21 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.04/8.21 Or (Ne (skS.0 2 a a_1) a)
% 8.04/8.21 (Or (Eq (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) True) (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) True))
% 8.07/8.24 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Ne (skS.0 2 a a_1) a)
% 8.07/8.24 (Or (Eq (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) False) (Ne (skS.0 3 a a_1 a_2 a_3) a_2))
% 8.07/8.24 Clause #26 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) False) (Eq (Eq a_1 (skS.0 1 a_2 a_3)) True)
% 8.07/8.24 Clause #27 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (Eq a (skS.0 0 a_2)) True)
% 8.07/8.24 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) False) (Eq a_1 (skS.0 1 a_2 a_3))
% 8.07/8.24 Clause #29 (by superposition #[28, 12]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 1 a a_1) (skS.0 1 a_2 a_3)) (Eq False True)
% 8.07/8.24 Clause #30 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq a (skS.0 0 a_2))
% 8.07/8.24 Clause #31 (by superposition #[30, 12]): ∀ (a a_1 : Iota), Or (Eq (skS.0 0 a) (skS.0 0 a_1)) (Eq False True)
% 8.07/8.24 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 0 a_1)
% 8.07/8.24 Clause #33 (by superposition #[32, 12]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) True
% 8.07/8.24 Clause #34 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 8.07/8.24 Or (Eq (Eq (skS.0 2 a a_1) a) True) (Eq (∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y (skS.0 4 a a_1 a_2))) True)
% 8.07/8.24 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 8.07/8.24 Or (Eq (∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y (skS.0 4 a a_1 a_2))) True) (Eq (skS.0 2 a a_1) a)
% 8.07/8.24 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Eq (skS.0 2 a a_1) a) (Eq (Iff (big_f (skS.0 2 a a_1) a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True)
% 8.07/8.24 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Eq (skS.0 2 a a_1) a) (Or (Eq (big_f (skS.0 2 a a_1) a_2) True) (Eq (Eq a_2 (skS.0 4 a a_1 a_3)) False))
% 8.07/8.24 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Eq (skS.0 2 a a_1) a) (Or (Eq (big_f (skS.0 2 a a_1) a_2) True) (Ne a_2 (skS.0 4 a a_1 a_3)))
% 8.07/8.24 Clause #40 (by destructive equality resolution #[39]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 a a_1) a) (Eq (big_f (skS.0 2 a a_1) (skS.0 4 a a_1 a_2)) True)
% 8.07/8.24 Clause #43 (by superposition #[40, 30]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 a a_1) a) (Or (Eq True False) (Eq (skS.0 2 a a_1) (skS.0 0 a_2)))
% 8.07/8.24 Clause #46 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 1 a a_1) (skS.0 1 a_2 a_3)
% 8.07/8.24 Clause #47 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 a a_1) a) (Eq (skS.0 2 a a_1) (skS.0 0 a_2))
% 8.07/8.24 Clause #56 (by equality factoring #[47]): ∀ (a a_1 a_2 : Iota), Or (Ne (skS.0 0 a) a_1) (Eq (skS.0 2 a_1 a_2) a_1)
% 8.07/8.24 Clause #57 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Ne (skS.0 2 a a_1) a)
% 8.07/8.24 (Or (Eq (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) True) (Eq (skS.0 3 a a_1 a_2 a_3) a_2))
% 8.07/8.24 Clause #59 (by destructive equality resolution #[56]): ∀ (a a_1 : Iota), Eq (skS.0 2 (skS.0 0 a) a_1) (skS.0 0 a)
% 8.07/8.24 Clause #60 (by superposition #[59, 25]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Ne (skS.0 0 a) (skS.0 0 a))
% 8.07/8.24 (Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) False) (Ne (skS.0 3 (skS.0 0 a) a_1 a_2 a_3) a_2))
% 8.07/8.24 Clause #61 (by superposition #[59, 57]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Ne (skS.0 0 a) (skS.0 0 a))
% 8.07/8.24 (Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) True) (Eq (skS.0 3 (skS.0 0 a) a_1 a_2 a_3) a_2))
% 8.07/8.24 Clause #233 (by eliminate resolved literals #[60]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) False) (Ne (skS.0 3 (skS.0 0 a) a_1 a_2 a_3) a_2)
% 8.07/8.24 Clause #255 (by eliminate resolved literals #[61]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) True) (Eq (skS.0 3 (skS.0 0 a) a_1 a_2 a_3) a_2)
% 8.07/8.24 Clause #263 (by superposition #[255, 233]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) True)
% 8.07/8.24 (Or (Eq (big_f (skS.0 0 a) a_2) False) (Ne a_2 a_2))
% 8.07/8.24 Clause #737 (by eliminate resolved literals #[263]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.07/8.24 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) True) (Eq (big_f (skS.0 0 a) a_2) False)
% 8.07/8.25 Clause #738 (by superposition #[737, 33]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.07/8.25 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 (skS.0 1 a_2 a_3) a_4)) True) (Eq False True)
% 8.07/8.25 Clause #743 (by clausification #[738]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 (skS.0 1 a_2 a_3) a_4)) True
% 8.07/8.25 Clause #750 (by superposition #[743, 28]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 8.07/8.25 Or (Eq True False) (Eq (skS.0 3 (skS.0 0 a) a_1 (skS.0 1 a_2 a_3) a_4) (skS.0 1 a_5 a_6))
% 8.07/8.25 Clause #760 (by clausification #[750]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), Eq (skS.0 3 (skS.0 0 a) a_1 (skS.0 1 a_2 a_3) a_4) (skS.0 1 a_5 a_6)
% 8.07/8.25 Clause #764 (by superposition #[760, 233]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.07/8.25 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) False) (Ne (skS.0 1 a_1 a_2) (skS.0 1 a_3 a_4))
% 8.07/8.25 Clause #778 (by forward contextual literal cutting #[764, 46]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) False
% 8.07/8.25 Clause #779 (by superposition #[778, 33]): Eq False True
% 8.07/8.25 Clause #781 (by clausification #[779]): False
% 8.07/8.25 SZS output end Proof for theBenchmark.p
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