TSTP Solution File: SYN075+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN075+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n013.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 25.34s 25.51s
% Output : Proof 25.34s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN075+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n013.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 21:00:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 25.34/25.51 SZS status Theorem for theBenchmark.p
% 25.34/25.51 SZS output start Proof for theBenchmark.p
% 25.34/25.51 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
% 25.34/25.51 Clause #1 (by assumption #[]): Eq (Not (Exists fun W => ∀ (Y : Iota), Iff (Exists fun Z => ∀ (X : Iota), Iff (big_f X Y) (Eq X Z)) (Eq Y W))) True
% 25.34/25.51 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
% 25.34/25.51 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
% 25.34/25.51 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
% 25.34/25.51 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
% 25.34/25.51 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)
% 25.34/25.51 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)
% 25.34/25.51 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.51 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))
% 25.34/25.51 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)))
% 25.34/25.51 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)))
% 25.34/25.51 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))
% 25.34/25.51 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
% 25.34/25.51 Clause #13 (by clausification #[1]): Eq (Exists fun W => ∀ (Y : Iota), Iff (Exists fun Z => ∀ (X : Iota), Iff (big_f X Y) (Eq X Z)) (Eq Y W)) False
% 25.34/25.51 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (Exists fun Z => ∀ (X : Iota), Iff (big_f X Y) (Eq X Z)) (Eq Y a)) False
% 25.34/25.51 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota),
% 25.34/25.51 Eq (Not (Iff (Exists fun Z => ∀ (X : Iota), Iff (big_f X (skS.0 2 a a_1)) (Eq X Z)) (Eq (skS.0 2 a a_1) a))) True
% 25.34/25.51 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota),
% 25.34/25.51 Eq (Iff (Exists fun Z => ∀ (X : Iota), Iff (big_f X (skS.0 2 a a_1)) (Eq X Z)) (Eq (skS.0 2 a a_1) a)) False
% 25.34/25.51 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota),
% 25.34/25.51 Or (Eq (Exists fun Z => ∀ (X : Iota), Iff (big_f X (skS.0 2 a a_1)) (Eq X Z)) False) (Eq (Eq (skS.0 2 a a_1) a) False)
% 25.34/25.51 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota),
% 25.34/25.51 Or (Eq (Exists fun Z => ∀ (X : Iota), Iff (big_f X (skS.0 2 a a_1)) (Eq X Z)) True) (Eq (Eq (skS.0 2 a a_1) a) True)
% 25.34/25.51 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota),
% 25.34/25.51 Or (Eq (Eq (skS.0 2 a a_1) a) False) (Eq (∀ (X : Iota), Iff (big_f X (skS.0 2 a a_1)) (Eq X a_2)) False)
% 25.34/25.51 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (X : Iota), Iff (big_f X (skS.0 2 a a_1)) (Eq X a_2)) False) (Ne (skS.0 2 a a_1) a)
% 25.34/25.51 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.51 Or (Ne (skS.0 2 a a_1) a)
% 25.34/25.51 (Eq (Not (Iff (big_f (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a a_1)) (Eq (skS.0 3 a a_1 a_2 a_3) a_2))) True)
% 25.34/25.51 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.51 Or (Ne (skS.0 2 a a_1) a)
% 25.34/25.51 (Eq (Iff (big_f (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a a_1)) (Eq (skS.0 3 a a_1 a_2 a_3) a_2)) False)
% 25.34/25.51 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.51 Or (Ne (skS.0 2 a a_1) a)
% 25.34/25.51 (Or (Eq (big_f (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a a_1)) False) (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) False))
% 25.34/25.51 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.51 Or (Ne (skS.0 2 a a_1) a)
% 25.34/25.51 (Or (Eq (big_f (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a a_1)) True) (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) True))
% 25.34/25.54 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.54 Or (Ne (skS.0 2 a a_1) a)
% 25.34/25.54 (Or (Eq (big_f (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a a_1)) False) (Ne (skS.0 3 a a_1 a_2 a_3) a_2))
% 25.34/25.54 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)
% 25.34/25.54 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)
% 25.34/25.54 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))
% 25.34/25.54 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))
% 25.34/25.54 Clause #31 (by superposition #[30, 12]): ∀ (a a_1 : Iota), Or (Eq (skS.0 0 a) (skS.0 0 a_1)) (Eq False True)
% 25.34/25.54 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 0 a_1)
% 25.34/25.54 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
% 25.34/25.54 Clause #34 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 25.34/25.54 Or (Eq (Eq (skS.0 2 a a_1) a) True) (Eq (∀ (X : Iota), Iff (big_f X (skS.0 2 a a_1)) (Eq X (skS.0 4 a a_1 a_2))) True)
% 25.34/25.54 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 25.34/25.54 Or (Eq (∀ (X : Iota), Iff (big_f X (skS.0 2 a a_1)) (Eq X (skS.0 4 a a_1 a_2))) True) (Eq (skS.0 2 a a_1) a)
% 25.34/25.54 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.54 Or (Eq (skS.0 2 a a_1) a) (Eq (Iff (big_f a_2 (skS.0 2 a a_1)) (Eq a_2 (skS.0 4 a a_1 a_3))) True)
% 25.34/25.54 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.54 Or (Eq (skS.0 2 a a_1) a) (Or (Eq (big_f a_2 (skS.0 2 a a_1)) True) (Eq (Eq a_2 (skS.0 4 a a_1 a_3)) False))
% 25.34/25.54 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.54 Or (Eq (skS.0 2 a a_1) a) (Or (Eq (big_f a_2 (skS.0 2 a a_1)) True) (Ne a_2 (skS.0 4 a a_1 a_3)))
% 25.34/25.54 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 4 a a_1 a_2) (skS.0 2 a a_1)) True)
% 25.34/25.54 Clause #42 (by superposition #[40, 28]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 2 a a_1) a) (Or (Eq True False) (Eq (skS.0 2 a a_1) (skS.0 1 a_2 a_3)))
% 25.34/25.54 Clause #47 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 2 a a_1) a) (Eq (skS.0 2 a a_1) (skS.0 1 a_2 a_3))
% 25.34/25.54 Clause #56 (by equality factoring #[47]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (skS.0 1 a a_1) a_2) (Eq (skS.0 2 a_2 a_3) a_2)
% 25.34/25.54 Clause #57 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.34/25.54 Or (Ne (skS.0 2 a a_1) a)
% 25.34/25.54 (Or (Eq (big_f (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a a_1)) True) (Eq (skS.0 3 a a_1 a_2 a_3) a_2))
% 25.34/25.54 Clause #59 (by destructive equality resolution #[56]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 2 (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)
% 25.34/25.54 Clause #60 (by superposition #[59, 25]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.34/25.54 Or (Ne (skS.0 1 a a_1) (skS.0 1 a a_1))
% 25.34/25.54 (Or (Eq (big_f (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 1 a a_1)) False)
% 25.34/25.54 (Ne (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) a_3))
% 25.34/25.54 Clause #61 (by superposition #[59, 57]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.34/25.54 Or (Ne (skS.0 1 a a_1) (skS.0 1 a a_1))
% 25.34/25.54 (Or (Eq (big_f (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 1 a a_1)) True)
% 25.34/25.54 (Eq (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) a_3))
% 25.34/25.54 Clause #197 (by eliminate resolved literals #[60]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.34/25.54 Or (Eq (big_f (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 1 a a_1)) False)
% 25.34/25.54 (Ne (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) a_3)
% 25.34/25.54 Clause #259 (by eliminate resolved literals #[61]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.34/25.54 Or (Eq (big_f (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 1 a a_1)) True)
% 25.34/25.54 (Eq (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) a_3)
% 25.34/25.54 Clause #267 (by superposition #[259, 197]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.34/25.54 Or (Eq (big_f (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 1 a a_1)) True)
% 25.34/25.54 (Or (Eq (big_f a_3 (skS.0 1 a a_1)) False) (Ne a_3 a_3))
% 25.34/25.54 Clause #3427 (by eliminate resolved literals #[267]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.34/25.54 Or (Eq (big_f (skS.0 3 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 1 a a_1)) True) (Eq (big_f a_3 (skS.0 1 a a_1)) False)
% 25.34/25.59 Clause #3428 (by superposition #[3427, 33]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.34/25.59 Or (Eq (big_f (skS.0 3 (skS.0 1 a a_1) a_2 (skS.0 0 a_3) a_4) (skS.0 1 a a_1)) True) (Eq False True)
% 25.34/25.59 Clause #3439 (by clausification #[3428]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f (skS.0 3 (skS.0 1 a a_1) a_2 (skS.0 0 a_3) a_4) (skS.0 1 a a_1)) True
% 25.34/25.59 Clause #3440 (by superposition #[3439, 197]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq True False) (Ne (skS.0 3 (skS.0 1 a a_1) a_2 (skS.0 0 a_3) a_4) (skS.0 0 a_3))
% 25.34/25.59 Clause #3451 (by superposition #[3439, 30]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq True False) (Eq (skS.0 3 (skS.0 1 a a_1) a_2 (skS.0 0 a_3) a_4) (skS.0 0 a_5))
% 25.34/25.59 Clause #3536 (by clausification #[3440]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Ne (skS.0 3 (skS.0 1 a a_1) a_2 (skS.0 0 a_3) a_4) (skS.0 0 a_3)
% 25.34/25.59 Clause #3546 (by clausification #[3451]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (skS.0 3 (skS.0 1 a a_1) a_2 (skS.0 0 a_3) a_4) (skS.0 0 a_5)
% 25.34/25.59 Clause #3547 (by backward contextual literal cutting #[3546, 3536]): False
% 25.34/25.59 SZS output end Proof for theBenchmark.p
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