TSTP Solution File: SYN070+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN070+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 02:10:27 EDT 2023
% Result : Theorem 4.50s 4.68s
% Output : Proof 4.51s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN070+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14 % Command : duper %s
% 0.13/0.34 % Computer : n023.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 19:16:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.50/4.68 SZS status Theorem for theBenchmark.p
% 4.50/4.68 SZS output start Proof for theBenchmark.p
% 4.50/4.68 Clause #0 (by assumption #[]): Eq (∀ (X Y : Iota), And (big_f X) (And (big_f Y) (big_h Y X) → big_g Y) → big_g X) True
% 4.50/4.68 Clause #1 (by assumption #[]): Eq
% 4.50/4.68 ((Exists fun X => And (big_f X) (Not (big_g X))) →
% 4.50/4.68 Exists fun X1 => And (And (big_f X1) (Not (big_g X1))) (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j X1 Y))
% 4.50/4.68 True
% 4.50/4.68 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), And (And (big_f X) (big_f Y)) (big_h X Y) → Not (big_j Y X)) True
% 4.50/4.68 Clause #3 (by assumption #[]): Eq (Not (∀ (X : Iota), big_f X → big_g X)) True
% 4.50/4.68 Clause #4 (by clausification #[3]): Eq (∀ (X : Iota), big_f X → big_g X) False
% 4.50/4.68 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (big_f (skS.0 0 a) → big_g (skS.0 0 a))) True
% 4.50/4.68 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (big_f (skS.0 0 a) → big_g (skS.0 0 a)) False
% 4.50/4.68 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (big_f (skS.0 0 a)) True
% 4.50/4.68 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (big_g (skS.0 0 a)) False
% 4.50/4.68 Clause #9 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (Y : Iota), And (big_f a) (And (big_f Y) (big_h Y a) → big_g Y) → big_g a) True
% 4.50/4.68 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (And (big_f a) (And (big_f a_1) (big_h a_1 a) → big_g a_1) → big_g a) True
% 4.50/4.68 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (And (big_f a) (And (big_f a_1) (big_h a_1 a) → big_g a_1)) False) (Eq (big_g a) True)
% 4.50/4.68 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota),
% 4.50/4.68 Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (And (big_f a_1) (big_h a_1 a) → big_g a_1) False))
% 4.50/4.68 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (And (big_f a_1) (big_h a_1 a)) True))
% 4.50/4.68 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (big_g a_1) False))
% 4.50/4.68 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (big_h a_1 a) True))
% 4.50/4.68 Clause #16 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (big_f a_1) True))
% 4.50/4.68 Clause #18 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), And (And (big_f a) (big_f Y)) (big_h a Y) → Not (big_j Y a)) True
% 4.50/4.68 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (And (And (big_f a) (big_f a_1)) (big_h a a_1) → Not (big_j a_1 a)) True
% 4.50/4.68 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (And (And (big_f a) (big_f a_1)) (big_h a a_1)) False) (Eq (Not (big_j a_1 a)) True)
% 4.50/4.68 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (Not (big_j a a_1)) True) (Or (Eq (And (big_f a_1) (big_f a)) False) (Eq (big_h a_1 a) False))
% 4.50/4.68 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (And (big_f a) (big_f a_1)) False) (Or (Eq (big_h a a_1) False) (Eq (big_j a_1 a) False))
% 4.50/4.68 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 4.50/4.68 Or (Eq (big_h a a_1) False) (Or (Eq (big_j a_1 a) False) (Or (Eq (big_f a) False) (Eq (big_f a_1) False)))
% 4.50/4.68 Clause #24 (by superposition #[16, 7]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_f a_1) True) (Eq False True))
% 4.50/4.68 Clause #25 (by clausification #[1]): Or (Eq (Exists fun X => And (big_f X) (Not (big_g X))) False)
% 4.50/4.68 (Eq
% 4.50/4.68 (Exists fun X1 => And (And (big_f X1) (Not (big_g X1))) (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j X1 Y))
% 4.50/4.68 True)
% 4.50/4.68 Clause #26 (by clausification #[25]): ∀ (a : Iota),
% 4.50/4.68 Or
% 4.50/4.68 (Eq
% 4.50/4.68 (Exists fun X1 =>
% 4.50/4.68 And (And (big_f X1) (Not (big_g X1))) (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j X1 Y))
% 4.50/4.68 True)
% 4.50/4.68 (Eq (And (big_f a) (Not (big_g a))) False)
% 4.50/4.68 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota),
% 4.50/4.68 Or (Eq (And (big_f a) (Not (big_g a))) False)
% 4.50/4.68 (Eq
% 4.50/4.68 (And (And (big_f (skS.0 1 a_1)) (Not (big_g (skS.0 1 a_1))))
% 4.50/4.68 (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j (skS.0 1 a_1) Y))
% 4.50/4.68 True)
% 4.50/4.68 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota),
% 4.51/4.71 Or
% 4.51/4.71 (Eq
% 4.51/4.71 (And (And (big_f (skS.0 1 a)) (Not (big_g (skS.0 1 a))))
% 4.51/4.71 (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j (skS.0 1 a) Y))
% 4.51/4.71 True)
% 4.51/4.71 (Or (Eq (big_f a_1) False) (Eq (Not (big_g a_1)) False))
% 4.51/4.71 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota),
% 4.51/4.71 Or (Eq (big_f a) False)
% 4.51/4.71 (Or (Eq (Not (big_g a)) False) (Eq (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j (skS.0 1 a_1) Y) True))
% 4.51/4.71 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota),
% 4.51/4.71 Or (Eq (big_f a) False)
% 4.51/4.71 (Or (Eq (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j (skS.0 1 a_1) Y) True) (Eq (big_g a) True))
% 4.51/4.71 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota),
% 4.51/4.71 Or (Eq (big_f a) False)
% 4.51/4.71 (Or (Eq (big_g a) True) (Eq (And (big_f a_1) (Not (big_g a_1)) → big_j (skS.0 1 a_2) a_1) True))
% 4.51/4.71 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota),
% 4.51/4.71 Or (Eq (big_f a) False)
% 4.51/4.71 (Or (Eq (big_g a) True) (Or (Eq (And (big_f a_1) (Not (big_g a_1))) False) (Eq (big_j (skS.0 1 a_2) a_1) True)))
% 4.51/4.71 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota),
% 4.51/4.71 Or (Eq (big_f a) False)
% 4.51/4.71 (Or (Eq (big_g a) True)
% 4.51/4.71 (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq (big_f a_2) False) (Eq (Not (big_g a_2)) False))))
% 4.51/4.71 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 4.51/4.71 Or (Eq (big_f a) False)
% 4.51/4.71 (Or (Eq (big_g a) True) (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq (big_f a_2) False) (Eq (big_g a_2) True))))
% 4.51/4.71 Clause #36 (by superposition #[35, 7]): ∀ (a a_1 a_2 : Iota),
% 4.51/4.71 Or (Eq (big_g (skS.0 0 a)) True)
% 4.51/4.71 (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq (big_f a_2) False) (Or (Eq (big_g a_2) True) (Eq False True))))
% 4.51/4.71 Clause #39 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Eq (big_f a_1) True)
% 4.51/4.71 Clause #40 (by superposition #[39, 8]): ∀ (a : Iota), Or (Eq (big_f a) True) (Eq True False)
% 4.51/4.71 Clause #46 (by clausification #[40]): ∀ (a : Iota), Eq (big_f a) True
% 4.51/4.71 Clause #47 (by backward demodulation #[46, 15]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq True False) (Eq (big_h a_1 a) True))
% 4.51/4.72 Clause #48 (by backward demodulation #[46, 23]): ∀ (a a_1 : Iota), Or (Eq (big_h a a_1) False) (Or (Eq (big_j a_1 a) False) (Or (Eq True False) (Eq (big_f a_1) False)))
% 4.51/4.72 Clause #51 (by backward demodulation #[46, 14]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq True False) (Eq (big_g a_1) False))
% 4.51/4.72 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_g a_1) False)
% 4.51/4.72 Clause #57 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_h a_1 a) True)
% 4.51/4.72 Clause #58 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (big_h a a_1) False) (Or (Eq (big_j a_1 a) False) (Eq (big_f a_1) False))
% 4.51/4.72 Clause #59 (by forward demodulation #[58, 46]): ∀ (a a_1 : Iota), Or (Eq (big_h a a_1) False) (Or (Eq (big_j a_1 a) False) (Eq True False))
% 4.51/4.72 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), Or (Eq (big_h a a_1) False) (Eq (big_j a_1 a) False)
% 4.51/4.72 Clause #62 (by superposition #[60, 57]): ∀ (a a_1 : Iota), Or (Eq (big_j a a_1) False) (Or (Eq (big_g a) True) (Eq False True))
% 4.51/4.72 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq (big_j a a_1) False) (Eq (big_g a) True)
% 4.51/4.72 Clause #77 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 4.51/4.72 Or (Eq (big_g (skS.0 0 a)) True)
% 4.51/4.72 (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq (big_f a_2) False) (Eq (big_g a_2) True)))
% 4.51/4.72 Clause #78 (by forward demodulation #[77, 46]): ∀ (a a_1 a_2 : Iota),
% 4.51/4.72 Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq True False) (Eq (big_g a_2) True)))
% 4.51/4.72 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Eq (big_g a_2) True))
% 4.51/4.72 Clause #80 (by superposition #[79, 8]): ∀ (a a_1 : Iota), Or (Eq (big_j (skS.0 1 a) a_1) True) (Or (Eq (big_g a_1) True) (Eq True False))
% 4.51/4.72 Clause #83 (by clausification #[80]): ∀ (a a_1 : Iota), Or (Eq (big_j (skS.0 1 a) a_1) True) (Eq (big_g a_1) True)
% 4.51/4.72 Clause #84 (by superposition #[83, 63]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq True False) (Eq (big_g (skS.0 1 a_1)) True))
% 4.51/4.72 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_g (skS.0 1 a_1)) True)
% 4.51/4.72 Clause #88 (by superposition #[85, 52]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_g a_1) True) (Eq True False))
% 4.51/4.72 Clause #90 (by clausification #[88]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_g a_1) True)
% 4.51/4.72 Clause #91 (by superposition #[90, 8]): ∀ (a : Iota), Or (Eq (big_g a) True) (Eq True False)
% 4.51/4.72 Clause #95 (by clausification #[91]): ∀ (a : Iota), Eq (big_g a) True
% 4.51/4.72 Clause #99 (by superposition #[95, 8]): Eq True False
% 4.51/4.72 Clause #100 (by clausification #[99]): False
% 4.51/4.72 SZS output end Proof for theBenchmark.p
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