TSTP Solution File: SYN066+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN066+1 : TPTP v8.1.2. Bugfixed v3.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n025.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 02:10:26 EDT 2023
% Result : Theorem 3.52s 3.72s
% Output : Proof 3.52s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN066+1 : TPTP v8.1.2. Bugfixed v3.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 22:07:38 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.52/3.72 SZS status Theorem for theBenchmark.p
% 3.52/3.72 SZS output start Proof for theBenchmark.p
% 3.52/3.72 Clause #0 (by assumption #[]): Eq
% 3.52/3.72 (∀ (Z : Iota),
% 3.52/3.72 Exists fun W =>
% 3.52/3.72 ∀ (X : Iota),
% 3.52/3.72 Exists fun Y => And (And (big_p X Z → big_p Y W) (big_p Y Z)) (big_p Y W → Exists fun U => big_q U W))
% 3.52/3.72 True
% 3.52/3.72 Clause #1 (by assumption #[]): Eq (∀ (X Z : Iota), Not (big_p X Z) → Exists fun Y => big_q Y Z) True
% 3.52/3.72 Clause #2 (by assumption #[]): Eq ((Exists fun X => Exists fun Y => big_q X Y) → ∀ (Z : Iota), big_r Z Z) True
% 3.52/3.72 Clause #3 (by assumption #[]): Eq (Not (∀ (X : Iota), Exists fun Y => big_r X Y)) True
% 3.52/3.72 Clause #4 (by betaEtaReduce #[2]): Eq ((Exists fun X => Exists (big_q X)) → ∀ (Z : Iota), big_r Z Z) True
% 3.52/3.72 Clause #5 (by clausification #[4]): Or (Eq (Exists fun X => Exists (big_q X)) False) (Eq (∀ (Z : Iota), big_r Z Z) True)
% 3.52/3.72 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (∀ (Z : Iota), big_r Z Z) True) (Eq (Exists (big_q a)) False)
% 3.52/3.72 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (Exists (big_q a)) False) (Eq (big_r a_1 a_1) True)
% 3.52/3.72 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_r a a) True) (Eq (big_q a_1 a_2) False)
% 3.52/3.72 Clause #9 (by betaEtaReduce #[3]): Eq (Not (∀ (X : Iota), Exists (big_r X))) True
% 3.52/3.72 Clause #10 (by clausification #[9]): Eq (∀ (X : Iota), Exists (big_r X)) False
% 3.52/3.72 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Not (Exists (big_r (skS.0 0 a)))) True
% 3.52/3.72 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (Exists (big_r (skS.0 0 a))) False
% 3.52/3.72 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (big_r (skS.0 0 a) a_1) False
% 3.52/3.72 Clause #14 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Z : Iota), Not (big_p a Z) → Exists fun Y => big_q Y Z) True
% 3.52/3.72 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Not (big_p a a_1) → Exists fun Y => big_q Y a_1) True
% 3.52/3.72 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Not (big_p a a_1)) False) (Eq (Exists fun Y => big_q Y a_1) True)
% 3.52/3.72 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (Exists fun Y => big_q Y a) True) (Eq (big_p a_1 a) True)
% 3.52/3.72 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) True) (Eq (big_q (skS.0 1 a_1 a_2) a_1) True)
% 3.52/3.72 Clause #19 (by superposition #[18, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) True) (Or (Eq (big_r a_2 a_2) True) (Eq True False))
% 3.52/3.72 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) True) (Eq (big_r a_2 a_2) True)
% 3.52/3.72 Clause #21 (by superposition #[20, 13]): ∀ (a a_1 : Iota), Or (Eq (big_p a a_1) True) (Eq True False)
% 3.52/3.72 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (big_p a a_1) True
% 3.52/3.72 Clause #23 (by clausification #[0]): ∀ (a : Iota),
% 3.52/3.72 Eq
% 3.52/3.72 (Exists fun W =>
% 3.52/3.72 ∀ (X : Iota),
% 3.52/3.72 Exists fun Y => And (And (big_p X a → big_p Y W) (big_p Y a)) (big_p Y W → Exists fun U => big_q U W))
% 3.52/3.72 True
% 3.52/3.72 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota),
% 3.52/3.72 Eq
% 3.52/3.72 (∀ (X : Iota),
% 3.52/3.72 Exists fun Y =>
% 3.52/3.72 And (And (big_p X a → big_p Y (skS.0 2 a a_1)) (big_p Y a))
% 3.52/3.72 (big_p Y (skS.0 2 a a_1) → Exists fun U => big_q U (skS.0 2 a a_1)))
% 3.52/3.72 True
% 3.52/3.72 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 3.52/3.72 Eq
% 3.52/3.72 (Exists fun Y =>
% 3.52/3.72 And (And (big_p a a_1 → big_p Y (skS.0 2 a_1 a_2)) (big_p Y a_1))
% 3.52/3.72 (big_p Y (skS.0 2 a_1 a_2) → Exists fun U => big_q U (skS.0 2 a_1 a_2)))
% 3.52/3.72 True
% 3.52/3.72 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.52/3.72 Eq
% 3.52/3.72 (And (And (big_p a a_1 → big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2)) (big_p (skS.0 3 a a_1 a_2 a_3) a_1))
% 3.52/3.72 (big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2) → Exists fun U => big_q U (skS.0 2 a_1 a_2)))
% 3.52/3.72 True
% 3.52/3.72 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.52/3.72 Eq (big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2) → Exists fun U => big_q U (skS.0 2 a_1 a_2)) True
% 3.52/3.72 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.52/3.72 Or (Eq (big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2)) False) (Eq (Exists fun U => big_q U (skS.0 2 a_1 a_2)) True)
% 3.52/3.73 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.52/3.73 Or (Eq (big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2)) False)
% 3.52/3.73 (Eq (big_q (skS.0 4 a_1 a_2 a_4) (skS.0 2 a_1 a_2)) True)
% 3.52/3.73 Clause #31 (by superposition #[30, 22]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_q (skS.0 4 a a_1 a_2) (skS.0 2 a a_1)) True) (Eq False True)
% 3.52/3.73 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (big_q (skS.0 4 a a_1 a_2) (skS.0 2 a a_1)) True
% 3.52/3.73 Clause #33 (by superposition #[32, 8]): ∀ (a : Iota), Or (Eq (big_r a a) True) (Eq True False)
% 3.52/3.73 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (big_r a a) True
% 3.52/3.73 Clause #35 (by superposition #[34, 13]): Eq True False
% 3.52/3.73 Clause #36 (by clausification #[35]): False
% 3.52/3.73 SZS output end Proof for theBenchmark.p
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