TSTP Solution File: SYN373+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN373+1 : TPTP v8.1.2. Released v2.0.0.
% 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 02:11:29 EDT 2023
% Result : Theorem 3.45s 3.67s
% Output : Proof 3.45s
% 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 : SYN373+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n025.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 21:24:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.45/3.67 SZS status Theorem for theBenchmark.p
% 3.45/3.67 SZS output start Proof for theBenchmark.p
% 3.45/3.67 Clause #0 (by assumption #[]): Eq (Not (Iff (Exists fun X => big_p X → big_q X) ((∀ (X : Iota), big_p X) → Exists fun X => big_q X))) True
% 3.45/3.67 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => big_p X → big_q X) ((∀ (X : Iota), big_p X) → Exists big_q))) True
% 3.45/3.67 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => big_p X → big_q X) ((∀ (X : Iota), big_p X) → Exists big_q)) False
% 3.45/3.67 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => big_p X → big_q X) False) (Eq ((∀ (X : Iota), big_p X) → Exists big_q) False)
% 3.45/3.67 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => big_p X → big_q X) True) (Eq ((∀ (X : Iota), big_p X) → Exists big_q) True)
% 3.45/3.67 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq ((∀ (X : Iota), big_p X) → Exists big_q) False) (Eq (big_p a → big_q a) False)
% 3.45/3.67 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (big_p a → big_q a) False) (Eq (∀ (X : Iota), big_p X) True)
% 3.45/3.67 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq (big_p a → big_q a) False) (Eq (Exists big_q) False)
% 3.45/3.67 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), big_p X) True) (Eq (big_p a) True)
% 3.45/3.67 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p a_1) True)
% 3.45/3.67 Clause #11 (by equality factoring #[10]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p a) True)
% 3.45/3.67 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (big_p a) True) (Or (Eq True False) (Eq True False))
% 3.45/3.67 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq True False)
% 3.45/3.67 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (big_p a) True
% 3.45/3.67 Clause #18 (by clausification #[7]): ∀ (a : Iota), Or (Eq (Exists big_q) False) (Eq (big_q a) False)
% 3.45/3.67 Clause #20 (by clausification #[4]): ∀ (a : Iota), Or (Eq ((∀ (X : Iota), big_p X) → Exists big_q) True) (Eq (big_p (skS.0 0 a) → big_q (skS.0 0 a)) True)
% 3.45/3.67 Clause #21 (by clausification #[20]): ∀ (a : Iota),
% 3.45/3.67 Or (Eq (big_p (skS.0 0 a) → big_q (skS.0 0 a)) True) (Or (Eq (∀ (X : Iota), big_p X) False) (Eq (Exists big_q) True))
% 3.45/3.67 Clause #22 (by clausification #[21]): ∀ (a : Iota),
% 3.45/3.67 Or (Eq (∀ (X : Iota), big_p X) False)
% 3.45/3.67 (Or (Eq (Exists big_q) True) (Or (Eq (big_p (skS.0 0 a)) False) (Eq (big_q (skS.0 0 a)) True)))
% 3.45/3.67 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 3.45/3.67 Or (Eq (Exists big_q) True)
% 3.45/3.67 (Or (Eq (big_p (skS.0 0 a)) False) (Or (Eq (big_q (skS.0 0 a)) True) (Eq (Not (big_p (skS.0 1 a_1))) True)))
% 3.45/3.67 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 3.45/3.67 Or (Eq (big_p (skS.0 0 a)) False)
% 3.45/3.67 (Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (Not (big_p (skS.0 1 a_1))) True) (Eq (big_q (skS.0 2 a_2)) True)))
% 3.45/3.67 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 3.45/3.67 Or (Eq (big_p (skS.0 0 a)) False)
% 3.45/3.67 (Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (big_q (skS.0 2 a_1)) True) (Eq (big_p (skS.0 1 a_2)) False)))
% 3.45/3.67 Clause #26 (by superposition #[25, 15]): ∀ (a a_1 a_2 : Iota),
% 3.45/3.67 Or (Eq (big_q (skS.0 0 a)) True)
% 3.45/3.67 (Or (Eq (big_q (skS.0 2 a_1)) True) (Or (Eq (big_p (skS.0 1 a_2)) False) (Eq False True)))
% 3.45/3.67 Clause #27 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_q a) False) (Eq (big_q a_1) False)
% 3.45/3.67 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 3.45/3.67 Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (big_q (skS.0 2 a_1)) True) (Eq (big_p (skS.0 1 a_2)) False))
% 3.45/3.67 Clause #29 (by superposition #[28, 15]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (big_q (skS.0 2 a_1)) True) (Eq False True))
% 3.45/3.67 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Eq (big_q (skS.0 2 a_1)) True)
% 3.45/3.67 Clause #31 (by superposition #[30, 27]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Or (Eq True False) (Eq (big_q a_1) False))
% 3.45/3.67 Clause #36 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Eq (big_q a_1) False)
% 3.45/3.67 Clause #37 (by superposition #[36, 30]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Or (Eq False True) (Eq (big_q (skS.0 2 a_1)) True))
% 3.45/3.67 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Eq (big_q (skS.0 2 a_1)) True)
% 3.45/3.67 Clause #42 (by equality factoring #[39]): ∀ (a : Iota), Or (Ne True True) (Eq (big_q (skS.0 2 a)) True)
% 3.45/3.67 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Or (Eq True False) (Eq True False))
% 3.45/3.67 Clause #45 (by clausification #[43]): ∀ (a : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Eq True False)
% 3.45/3.67 Clause #46 (by clausification #[45]): ∀ (a : Iota), Eq (big_q (skS.0 2 a)) True
% 3.45/3.67 Clause #47 (by superposition #[46, 27]): ∀ (a : Iota), Or (Eq True False) (Eq (big_q a) False)
% 3.45/3.67 Clause #49 (by clausification #[47]): ∀ (a : Iota), Eq (big_q a) False
% 3.45/3.67 Clause #50 (by superposition #[49, 46]): Eq False True
% 3.45/3.67 Clause #51 (by clausification #[50]): False
% 3.45/3.67 SZS output end Proof for theBenchmark.p
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