TSTP Solution File: SYN364+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN364+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 02:11:26 EDT 2023
% Result : Theorem 3.38s 3.69s
% Output : Proof 3.38s
% 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 : SYN364+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n022.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 21:21:55 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.38/3.69 SZS status Theorem for theBenchmark.p
% 3.38/3.69 SZS output start Proof for theBenchmark.p
% 3.38/3.69 Clause #0 (by assumption #[]): Eq
% 3.38/3.69 (Not
% 3.38/3.69 (And
% 3.38/3.69 (And (∀ (X : Iota), (Exists fun Y => big_p X Y) → ∀ (Z : Iota), big_p Z Z)
% 3.38/3.69 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V)))))
% 3.38/3.69 (∀ (W : Iota), big_q W → Not (big_m (g W))) →
% 3.38/3.69 ∀ (U : Iota), Exists fun V => And (big_p (g U) V) (big_p U U)))
% 3.38/3.69 True
% 3.38/3.69 Clause #1 (by betaEtaReduce #[0]): Eq
% 3.38/3.69 (Not
% 3.38/3.69 (And
% 3.38/3.69 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z)
% 3.38/3.69 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V)))))
% 3.38/3.69 (∀ (W : Iota), big_q W → Not (big_m (g W))) →
% 3.38/3.69 ∀ (U : Iota), Exists fun V => And (big_p (g U) V) (big_p U U)))
% 3.38/3.69 True
% 3.38/3.69 Clause #2 (by clausification #[1]): Eq
% 3.38/3.69 (And
% 3.38/3.69 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z)
% 3.38/3.69 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V)))))
% 3.38/3.69 (∀ (W : Iota), big_q W → Not (big_m (g W))) →
% 3.38/3.69 ∀ (U : Iota), Exists fun V => And (big_p (g U) V) (big_p U U))
% 3.38/3.69 False
% 3.38/3.69 Clause #3 (by clausification #[2]): Eq
% 3.38/3.69 (And
% 3.38/3.69 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z)
% 3.38/3.69 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V)))))
% 3.38/3.69 (∀ (W : Iota), big_q W → Not (big_m (g W))))
% 3.38/3.69 True
% 3.38/3.69 Clause #4 (by clausification #[2]): Eq (∀ (U : Iota), Exists fun V => And (big_p (g U) V) (big_p U U)) False
% 3.38/3.69 Clause #5 (by clausification #[3]): Eq (∀ (W : Iota), big_q W → Not (big_m (g W))) True
% 3.38/3.69 Clause #6 (by clausification #[3]): Eq
% 3.38/3.69 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z)
% 3.38/3.69 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V)))))
% 3.38/3.69 True
% 3.38/3.69 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (big_q a → Not (big_m (g a))) True
% 3.38/3.69 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (big_q a) False) (Eq (Not (big_m (g a))) True)
% 3.38/3.69 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (big_q a) False) (Eq (big_m (g a)) False)
% 3.38/3.69 Clause #10 (by clausification #[4]): ∀ (a : Iota), Eq (Not (Exists fun V => And (big_p (g (skS.0 0 a)) V) (big_p (skS.0 0 a) (skS.0 0 a)))) True
% 3.38/3.69 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Exists fun V => And (big_p (g (skS.0 0 a)) V) (big_p (skS.0 0 a) (skS.0 0 a))) False
% 3.38/3.69 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (And (big_p (g (skS.0 0 a)) a_1) (big_p (skS.0 0 a) (skS.0 0 a))) False
% 3.38/3.69 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_p (g (skS.0 0 a)) a_1) False) (Eq (big_p (skS.0 0 a) (skS.0 0 a)) False)
% 3.38/3.69 Clause #14 (by clausification #[6]): Eq (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V)))) True
% 3.38/3.69 Clause #15 (by clausification #[6]): Eq (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z) True
% 3.38/3.69 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Exists fun V => Or (big_p a V) (And (big_m a) (big_q (f a V)))) True
% 3.38/3.69 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Or (big_p a (skS.0 1 a a_1)) (And (big_m a) (big_q (f a (skS.0 1 a a_1))))) True
% 3.38/3.69 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (big_p a (skS.0 1 a a_1)) True) (Eq (And (big_m a) (big_q (f a (skS.0 1 a a_1)))) True)
% 3.38/3.69 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_p a (skS.0 1 a a_1)) True) (Eq (big_q (f a (skS.0 1 a a_1))) True)
% 3.38/3.69 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_p a (skS.0 1 a a_1)) True) (Eq (big_m a) True)
% 3.38/3.69 Clause #21 (by superposition #[19, 9]): ∀ (a a_1 : Iota),
% 3.38/3.69 Or (Eq (big_p a (skS.0 1 a a_1)) True) (Or (Eq True False) (Eq (big_m (g (f a (skS.0 1 a a_1)))) False))
% 3.38/3.69 Clause #22 (by clausification #[15]): ∀ (a : Iota), Eq (Exists (big_p a) → ∀ (Z : Iota), big_p Z Z) True
% 3.38/3.69 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (Exists (big_p a)) False) (Eq (∀ (Z : Iota), big_p Z Z) True)
% 3.38/3.69 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (∀ (Z : Iota), big_p Z Z) True) (Eq (big_p a a_1) False)
% 3.38/3.70 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) False) (Eq (big_p a_2 a_2) True)
% 3.38/3.70 Clause #27 (by superposition #[20, 25]): ∀ (a a_1 : Iota), Or (Eq (big_p a a) True) (Or (Eq False True) (Eq (big_m a_1) True))
% 3.38/3.70 Clause #28 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (big_p a (skS.0 1 a a_1)) True) (Eq (big_m (g (f a (skS.0 1 a a_1)))) False)
% 3.38/3.70 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (big_p a a) True) (Eq (big_m a_1) True)
% 3.38/3.70 Clause #32 (by superposition #[29, 28]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a) True) (Or (Eq (big_p a_1 (skS.0 1 a_1 a_2)) True) (Eq True False))
% 3.38/3.70 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a) True) (Eq (big_p a_1 (skS.0 1 a_1 a_2)) True)
% 3.38/3.70 Clause #38 (by superposition #[34, 25]): ∀ (a a_1 : Iota), Or (Eq (big_p a a) True) (Or (Eq True False) (Eq (big_p a_1 a_1) True))
% 3.38/3.70 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (big_p a a) True) (Eq (big_p a_1 a_1) True)
% 3.38/3.70 Clause #40 (by equality factoring #[39]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p a a) True)
% 3.38/3.70 Clause #41 (by clausification #[40]): ∀ (a : Iota), Or (Eq (big_p a a) True) (Or (Eq True False) (Eq True False))
% 3.38/3.70 Clause #43 (by clausification #[41]): ∀ (a : Iota), Or (Eq (big_p a a) True) (Eq True False)
% 3.38/3.70 Clause #44 (by clausification #[43]): ∀ (a : Iota), Eq (big_p a a) True
% 3.38/3.70 Clause #45 (by superposition #[44, 13]): ∀ (a : Iota), Or (Eq True False) (Eq (big_p (skS.0 0 a) (skS.0 0 a)) False)
% 3.38/3.70 Clause #50 (by clausification #[45]): ∀ (a : Iota), Eq (big_p (skS.0 0 a) (skS.0 0 a)) False
% 3.38/3.70 Clause #51 (by superposition #[50, 44]): Eq False True
% 3.38/3.70 Clause #52 (by clausification #[51]): False
% 3.38/3.70 SZS output end Proof for theBenchmark.p
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