TSTP Solution File: SYN054+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN054+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 02:10:20 EDT 2023
% Result : Theorem 3.68s 3.84s
% Output : Proof 3.68s
% 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 : SYN054+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n016.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 22:25:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.68/3.84 SZS status Theorem for theBenchmark.p
% 3.68/3.84 SZS output start Proof for theBenchmark.p
% 3.68/3.84 Clause #0 (by assumption #[]): Eq (Not (Exists fun X => And (big_s X) (big_q X))) True
% 3.68/3.84 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), big_p X → Or (big_q X) (big_r X)) True
% 3.68/3.84 Clause #2 (by assumption #[]): Eq (Not (Exists fun X => big_p X) → Exists fun Y => big_q Y) True
% 3.68/3.84 Clause #3 (by assumption #[]): Eq (∀ (X : Iota), Or (big_q X) (big_r X) → big_s X) True
% 3.68/3.84 Clause #4 (by assumption #[]): Eq (Not (Exists fun X => And (big_p X) (big_r X))) True
% 3.68/3.84 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (Or (big_q a) (big_r a) → big_s a) True
% 3.68/3.84 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Or (big_q a) (big_r a)) False) (Eq (big_s a) True)
% 3.68/3.84 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq (big_s a) True) (Eq (big_q a) False)
% 3.68/3.84 Clause #9 (by betaEtaReduce #[2]): Eq (Not (Exists big_p) → Exists big_q) True
% 3.68/3.84 Clause #10 (by clausification #[9]): Or (Eq (Not (Exists big_p)) False) (Eq (Exists big_q) True)
% 3.68/3.84 Clause #11 (by clausification #[10]): Or (Eq (Exists big_q) True) (Eq (Exists big_p) True)
% 3.68/3.84 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (Exists big_p) True) (Eq (big_q (skS.0 0 a)) True)
% 3.68/3.84 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Eq (big_p (skS.0 1 a_1)) True)
% 3.68/3.84 Clause #14 (by superposition #[13, 8]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq (big_s (skS.0 0 a_1)) True) (Eq True False))
% 3.68/3.84 Clause #15 (by clausification #[1]): ∀ (a : Iota), Eq (big_p a → Or (big_q a) (big_r a)) True
% 3.68/3.84 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq (Or (big_q a) (big_r a)) True)
% 3.68/3.84 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (big_p a) False) (Or (Eq (big_q a) True) (Eq (big_r a) True))
% 3.68/3.84 Clause #19 (by clausification #[4]): Eq (Exists fun X => And (big_p X) (big_r X)) False
% 3.68/3.84 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (And (big_p a) (big_r a)) False
% 3.68/3.84 Clause #21 (by clausification #[20]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq (big_r a) False)
% 3.68/3.84 Clause #23 (by clausification #[0]): Eq (Exists fun X => And (big_s X) (big_q X)) False
% 3.68/3.84 Clause #24 (by clausification #[23]): ∀ (a : Iota), Eq (And (big_s a) (big_q a)) False
% 3.68/3.84 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (big_s a) False) (Eq (big_q a) False)
% 3.68/3.84 Clause #26 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (big_s (skS.0 0 a_1)) True)
% 3.68/3.84 Clause #29 (by superposition #[26, 25]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq True False) (Eq (big_q (skS.0 0 a_1)) False))
% 3.68/3.84 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (big_q (skS.0 0 a_1)) False)
% 3.68/3.84 Clause #31 (by superposition #[30, 13]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq False True) (Eq (big_p (skS.0 1 a_1)) True))
% 3.68/3.84 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (big_p (skS.0 1 a_1)) True)
% 3.68/3.84 Clause #35 (by equality factoring #[32]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 1 a)) True)
% 3.68/3.84 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq True False) (Eq True False))
% 3.68/3.84 Clause #38 (by clausification #[36]): ∀ (a : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq True False)
% 3.68/3.84 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (big_p (skS.0 1 a)) True
% 3.68/3.84 Clause #40 (by superposition #[39, 17]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (big_q (skS.0 1 a)) True) (Eq (big_r (skS.0 1 a)) True))
% 3.68/3.84 Clause #41 (by superposition #[39, 21]): ∀ (a : Iota), Or (Eq True False) (Eq (big_r (skS.0 1 a)) False)
% 3.68/3.84 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (big_r (skS.0 1 a)) False
% 3.68/3.84 Clause #47 (by clausification #[40]): ∀ (a : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Eq (big_r (skS.0 1 a)) True)
% 3.68/3.84 Clause #48 (by superposition #[47, 42]): ∀ (a : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Eq True False)
% 3.68/3.84 Clause #50 (by clausification #[48]): ∀ (a : Iota), Eq (big_q (skS.0 1 a)) True
% 3.68/3.84 Clause #52 (by superposition #[50, 8]): ∀ (a : Iota), Or (Eq (big_s (skS.0 1 a)) True) (Eq True False)
% 3.68/3.84 Clause #53 (by clausification #[52]): ∀ (a : Iota), Eq (big_s (skS.0 1 a)) True
% 3.68/3.84 Clause #54 (by superposition #[53, 25]): ∀ (a : Iota), Or (Eq True False) (Eq (big_q (skS.0 1 a)) False)
% 3.68/3.84 Clause #55 (by clausification #[54]): ∀ (a : Iota), Eq (big_q (skS.0 1 a)) False
% 3.68/3.84 Clause #56 (by superposition #[55, 50]): Eq False True
% 3.68/3.84 Clause #58 (by clausification #[56]): False
% 3.68/3.84 SZS output end Proof for theBenchmark.p
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