TSTP Solution File: MSC012+1 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : MSC012+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 : Thu Aug 31 09:21:53 EDT 2023
% Result : Theorem 4.04s 4.26s
% Output : Proof 4.04s
% 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 : MSC012+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.36 % Computer : n019.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 24 13:53:29 EDT 2023
% 0.13/0.36 % CPUTime :
% 4.04/4.26 SZS status Theorem for theBenchmark.p
% 4.04/4.26 SZS output start Proof for theBenchmark.p
% 4.04/4.26 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), And (And (p A) (less A B)) (p B) → goal) True
% 4.04/4.26 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), Or (p A) (Exists fun B => And (less A B) (p B))) True
% 4.04/4.26 Clause #2 (by assumption #[]): Eq (∀ (A B C : Iota), And (less A B) (less B C) → less A C) True
% 4.04/4.26 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Exists fun B => less A B) True
% 4.04/4.26 Clause #4 (by assumption #[]): Eq (Not goal) True
% 4.04/4.26 Clause #5 (by clausification #[4]): Eq goal False
% 4.04/4.26 Clause #6 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), And (And (p a) (less a B)) (p B) → goal) True
% 4.04/4.26 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (And (And (p a) (less a a_1)) (p a_1) → goal) True
% 4.04/4.26 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (And (And (p a) (less a a_1)) (p a_1)) False) (Eq goal True)
% 4.04/4.26 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq goal True) (Or (Eq (And (p a) (less a a_1)) False) (Eq (p a_1) False))
% 4.04/4.26 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq goal True) (Or (Eq (p a) False) (Or (Eq (p a_1) False) (Eq (less a_1 a) False)))
% 4.04/4.26 Clause #11 (by forward demodulation #[10, 5]): ∀ (a a_1 : Iota), Or (Eq False True) (Or (Eq (p a) False) (Or (Eq (p a_1) False) (Eq (less a_1 a) False)))
% 4.04/4.26 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Or (Eq (p a_1) False) (Eq (less a_1 a) False))
% 4.04/4.26 Clause #13 (by betaEtaReduce #[3]): Eq (∀ (A : Iota), Exists (less A)) True
% 4.04/4.26 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (Exists (less a)) True
% 4.04/4.26 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (less a (skS.0 0 a a_1)) True
% 4.04/4.26 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (less a B) (less B C) → less a C) True
% 4.04/4.26 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (less a a_1) (less a_1 C) → less a C) True
% 4.04/4.26 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (And (less a a_1) (less a_1 a_2) → less a a_2) True
% 4.04/4.26 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (less a a_1) (less a_1 a_2)) False) (Eq (less a a_2) True)
% 4.04/4.26 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (less a a_1) True) (Or (Eq (less a a_2) False) (Eq (less a_2 a_1) False))
% 4.04/4.26 Clause #21 (by superposition #[20, 15]): ∀ (a a_1 a_2 : Iota), Or (Eq (less a a_1) True) (Or (Eq (less (skS.0 0 a a_2) a_1) False) (Eq False True))
% 4.04/4.26 Clause #22 (by clausification #[1]): ∀ (a : Iota), Eq (Or (p a) (Exists fun B => And (less a B) (p B))) True
% 4.04/4.26 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (p a) True) (Eq (Exists fun B => And (less a B) (p B)) True)
% 4.04/4.26 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (p a) True) (Eq (And (less a (skS.0 1 a a_1)) (p (skS.0 1 a a_1))) True)
% 4.04/4.26 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (p a) True) (Eq (p (skS.0 1 a a_1)) True)
% 4.04/4.26 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (p a) True) (Eq (less a (skS.0 1 a a_1)) True)
% 4.04/4.26 Clause #27 (by superposition #[25, 12]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.26 Or (Eq (p a) True) (Or (Eq True False) (Or (Eq (p a_1) False) (Eq (less a_1 (skS.0 1 a a_2)) False)))
% 4.04/4.26 Clause #28 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (less a a_1) True) (Eq (less (skS.0 0 a a_2) a_1) False)
% 4.04/4.26 Clause #31 (by superposition #[26, 28]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.26 Or (Eq (less a (skS.0 1 (skS.0 0 a a_1) a_2)) True) (Or (Eq (p (skS.0 0 a a_1)) True) (Eq False True))
% 4.04/4.26 Clause #32 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a) True) (Or (Eq (p a_1) False) (Eq (less a_1 (skS.0 1 a a_2)) False))
% 4.04/4.26 Clause #33 (by superposition #[32, 25]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.04/4.26 Or (Eq (p a) True) (Or (Eq (less (skS.0 1 a_1 a_2) (skS.0 1 a a_3)) False) (Or (Eq (p a_1) True) (Eq False True)))
% 4.04/4.26 Clause #45 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (less a (skS.0 1 (skS.0 0 a a_1) a_2)) True) (Eq (p (skS.0 0 a a_1)) True)
% 4.04/4.26 Clause #55 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a) True) (Or (Eq (less (skS.0 1 a_1 a_2) (skS.0 1 a a_3)) False) (Eq (p a_1) True))
% 4.04/4.28 Clause #56 (by superposition #[55, 26]): ∀ (a a_1 : Iota),
% 4.04/4.28 Or (Eq (p (skS.0 1 a a_1)) True) (Or (Eq (p a) True) (Or (Eq (p (skS.0 1 a a_1)) True) (Eq False True)))
% 4.04/4.28 Clause #57 (by superposition #[55, 45]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.28 Or (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True)
% 4.04/4.28 (Or (Eq (p a) True) (Or (Eq False True) (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True)))
% 4.04/4.28 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a a_1)) True) (Or (Eq (p a) True) (Eq (p (skS.0 1 a a_1)) True))
% 4.04/4.28 Clause #59 (by eliminate duplicate literals #[58]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a a_1)) True) (Eq (p a) True)
% 4.04/4.28 Clause #140 (by clausification #[57]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.28 Or (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True) (Or (Eq (p a) True) (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True))
% 4.04/4.28 Clause #141 (by eliminate duplicate literals #[140]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True) (Eq (p a) True)
% 4.04/4.28 Clause #142 (by superposition #[141, 12]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.04/4.28 Or (Eq (p a) True) (Or (Eq True False) (Or (Eq (p a_1) False) (Eq (less a_1 (skS.0 0 (skS.0 1 a a_2) a_3)) False)))
% 4.04/4.28 Clause #156 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a) True) (Or (Eq (p a_1) False) (Eq (less a_1 (skS.0 0 (skS.0 1 a a_2) a_3)) False))
% 4.04/4.28 Clause #157 (by superposition #[156, 59]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.04/4.28 Or (Eq (p a) True)
% 4.04/4.28 (Or (Eq (less (skS.0 1 a_1 a_2) (skS.0 0 (skS.0 1 a a_3) a_4)) False) (Or (Eq False True) (Eq (p a_1) True)))
% 4.04/4.28 Clause #159 (by clausification #[157]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.04/4.28 Or (Eq (p a) True) (Or (Eq (less (skS.0 1 a_1 a_2) (skS.0 0 (skS.0 1 a a_3) a_4)) False) (Eq (p a_1) True))
% 4.04/4.28 Clause #160 (by superposition #[159, 15]): ∀ (a : Iota), Or (Eq (p a) True) (Or (Eq (p a) True) (Eq False True))
% 4.04/4.28 Clause #162 (by clausification #[160]): ∀ (a : Iota), Or (Eq (p a) True) (Eq (p a) True)
% 4.04/4.28 Clause #163 (by eliminate duplicate literals #[162]): ∀ (a : Iota), Eq (p a) True
% 4.04/4.28 Clause #168 (by backward demodulation #[163, 12]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (p a) False) (Eq (less a a_1) False))
% 4.04/4.28 Clause #183 (by clausification #[168]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (less a a_1) False)
% 4.04/4.28 Clause #184 (by forward demodulation #[183, 163]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (less a a_1) False)
% 4.04/4.28 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), Eq (less a a_1) False
% 4.04/4.28 Clause #190 (by superposition #[185, 15]): Eq False True
% 4.04/4.28 Clause #191 (by clausification #[190]): False
% 4.04/4.28 SZS output end Proof for theBenchmark.p
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