TSTP Solution File: SEV259^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV259^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 19:24:37 EDT 2023
% Result : Theorem 3.77s 4.00s
% Output : Proof 3.86s
% 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 : SEV259^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 02:24:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.77/4.00 SZS status Theorem for theBenchmark.p
% 3.77/4.00 SZS output start Proof for theBenchmark.p
% 3.77/4.00 Clause #0 (by assumption #[]): Eq
% 3.77/4.00 (Not
% 3.77/4.00 (∀ (S : (b → Prop) → Prop),
% 3.77/4.00 And
% 3.77/4.00 (And
% 3.77/4.00 (And (∀ (R : b → Prop), (Eq R fun Xx => False) → S R) (∀ (R : b → Prop), (Eq R fun Xx => Not False) → S R))
% 3.77/4.00 (∀ (K : (b → Prop) → Prop) (R : b → Prop),
% 3.77/4.00 And (∀ (Xx : b → Prop), K Xx → S Xx) (Eq R fun Xx => Exists fun S0 => And (K S0) (S0 Xx)) → S R))
% 3.77/4.00 (∀ (Y Z S0 : b → Prop), And (And (S Y) (S Z)) (Eq S0 fun Xx => And (Y Xx) (Z Xx)) → S S0) →
% 3.77/4.00 ∀ (W : b → Prop) (Xx : b),
% 3.77/4.00 W Xx →
% 3.77/4.00 ∀ (S0 : b → Prop),
% 3.77/4.00 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → S R) → S0 Xx))
% 3.77/4.00 True
% 3.77/4.00 Clause #1 (by clausification #[0]): Eq
% 3.77/4.00 (∀ (S : (b → Prop) → Prop),
% 3.77/4.00 And
% 3.77/4.00 (And (And (∀ (R : b → Prop), (Eq R fun Xx => False) → S R) (∀ (R : b → Prop), (Eq R fun Xx => Not False) → S R))
% 3.77/4.00 (∀ (K : (b → Prop) → Prop) (R : b → Prop),
% 3.77/4.00 And (∀ (Xx : b → Prop), K Xx → S Xx) (Eq R fun Xx => Exists fun S0 => And (K S0) (S0 Xx)) → S R))
% 3.77/4.00 (∀ (Y Z S0 : b → Prop), And (And (S Y) (S Z)) (Eq S0 fun Xx => And (Y Xx) (Z Xx)) → S S0) →
% 3.77/4.00 ∀ (W : b → Prop) (Xx : b),
% 3.77/4.00 W Xx →
% 3.77/4.00 ∀ (S0 : b → Prop),
% 3.77/4.00 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → S R) → S0 Xx)
% 3.77/4.00 False
% 3.77/4.00 Clause #2 (by clausification #[1]): ∀ (a : (b → Prop) → Prop),
% 3.77/4.00 Eq
% 3.77/4.00 (Not
% 3.77/4.00 (And
% 3.77/4.00 (And
% 3.77/4.00 (And (∀ (R : b → Prop), (Eq R fun Xx => False) → skS.0 0 a R)
% 3.77/4.00 (∀ (R : b → Prop), (Eq R fun Xx => Not False) → skS.0 0 a R))
% 3.77/4.00 (∀ (K : (b → Prop) → Prop) (R : b → Prop),
% 3.77/4.00 And (∀ (Xx : b → Prop), K Xx → skS.0 0 a Xx) (Eq R fun Xx => Exists fun S0 => And (K S0) (S0 Xx)) →
% 3.77/4.00 skS.0 0 a R))
% 3.77/4.00 (∀ (Y Z S0 : b → Prop),
% 3.77/4.00 And (And (skS.0 0 a Y) (skS.0 0 a Z)) (Eq S0 fun Xx => And (Y Xx) (Z Xx)) → skS.0 0 a S0) →
% 3.77/4.00 ∀ (W : b → Prop) (Xx : b),
% 3.77/4.00 W Xx →
% 3.77/4.00 ∀ (S0 : b → Prop),
% 3.77/4.00 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) →
% 3.77/4.00 S0 Xx))
% 3.77/4.00 True
% 3.77/4.00 Clause #3 (by clausification #[2]): ∀ (a : (b → Prop) → Prop),
% 3.77/4.00 Eq
% 3.77/4.00 (And
% 3.77/4.00 (And
% 3.77/4.00 (And (∀ (R : b → Prop), (Eq R fun Xx => False) → skS.0 0 a R)
% 3.77/4.00 (∀ (R : b → Prop), (Eq R fun Xx => Not False) → skS.0 0 a R))
% 3.77/4.00 (∀ (K : (b → Prop) → Prop) (R : b → Prop),
% 3.77/4.00 And (∀ (Xx : b → Prop), K Xx → skS.0 0 a Xx) (Eq R fun Xx => Exists fun S0 => And (K S0) (S0 Xx)) →
% 3.77/4.00 skS.0 0 a R))
% 3.77/4.00 (∀ (Y Z S0 : b → Prop),
% 3.77/4.00 And (And (skS.0 0 a Y) (skS.0 0 a Z)) (Eq S0 fun Xx => And (Y Xx) (Z Xx)) → skS.0 0 a S0) →
% 3.77/4.00 ∀ (W : b → Prop) (Xx : b),
% 3.77/4.00 W Xx →
% 3.77/4.00 ∀ (S0 : b → Prop),
% 3.77/4.00 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → S0 Xx)
% 3.77/4.00 False
% 3.77/4.00 Clause #5 (by clausification #[3]): ∀ (a : (b → Prop) → Prop),
% 3.77/4.00 Eq
% 3.77/4.00 (∀ (W : b → Prop) (Xx : b),
% 3.77/4.00 W Xx →
% 3.77/4.00 ∀ (S0 : b → Prop),
% 3.77/4.00 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → S0 Xx)
% 3.77/4.00 False
% 3.77/4.00 Clause #15 (by clausification #[5]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop),
% 3.77/4.00 Eq
% 3.77/4.00 (Not
% 3.77/4.00 (∀ (Xx : b),
% 3.77/4.00 skS.0 1 a a_1 Xx →
% 3.77/4.00 ∀ (S0 : b → Prop),
% 3.77/4.00 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0)
% 3.77/4.00 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) →
% 3.77/4.00 S0 Xx))
% 3.77/4.00 True
% 3.77/4.00 Clause #16 (by clausification #[15]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop),
% 3.77/4.00 Eq
% 3.77/4.00 (∀ (Xx : b),
% 3.77/4.00 skS.0 1 a a_1 Xx →
% 3.77/4.00 ∀ (S0 : b → Prop),
% 3.86/4.03 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0)
% 3.86/4.03 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) →
% 3.86/4.03 S0 Xx)
% 3.86/4.03 False
% 3.86/4.03 Clause #17 (by clausification #[16]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b),
% 3.86/4.03 Eq
% 3.86/4.03 (Not
% 3.86/4.03 (skS.0 1 a a_1 (skS.0 2 a a_1 a_2) →
% 3.86/4.03 ∀ (S0 : b → Prop),
% 3.86/4.03 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0)
% 3.86/4.03 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) →
% 3.86/4.03 S0 (skS.0 2 a a_1 a_2)))
% 3.86/4.03 True
% 3.86/4.03 Clause #18 (by clausification #[17]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b),
% 3.86/4.03 Eq
% 3.86/4.03 (skS.0 1 a a_1 (skS.0 2 a a_1 a_2) →
% 3.86/4.03 ∀ (S0 : b → Prop),
% 3.86/4.03 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) →
% 3.86/4.03 S0 (skS.0 2 a a_1 a_2))
% 3.86/4.03 False
% 3.86/4.03 Clause #19 (by clausification #[18]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b), Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) True
% 3.86/4.03 Clause #20 (by clausification #[18]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b),
% 3.86/4.03 Eq
% 3.86/4.03 (∀ (S0 : b → Prop),
% 3.86/4.03 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) →
% 3.86/4.03 S0 (skS.0 2 a a_1 a_2))
% 3.86/4.03 False
% 3.86/4.03 Clause #22 (by clausification #[20]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop),
% 3.86/4.03 Eq
% 3.86/4.03 (Not
% 3.86/4.03 (And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → skS.0 3 a a_1 a_2 a_3 Xx0)
% 3.86/4.03 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (skS.0 3 a a_1 a_2 a_3 Xx0)) → skS.0 0 a R) →
% 3.86/4.03 skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_2)))
% 3.86/4.03 True
% 3.86/4.03 Clause #23 (by clausification #[22]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop),
% 3.86/4.03 Eq
% 3.86/4.03 (And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → skS.0 3 a a_1 a_2 a_3 Xx0)
% 3.86/4.03 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (skS.0 3 a a_1 a_2 a_3 Xx0)) → skS.0 0 a R) →
% 3.86/4.03 skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_2))
% 3.86/4.03 False
% 3.86/4.03 Clause #24 (by clausification #[23]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop),
% 3.86/4.03 Eq
% 3.86/4.03 (And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → skS.0 3 a a_1 a_2 a_3 Xx0)
% 3.86/4.03 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (skS.0 3 a a_1 a_2 a_3 Xx0)) → skS.0 0 a R))
% 3.86/4.03 True
% 3.86/4.03 Clause #25 (by clausification #[23]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop),
% 3.86/4.03 Eq (skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_2)) False
% 3.86/4.03 Clause #27 (by clausification #[24]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop),
% 3.86/4.03 Eq (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → skS.0 3 a a_1 a_2 a_3 Xx0) True
% 3.86/4.03 Clause #32 (by clausification #[27]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 a_3 : b) (a_4 : b → Prop),
% 3.86/4.03 Eq (skS.0 1 a a_1 a_2 → skS.0 3 a a_1 a_3 a_4 a_2) True
% 3.86/4.03 Clause #33 (by clausification #[32]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 a_3 : b) (a_4 : b → Prop),
% 3.86/4.03 Or (Eq (skS.0 1 a a_1 a_2) False) (Eq (skS.0 3 a a_1 a_3 a_4 a_2) True)
% 3.86/4.03 Clause #34 (by superposition #[33, 19]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop) (a_4 : b),
% 3.86/4.03 Or (Eq (skS.0 3 (fun x => a x) (fun x => a_1 x) a_2 a_3 (skS.0 2 a a_1 a_4)) True) (Eq False True)
% 3.86/4.03 Clause #97 (by betaEtaReduce #[34]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop) (a_4 : b),
% 3.86/4.03 Or (Eq (skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_4)) True) (Eq False True)
% 3.86/4.03 Clause #98 (by clausification #[97]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop) (a_4 : b),
% 3.86/4.03 Eq (skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_4)) True
% 3.86/4.03 Clause #99 (by superposition #[98, 25]): Eq True False
% 3.86/4.03 Clause #103 (by clausification #[99]): False
% 3.86/4.03 SZS output end Proof for theBenchmark.p
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