TSTP Solution File: SEV233^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV233^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 19:24:33 EDT 2023
% Result : Theorem 5.50s 5.74s
% Output : Proof 5.57s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV233^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : duper %s
% 0.10/0.32 % Computer : n021.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Aug 24 03:50:24 EDT 2023
% 0.10/0.32 % CPUTime :
% 5.50/5.74 SZS status Theorem for theBenchmark.p
% 5.50/5.74 SZS output start Proof for theBenchmark.p
% 5.50/5.74 Clause #0 (by assumption #[]): Eq
% 5.50/5.74 (Not
% 5.50/5.74 (∀ (Xx : Iota → Prop),
% 5.50/5.74 (∀ (Xx0 : Iota), Xx Xx0 → And (cD Xx0) (cE Xx0)) →
% 5.50/5.74 And (∀ (Xx0 : Iota), Xx Xx0 → cD Xx0) (∀ (Xx0 : Iota), Xx Xx0 → cE Xx0)))
% 5.50/5.74 True
% 5.50/5.74 Clause #1 (by clausification #[0]): Eq
% 5.50/5.74 (∀ (Xx : Iota → Prop),
% 5.50/5.74 (∀ (Xx0 : Iota), Xx Xx0 → And (cD Xx0) (cE Xx0)) →
% 5.50/5.74 And (∀ (Xx0 : Iota), Xx Xx0 → cD Xx0) (∀ (Xx0 : Iota), Xx Xx0 → cE Xx0))
% 5.50/5.74 False
% 5.50/5.74 Clause #2 (by clausification #[1]): ∀ (a : Iota → Prop),
% 5.50/5.74 Eq
% 5.50/5.74 (Not
% 5.50/5.74 ((∀ (Xx0 : Iota), skS.0 0 a Xx0 → And (cD Xx0) (cE Xx0)) →
% 5.50/5.74 And (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cD Xx0) (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0)))
% 5.50/5.74 True
% 5.50/5.74 Clause #3 (by clausification #[2]): ∀ (a : Iota → Prop),
% 5.50/5.74 Eq
% 5.50/5.74 ((∀ (Xx0 : Iota), skS.0 0 a Xx0 → And (cD Xx0) (cE Xx0)) →
% 5.50/5.74 And (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cD Xx0) (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0))
% 5.50/5.74 False
% 5.50/5.74 Clause #4 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (∀ (Xx0 : Iota), skS.0 0 a Xx0 → And (cD Xx0) (cE Xx0)) True
% 5.50/5.74 Clause #5 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (And (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cD Xx0) (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0)) False
% 5.50/5.74 Clause #6 (by clausification #[4]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (skS.0 0 a a_1 → And (cD a_1) (cE a_1)) True
% 5.50/5.74 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a a_1) False) (Eq (And (cD a_1) (cE a_1)) True)
% 5.50/5.74 Clause #8 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a a_1) False) (Eq (cE a_1) True)
% 5.50/5.74 Clause #9 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a a_1) False) (Eq (cD a_1) True)
% 5.50/5.74 Clause #10 (by clausification #[5]): ∀ (a : Iota → Prop),
% 5.50/5.74 Or (Eq (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cD Xx0) False) (Eq (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0) False)
% 5.50/5.74 Clause #11 (by clausification #[10]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 5.50/5.74 Or (Eq (∀ (Xx0 : Iota), skS.0 0 a Xx0 → cE Xx0) False)
% 5.50/5.74 (Eq (Not (skS.0 0 a (skS.0 1 a a_1) → cD (skS.0 1 a a_1))) True)
% 5.50/5.74 Clause #12 (by clausification #[11]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.50/5.74 Or (Eq (Not (skS.0 0 a (skS.0 1 a a_1) → cD (skS.0 1 a a_1))) True)
% 5.50/5.74 (Eq (Not (skS.0 0 a (skS.0 2 a a_2) → cE (skS.0 2 a a_2))) True)
% 5.50/5.74 Clause #13 (by clausification #[12]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.50/5.74 Or (Eq (Not (skS.0 0 a (skS.0 2 a a_1) → cE (skS.0 2 a a_1))) True)
% 5.50/5.74 (Eq (skS.0 0 a (skS.0 1 a a_2) → cD (skS.0 1 a a_2)) False)
% 5.50/5.74 Clause #14 (by clausification #[13]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.50/5.74 Or (Eq (skS.0 0 a (skS.0 1 a a_1) → cD (skS.0 1 a a_1)) False)
% 5.50/5.74 (Eq (skS.0 0 a (skS.0 2 a a_2) → cE (skS.0 2 a a_2)) False)
% 5.50/5.74 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.50/5.74 Or (Eq (skS.0 0 a (skS.0 2 a a_1) → cE (skS.0 2 a a_1)) False) (Eq (skS.0 0 a (skS.0 1 a a_2)) True)
% 5.50/5.74 Clause #16 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.50/5.74 Or (Eq (skS.0 0 a (skS.0 2 a a_1) → cE (skS.0 2 a a_1)) False) (Eq (cD (skS.0 1 a a_2)) False)
% 5.50/5.74 Clause #17 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Eq (skS.0 0 a (skS.0 2 a a_2)) True)
% 5.50/5.74 Clause #18 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Eq (cE (skS.0 2 a a_2)) False)
% 5.50/5.74 Clause #20 (by superposition #[17, 8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.50/5.74 Or (Eq (skS.0 0 (fun x => a x) (skS.0 1 (fun x => a x) a_1)) True) (Or (Eq True False) (Eq (cE (skS.0 2 a a_2)) True))
% 5.50/5.74 Clause #23 (by clausification #[16]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cD (skS.0 1 a a_1)) False) (Eq (skS.0 0 a (skS.0 2 a a_2)) True)
% 5.50/5.74 Clause #24 (by clausification #[16]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cD (skS.0 1 a a_1)) False) (Eq (cE (skS.0 2 a a_2)) False)
% 5.50/5.74 Clause #59 (by betaEtaReduce #[20]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.57/5.76 Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Or (Eq True False) (Eq (cE (skS.0 2 a a_2)) True))
% 5.57/5.76 Clause #60 (by clausification #[59]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Eq (cE (skS.0 2 a a_2)) True)
% 5.57/5.76 Clause #62 (by superposition #[60, 9]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.57/5.76 Or (Eq (cE (skS.0 2 (fun x => a x) a_1)) True) (Or (Eq True False) (Eq (cD (skS.0 1 a a_2)) True))
% 5.57/5.76 Clause #71 (by betaEtaReduce #[62]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.57/5.76 Or (Eq (cE (skS.0 2 a a_1)) True) (Or (Eq True False) (Eq (cD (skS.0 1 a a_2)) True))
% 5.57/5.76 Clause #72 (by clausification #[71]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Eq (cD (skS.0 1 a a_2)) True)
% 5.57/5.76 Clause #74 (by superposition #[72, 23]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.57/5.76 Or (Eq (cE (skS.0 2 (fun x => a x) a_1)) True) (Or (Eq True False) (Eq (skS.0 0 a (skS.0 2 a a_2)) True))
% 5.57/5.76 Clause #118 (by betaEtaReduce #[74]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.57/5.76 Or (Eq (cE (skS.0 2 a a_1)) True) (Or (Eq True False) (Eq (skS.0 0 a (skS.0 2 a a_2)) True))
% 5.57/5.76 Clause #119 (by clausification #[118]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Eq (skS.0 0 a (skS.0 2 a a_2)) True)
% 5.57/5.76 Clause #122 (by superposition #[119, 8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.57/5.76 Or (Eq (cE (skS.0 2 (fun x => a x) a_1)) True) (Or (Eq True False) (Eq (cE (skS.0 2 a a_2)) True))
% 5.57/5.76 Clause #126 (by betaEtaReduce #[122]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota),
% 5.57/5.76 Or (Eq (cE (skS.0 2 a a_1)) True) (Or (Eq True False) (Eq (cE (skS.0 2 a a_2)) True))
% 5.57/5.76 Clause #127 (by clausification #[126]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Eq (cE (skS.0 2 a a_2)) True)
% 5.57/5.76 Clause #130 (by equality factoring #[127]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Ne True True) (Eq (cE (skS.0 2 a a_1)) True)
% 5.57/5.76 Clause #136 (by clausification #[130]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Or (Eq True False) (Eq True False))
% 5.57/5.76 Clause #138 (by clausification #[136]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cE (skS.0 2 a a_1)) True) (Eq True False)
% 5.57/5.76 Clause #139 (by clausification #[138]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cE (skS.0 2 a a_1)) True
% 5.57/5.76 Clause #140 (by superposition #[139, 18]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a (skS.0 1 a a_1)) True) (Eq True False)
% 5.57/5.76 Clause #143 (by clausification #[140]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (skS.0 0 a (skS.0 1 a a_1)) True
% 5.57/5.76 Clause #145 (by superposition #[143, 9]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq True False) (Eq (cD (skS.0 1 a a_1)) True)
% 5.57/5.76 Clause #146 (by clausification #[145]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cD (skS.0 1 a a_1)) True
% 5.57/5.76 Clause #148 (by superposition #[146, 24]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq True False) (Eq (cE (skS.0 2 a a_1)) False)
% 5.57/5.76 Clause #149 (by clausification #[148]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (cE (skS.0 2 a a_1)) False
% 5.57/5.76 Clause #150 (by superposition #[149, 139]): Eq False True
% 5.57/5.76 Clause #152 (by clausification #[150]): False
% 5.57/5.76 SZS output end Proof for theBenchmark.p
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