TSTP Solution File: SEU811^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU811^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 16:44:00 EDT 2023
% Result : Theorem 4.08s 4.30s
% Output : Proof 4.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU811^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.17/0.35 % Computer : n028.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Wed Aug 23 16:42:19 EDT 2023
% 0.17/0.35 % CPUTime :
% 4.08/4.30 SZS status Theorem for theBenchmark.p
% 4.08/4.30 SZS output start Proof for theBenchmark.p
% 4.08/4.30 Clause #0 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True
% 4.08/4.30 Clause #1 (by assumption #[]): Eq
% 4.08/4.30 (Eq setadjoinE
% 4.08/4.30 (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi))
% 4.08/4.30 True
% 4.08/4.30 Clause #3 (by assumption #[]): Eq (Eq notinself2 (∀ (A B : Iota), in A B → Not (in B A))) True
% 4.08/4.30 Clause #4 (by assumption #[]): Eq (Eq omegaS fun Xx => setadjoin Xx Xx) True
% 4.08/4.30 Clause #5 (by assumption #[]): Eq
% 4.08/4.30 (Not
% 4.08/4.30 (setadjoinIL →
% 4.08/4.30 setadjoinE →
% 4.08/4.30 in__Cong →
% 4.08/4.30 notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy))
% 4.08/4.30 True
% 4.08/4.30 Clause #6 (by clausification #[4]): Eq omegaS fun Xx => setadjoin Xx Xx
% 4.08/4.30 Clause #7 (by argument congruence #[6]): ∀ (a : Iota), Eq (omegaS a) ((fun Xx => setadjoin Xx Xx) a)
% 4.08/4.30 Clause #8 (by betaEtaReduce #[7]): ∀ (a : Iota), Eq (omegaS a) (setadjoin a a)
% 4.08/4.30 Clause #9 (by clausification #[3]): Eq notinself2 (∀ (A B : Iota), in A B → Not (in B A))
% 4.08/4.30 Clause #23 (by clausification #[0]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))
% 4.08/4.30 Clause #25 (by clausify Prop equality #[23]): Or (Eq setadjoinIL False) (Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) True)
% 4.08/4.30 Clause #27 (by clausification #[25]): ∀ (a : Iota), Or (Eq setadjoinIL False) (Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True)
% 4.08/4.30 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq setadjoinIL False) (Eq (in a (setadjoin a a_1)) True)
% 4.08/4.30 Clause #33 (by clausification #[1]): Eq setadjoinE
% 4.08/4.30 (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi)
% 4.08/4.30 Clause #72 (by clausification #[5]): Eq
% 4.08/4.30 (setadjoinIL →
% 4.08/4.30 setadjoinE →
% 4.08/4.30 in__Cong →
% 4.08/4.30 notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy)
% 4.08/4.30 False
% 4.08/4.30 Clause #73 (by clausification #[72]): Eq setadjoinIL True
% 4.08/4.30 Clause #74 (by clausification #[72]): Eq
% 4.08/4.30 (setadjoinE →
% 4.08/4.30 in__Cong →
% 4.08/4.30 notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy)
% 4.08/4.30 False
% 4.08/4.30 Clause #76 (by backward demodulation #[73, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a a_1)) True)
% 4.08/4.30 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True
% 4.08/4.30 Clause #79 (by superposition #[78, 8]): ∀ (a : Iota), Eq (in a (omegaS a)) True
% 4.08/4.30 Clause #81 (by clausification #[74]): Eq setadjoinE True
% 4.08/4.30 Clause #82 (by clausification #[74]): Eq
% 4.08/4.30 (in__Cong →
% 4.08/4.30 notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy)
% 4.08/4.30 False
% 4.08/4.30 Clause #83 (by backward demodulation #[81, 33]): Eq True (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi)
% 4.08/4.30 Clause #87 (by clausification #[83]): ∀ (a : Iota),
% 4.08/4.30 Eq (∀ (A Xy : Iota), in Xy (setadjoin a A) → ∀ (Xphi : Prop), (Eq Xy a → Xphi) → (in Xy A → Xphi) → Xphi) True
% 4.08/4.30 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota),
% 4.08/4.30 Eq (∀ (Xy : Iota), in Xy (setadjoin a a_1) → ∀ (Xphi : Prop), (Eq Xy a → Xphi) → (in Xy a_1 → Xphi) → Xphi) True
% 4.08/4.30 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Eq (in a (setadjoin a_1 a_2) → ∀ (Xphi : Prop), (Eq a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True
% 4.08/4.30 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota),
% 4.08/4.30 Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq (∀ (Xphi : Prop), (Eq a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True)
% 4.08/4.30 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.08/4.30 Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq ((Eq a a_1 → a_3) → (in a a_2 → a_3) → a_3) True)
% 4.08/4.30 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.08/4.30 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1 → a_3) False) (Eq ((in a a_2 → a_3) → a_3) True))
% 4.16/4.33 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.16/4.33 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq ((in a a_2 → a_3) → a_3) True) (Eq (Eq a a_1) True))
% 4.16/4.33 Clause #95 (by clausification #[93]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.16/4.33 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1) True) (Or (Eq (in a a_2 → a_3) False) (Eq a_3 True)))
% 4.16/4.33 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.16/4.33 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (in a a_2 → a_3) False) (Or (Eq a_3 True) (Eq a a_1)))
% 4.16/4.33 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.16/4.33 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq a_3 True) (Or (Eq a a_1) (Eq (in a a_2) True)))
% 4.16/4.33 Clause #100 (by superposition #[97, 8]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq (in a (omegaS a_1)) False) (Or (Eq a_2 True) (Or (Eq a a_1) (Eq (in a a_1) True)))
% 4.16/4.33 Clause #107 (by clausification #[82]): Eq (notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy) False
% 4.16/4.33 Clause #117 (by clausification #[107]): Eq notinself2 True
% 4.16/4.33 Clause #118 (by clausification #[107]): Eq (∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy) False
% 4.16/4.33 Clause #119 (by backward demodulation #[117, 9]): Eq True (∀ (A B : Iota), in A B → Not (in B A))
% 4.16/4.33 Clause #123 (by clausification #[119]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → Not (in B a)) True
% 4.16/4.33 Clause #124 (by clausification #[123]): ∀ (a a_1 : Iota), Eq (in a a_1 → Not (in a_1 a)) True
% 4.16/4.33 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (Not (in a_1 a)) True)
% 4.16/4.33 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (in a_1 a) False)
% 4.16/4.33 Clause #143 (by clausification #[118]): ∀ (a : Iota),
% 4.16/4.33 Eq
% 4.16/4.33 (Not
% 4.16/4.33 (in (skS.0 10 a) omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS (skS.0 10 a)) (omegaS Xy) → Eq (skS.0 10 a) Xy))
% 4.16/4.33 True
% 4.16/4.33 Clause #144 (by clausification #[143]): ∀ (a : Iota),
% 4.16/4.33 Eq (in (skS.0 10 a) omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS (skS.0 10 a)) (omegaS Xy) → Eq (skS.0 10 a) Xy)
% 4.16/4.33 False
% 4.16/4.33 Clause #145 (by clausification #[144]): ∀ (a : Iota), Eq (in (skS.0 10 a) omega) True
% 4.16/4.33 Clause #146 (by clausification #[144]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in Xy omega → Eq (omegaS (skS.0 10 a)) (omegaS Xy) → Eq (skS.0 10 a) Xy) False
% 4.16/4.33 Clause #147 (by superposition #[145, 126]): ∀ (a : Iota), Or (Eq True False) (Eq (in omega (skS.0 10 a)) False)
% 4.16/4.33 Clause #148 (by clausification #[147]): ∀ (a : Iota), Eq (in omega (skS.0 10 a)) False
% 4.16/4.33 Clause #151 (by clausification #[146]): ∀ (a a_1 : Iota),
% 4.16/4.33 Eq
% 4.16/4.33 (Not
% 4.16/4.33 (in (skS.0 11 a a_1) omega →
% 4.16/4.33 Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1)) → Eq (skS.0 10 a) (skS.0 11 a a_1)))
% 4.16/4.33 True
% 4.16/4.33 Clause #152 (by clausification #[151]): ∀ (a a_1 : Iota),
% 4.16/4.33 Eq (in (skS.0 11 a a_1) omega → Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1)) → Eq (skS.0 10 a) (skS.0 11 a a_1))
% 4.16/4.33 False
% 4.16/4.33 Clause #154 (by clausification #[152]): ∀ (a a_1 : Iota), Eq (Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1)) → Eq (skS.0 10 a) (skS.0 11 a a_1)) False
% 4.16/4.33 Clause #178 (by clausification #[154]): ∀ (a a_1 : Iota), Eq (Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1))) True
% 4.16/4.33 Clause #179 (by clausification #[154]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 10 a) (skS.0 11 a a_1)) False
% 4.16/4.33 Clause #180 (by clausification #[178]): ∀ (a a_1 : Iota), Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1))
% 4.16/4.33 Clause #181 (by superposition #[180, 79]): ∀ (a a_1 : Iota), Eq (in (skS.0 11 a a_1) (omegaS (skS.0 10 a))) True
% 4.16/4.33 Clause #183 (by superposition #[180, 100]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 4.16/4.33 Or (Eq (in a (omegaS (skS.0 10 a_1))) False)
% 4.16/4.33 (Or (Eq a_2 True) (Or (Eq a (skS.0 11 a_1 a_3)) (Eq (in a (skS.0 11 a_1 a_3)) True)))
% 4.16/4.33 Clause #185 (by superposition #[181, 100]): ∀ (a : Prop) (a_1 a_2 : Iota),
% 4.16/4.33 Or (Eq True False)
% 4.16/4.33 (Or (Eq a True) (Or (Eq (skS.0 11 a_1 a_2) (skS.0 10 a_1)) (Eq (in (skS.0 11 a_1 a_2) (skS.0 10 a_1)) True)))
% 4.16/4.34 Clause #187 (by clausification #[179]): ∀ (a a_1 : Iota), Ne (skS.0 10 a) (skS.0 11 a a_1)
% 4.16/4.34 Clause #197 (by superposition #[183, 79]): ∀ (a : Prop) (a_1 a_2 : Iota),
% 4.16/4.34 Or (Eq a True)
% 4.16/4.34 (Or (Eq (skS.0 10 a_1) (skS.0 11 a_1 a_2)) (Or (Eq (in (skS.0 10 a_1) (skS.0 11 a_1 a_2)) True) (Eq False True)))
% 4.16/4.34 Clause #198 (by clausification #[185]): ∀ (a : Prop) (a_1 a_2 : Iota),
% 4.16/4.34 Or (Eq a True) (Or (Eq (skS.0 11 a_1 a_2) (skS.0 10 a_1)) (Eq (in (skS.0 11 a_1 a_2) (skS.0 10 a_1)) True))
% 4.16/4.34 Clause #199 (by forward contextual literal cutting #[198, 187]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Eq (in (skS.0 11 a_1 a_2) (skS.0 10 a_1)) True)
% 4.16/4.34 Clause #200 (by superposition #[199, 148]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 11 a a_1) (skS.0 10 a)) True) (Eq True False)
% 4.16/4.34 Clause #213 (by clausification #[200]): ∀ (a a_1 : Iota), Eq (in (skS.0 11 a a_1) (skS.0 10 a)) True
% 4.16/4.34 Clause #214 (by superposition #[213, 126]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (skS.0 10 a) (skS.0 11 a a_1)) False)
% 4.16/4.34 Clause #215 (by clausification #[214]): ∀ (a a_1 : Iota), Eq (in (skS.0 10 a) (skS.0 11 a a_1)) False
% 4.16/4.34 Clause #232 (by clausification #[197]): ∀ (a : Prop) (a_1 a_2 : Iota),
% 4.16/4.34 Or (Eq a True) (Or (Eq (skS.0 10 a_1) (skS.0 11 a_1 a_2)) (Eq (in (skS.0 10 a_1) (skS.0 11 a_1 a_2)) True))
% 4.16/4.34 Clause #233 (by forward contextual literal cutting #[232, 187]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Eq (in (skS.0 10 a_1) (skS.0 11 a_1 a_2)) True)
% 4.16/4.34 Clause #239 (by superposition #[233, 215]): ∀ (a : Prop), Or (Eq a True) (Eq True False)
% 4.16/4.34 Clause #244 (by clausification #[239]): ∀ (a : Prop), Eq a True
% 4.16/4.34 Clause #247 (by falseElim #[244]): False
% 4.16/4.34 SZS output end Proof for theBenchmark.p
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