TSTP Solution File: SEU706^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU706^2 : TPTP v8.1.2. Released v3.7.0.
% 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 16:43:29 EDT 2023
% Result : Theorem 4.82s 4.98s
% Output : Proof 4.82s
% 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 : SEU706^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 20:21:04 EDT 2023
% 0.16/0.34 % CPUTime :
% 4.82/4.98 SZS status Theorem for theBenchmark.p
% 4.82/4.98 SZS output start Proof for theBenchmark.p
% 4.82/4.98 Clause #0 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True
% 4.82/4.98 Clause #4 (by assumption #[]): Eq (Eq setunionsingleton (∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx)) True
% 4.82/4.98 Clause #5 (by assumption #[]): Eq (Eq singleton fun A => Exists fun Xx => And (in Xx A) (Eq A (setadjoin Xx emptyset))) True
% 4.82/4.98 Clause #6 (by assumption #[]): Eq
% 4.82/4.98 (Not
% 4.82/4.98 (uniqinunit →
% 4.82/4.98 in__Cong →
% 4.82/4.98 setadjoin__Cong →
% 4.82/4.98 setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx))
% 4.82/4.98 True
% 4.82/4.98 Clause #7 (by clausification #[0]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)
% 4.82/4.98 Clause #21 (by clausification #[4]): Eq setunionsingleton (∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx)
% 4.82/4.98 Clause #23 (by clausify Prop equality #[21]): Or (Eq setunionsingleton False) (Eq (∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx) True)
% 4.82/4.98 Clause #29 (by clausification #[23]): ∀ (a : Iota), Or (Eq setunionsingleton False) (Eq (Eq (setunion (setadjoin a emptyset)) a) True)
% 4.82/4.98 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq setunionsingleton False) (Eq (setunion (setadjoin a emptyset)) a)
% 4.82/4.98 Clause #55 (by clausification #[6]): Eq
% 4.82/4.98 (uniqinunit →
% 4.82/4.98 in__Cong →
% 4.82/4.98 setadjoin__Cong →
% 4.82/4.98 setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx)
% 4.82/4.98 False
% 4.82/4.98 Clause #56 (by clausification #[55]): Eq uniqinunit True
% 4.82/4.98 Clause #57 (by clausification #[55]): Eq
% 4.82/4.98 (in__Cong →
% 4.82/4.98 setadjoin__Cong →
% 4.82/4.98 setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx)
% 4.82/4.98 False
% 4.82/4.98 Clause #58 (by backward demodulation #[56, 7]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)
% 4.82/4.98 Clause #61 (by clausification #[58]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True
% 4.82/4.98 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True
% 4.82/4.98 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True)
% 4.82/4.98 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1)
% 4.82/4.98 Clause #65 (by clausification #[5]): Eq singleton fun A => Exists fun Xx => And (in Xx A) (Eq A (setadjoin Xx emptyset))
% 4.82/4.98 Clause #66 (by argument congruence #[65]): ∀ (a : Iota), Eq (singleton a) ((fun A => Exists fun Xx => And (in Xx A) (Eq A (setadjoin Xx emptyset))) a)
% 4.82/4.98 Clause #68 (by clausification #[57]): Eq
% 4.82/4.98 (setadjoin__Cong →
% 4.82/4.98 setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx)
% 4.82/4.98 False
% 4.82/4.98 Clause #71 (by clausification #[68]): Eq (setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) False
% 4.82/4.98 Clause #74 (by clausification #[71]): Eq (setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) False
% 4.82/4.98 Clause #83 (by clausification #[74]): Eq setunionsingleton True
% 4.82/4.98 Clause #84 (by clausification #[74]): Eq (∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) False
% 4.82/4.98 Clause #87 (by superposition #[83, 30]): ∀ (a : Iota), Or (Eq True False) (Eq (setunion (setadjoin a emptyset)) a)
% 4.82/4.98 Clause #90 (by clausification #[87]): ∀ (a : Iota), Eq (setunion (setadjoin a emptyset)) a
% 4.82/4.98 Clause #92 (by clausification #[84]): ∀ (a : Iota), Eq (Not (singleton (skS.0 5 a) → ∀ (Xx : Iota), in Xx (skS.0 5 a) → Eq (setunion (skS.0 5 a)) Xx)) True
% 4.82/4.98 Clause #93 (by clausification #[92]): ∀ (a : Iota), Eq (singleton (skS.0 5 a) → ∀ (Xx : Iota), in Xx (skS.0 5 a) → Eq (setunion (skS.0 5 a)) Xx) False
% 4.82/4.98 Clause #94 (by clausification #[93]): ∀ (a : Iota), Eq (singleton (skS.0 5 a)) True
% 4.82/4.98 Clause #95 (by clausification #[93]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 5 a) → Eq (setunion (skS.0 5 a)) Xx) False
% 4.82/5.01 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 6 a a_1) (skS.0 5 a) → Eq (setunion (skS.0 5 a)) (skS.0 6 a a_1))) True
% 4.82/5.01 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 5 a) → Eq (setunion (skS.0 5 a)) (skS.0 6 a a_1)) False
% 4.82/5.01 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 5 a)) True
% 4.82/5.01 Clause #99 (by clausification #[97]): ∀ (a a_1 : Iota), Eq (Eq (setunion (skS.0 5 a)) (skS.0 6 a a_1)) False
% 4.82/5.01 Clause #166 (by betaEtaReduce #[66]): ∀ (a : Iota), Eq (singleton a) (Exists fun Xx => And (in Xx a) (Eq a (setadjoin Xx emptyset)))
% 4.82/5.01 Clause #168 (by clausify Prop equality #[166]): ∀ (a : Iota), Or (Eq (singleton a) False) (Eq (Exists fun Xx => And (in Xx a) (Eq a (setadjoin Xx emptyset))) True)
% 4.82/5.01 Clause #174 (by clausification #[168]): ∀ (a a_1 : Iota),
% 4.82/5.01 Or (Eq (singleton a) False) (Eq (And (in (skS.0 11 a a_1) a) (Eq a (setadjoin (skS.0 11 a a_1) emptyset))) True)
% 4.82/5.01 Clause #175 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (singleton a) False) (Eq (Eq a (setadjoin (skS.0 11 a a_1) emptyset)) True)
% 4.82/5.01 Clause #177 (by clausification #[175]): ∀ (a a_1 : Iota), Or (Eq (singleton a) False) (Eq a (setadjoin (skS.0 11 a a_1) emptyset))
% 4.82/5.01 Clause #178 (by superposition #[177, 94]): ∀ (a a_1 : Iota), Or (Eq (skS.0 5 a) (setadjoin (skS.0 11 (skS.0 5 a) a_1) emptyset)) (Eq False True)
% 4.82/5.01 Clause #182 (by clausification #[99]): ∀ (a a_1 : Iota), Ne (setunion (skS.0 5 a)) (skS.0 6 a a_1)
% 4.82/5.01 Clause #400 (by clausification #[178]): ∀ (a a_1 : Iota), Eq (skS.0 5 a) (setadjoin (skS.0 11 (skS.0 5 a) a_1) emptyset)
% 4.82/5.01 Clause #402 (by superposition #[400, 90]): ∀ (a a_1 : Iota), Eq (setunion (skS.0 5 a)) (skS.0 11 (skS.0 5 a) a_1)
% 4.82/5.01 Clause #433 (by backward demodulation #[402, 400]): ∀ (a : Iota), Eq (skS.0 5 a) (setadjoin (setunion (skS.0 5 a)) emptyset)
% 4.82/5.01 Clause #463 (by superposition #[433, 64]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 5 a_1)) False) (Eq a (setunion (skS.0 5 a_1)))
% 4.82/5.01 Clause #468 (by superposition #[463, 98]): ∀ (a a_1 : Iota), Or (Eq (skS.0 6 a a_1) (setunion (skS.0 5 a))) (Eq False True)
% 4.82/5.01 Clause #478 (by clausification #[468]): ∀ (a a_1 : Iota), Eq (skS.0 6 a a_1) (setunion (skS.0 5 a))
% 4.82/5.01 Clause #479 (by forward contextual literal cutting #[478, 182]): False
% 4.82/5.01 SZS output end Proof for theBenchmark.p
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