TSTP Solution File: SEU584^2 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU584^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 16:42:50 EDT 2023
% Result : Theorem 4.15s 4.49s
% Output : Proof 4.15s
% 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 : SEU584^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 21:56:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.15/4.49 SZS status Theorem for theBenchmark.p
% 4.15/4.49 SZS output start Proof for theBenchmark.p
% 4.15/4.49 Clause #0 (by assumption #[]): Eq (Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))) True
% 4.15/4.49 Clause #1 (by assumption #[]): Eq (Eq binunion fun Xx Xy => setunion (setadjoin Xx (setadjoin Xy emptyset))) True
% 4.15/4.49 Clause #2 (by assumption #[]): Eq (Eq upairset2IR (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))) True
% 4.15/4.49 Clause #3 (by assumption #[]): Eq (Not (setunionI → upairset2IR → ∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B))) True
% 4.15/4.49 Clause #4 (by clausification #[3]): Eq (setunionI → upairset2IR → ∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B)) False
% 4.15/4.49 Clause #5 (by clausification #[4]): Eq setunionI True
% 4.15/4.49 Clause #6 (by clausification #[4]): Eq (upairset2IR → ∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B)) False
% 4.15/4.49 Clause #7 (by clausification #[6]): Eq upairset2IR True
% 4.15/4.49 Clause #8 (by clausification #[6]): Eq (∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B)) False
% 4.15/4.49 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in Xx B → in Xx (binunion (skS.0 0 a) B))) True
% 4.15/4.49 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx B → in Xx (binunion (skS.0 0 a) B)) False
% 4.15/4.49 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Not (∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (binunion (skS.0 0 a) (skS.0 1 a a_1)))) True
% 4.15/4.49 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (binunion (skS.0 0 a) (skS.0 1 a a_1))) False
% 4.15/4.49 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota),
% 4.15/4.49 Eq (Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (binunion (skS.0 0 a) (skS.0 1 a a_1)))) True
% 4.15/4.49 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota),
% 4.15/4.49 Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (binunion (skS.0 0 a) (skS.0 1 a a_1))) False
% 4.15/4.49 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True
% 4.15/4.49 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (binunion (skS.0 0 a) (skS.0 1 a a_1))) False
% 4.15/4.49 Clause #17 (by clausification #[0]): Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))
% 4.15/4.49 Clause #18 (by forward demodulation #[17, 5]): Eq True (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))
% 4.15/4.49 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (Xx B : Iota), in Xx B → in B a → in Xx (setunion a)) True
% 4.15/4.49 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (∀ (B : Iota), in a B → in B a_1 → in a (setunion a_1)) True
% 4.15/4.49 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a_1 a_2 → in a (setunion a_2)) True
% 4.15/4.49 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a_1 a_2 → in a (setunion a_2)) True)
% 4.15/4.49 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_1 a_2) False) (Eq (in a (setunion a_2)) True))
% 4.15/4.49 Clause #24 (by superposition #[23, 15]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.15/4.49 Or (Eq (in (skS.0 1 a a_1) a_2) False) (Or (Eq (in (skS.0 2 a a_1 a_3) (setunion a_2)) True) (Eq False True))
% 4.15/4.49 Clause #25 (by clausification #[2]): Eq upairset2IR (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))
% 4.15/4.49 Clause #26 (by forward demodulation #[25, 7]): Eq True (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))
% 4.15/4.49 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in Xy (setadjoin a (setadjoin Xy emptyset))) True
% 4.15/4.49 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True
% 4.15/4.49 Clause #30 (by clausification #[1]): Eq binunion fun Xx Xy => setunion (setadjoin Xx (setadjoin Xy emptyset))
% 4.15/4.49 Clause #31 (by argument congruence #[30]): ∀ (a : Iota), Eq (binunion a) ((fun Xx Xy => setunion (setadjoin Xx (setadjoin Xy emptyset))) a)
% 4.15/4.49 Clause #33 (by betaEtaReduce #[31]): ∀ (a : Iota), Eq (binunion a) fun Xy => setunion (setadjoin a (setadjoin Xy emptyset))
% 4.15/4.51 Clause #34 (by argument congruence #[33]): ∀ (a a_1 : Iota), Eq (binunion a a_1) ((fun Xy => setunion (setadjoin a (setadjoin Xy emptyset))) a_1)
% 4.15/4.51 Clause #40 (by betaEtaReduce #[34]): ∀ (a a_1 : Iota), Eq (binunion a a_1) (setunion (setadjoin a (setadjoin a_1 emptyset)))
% 4.15/4.51 Clause #55 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 1 a a_1) a_2) False) (Eq (in (skS.0 2 a a_1 a_3) (setunion a_2)) True)
% 4.15/4.51 Clause #56 (by superposition #[55, 28]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.15/4.51 Or (Eq (in (skS.0 2 a a_1 a_2) (setunion (setadjoin a_3 (setadjoin (skS.0 1 a a_1) emptyset)))) True) (Eq False True)
% 4.15/4.51 Clause #194 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.15/4.51 Eq (in (skS.0 2 a a_1 a_2) (setunion (setadjoin a_3 (setadjoin (skS.0 1 a a_1) emptyset)))) True
% 4.15/4.51 Clause #195 (by forward demodulation #[194, 40]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 2 a a_1 a_2) (binunion a_3 (skS.0 1 a a_1))) True
% 4.15/4.51 Clause #196 (by superposition #[195, 16]): Eq True False
% 4.15/4.51 Clause #202 (by clausification #[196]): False
% 4.15/4.51 SZS output end Proof for theBenchmark.p
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