TSTP Solution File: SET949+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 14:48:09 EDT 2023
% Result : Theorem 167.31s 167.54s
% Output : Proof 167.59s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n002.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 : Sat Aug 26 12:40:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 167.31/167.54 SZS status Theorem for theBenchmark.p
% 167.31/167.54 SZS output start Proof for theBenchmark.p
% 167.31/167.54 Clause #2 (by assumption #[]): Eq
% 167.31/167.54 (∀ (A B C : Iota),
% 167.31/167.54 Iff (Eq C (cartesian_product2 A B))
% 167.31/167.54 (∀ (D : Iota),
% 167.31/167.54 Iff (in D C) (Exists fun E => Exists fun F => And (And (in E A) (in F B)) (Eq D (ordered_pair E F)))))
% 167.31/167.54 True
% 167.31/167.54 Clause #7 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Not (And (in A (cartesian_product2 B C)) (∀ (D E : Iota), Ne (ordered_pair D E) A)))) True
% 167.31/167.54 Clause #22 (by clausification #[2]): ∀ (a : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (∀ (B C : Iota),
% 167.31/167.54 Iff (Eq C (cartesian_product2 a B))
% 167.31/167.54 (∀ (D : Iota),
% 167.31/167.54 Iff (in D C) (Exists fun E => Exists fun F => And (And (in E a) (in F B)) (Eq D (ordered_pair E F)))))
% 167.31/167.54 True
% 167.31/167.54 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (∀ (C : Iota),
% 167.31/167.54 Iff (Eq C (cartesian_product2 a a_1))
% 167.31/167.54 (∀ (D : Iota),
% 167.31/167.54 Iff (in D C) (Exists fun E => Exists fun F => And (And (in E a) (in F a_1)) (Eq D (ordered_pair E F)))))
% 167.31/167.54 True
% 167.31/167.54 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (Iff (Eq a (cartesian_product2 a_1 a_2))
% 167.31/167.54 (∀ (D : Iota),
% 167.31/167.54 Iff (in D a) (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq D (ordered_pair E F)))))
% 167.31/167.54 True
% 167.31/167.54 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 167.31/167.54 Or (Eq (Eq a (cartesian_product2 a_1 a_2)) False)
% 167.31/167.54 (Eq
% 167.31/167.54 (∀ (D : Iota),
% 167.31/167.54 Iff (in D a) (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq D (ordered_pair E F))))
% 167.31/167.54 True)
% 167.31/167.54 Clause #53 (by clausification #[7]): Eq (∀ (A B C : Iota), Not (And (in A (cartesian_product2 B C)) (∀ (D E : Iota), Ne (ordered_pair D E) A))) False
% 167.31/167.54 Clause #54 (by clausification #[53]): ∀ (a : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (Not
% 167.31/167.54 (∀ (B C : Iota),
% 167.31/167.54 Not (And (in (skS.0 3 a) (cartesian_product2 B C)) (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)))))
% 167.31/167.54 True
% 167.31/167.54 Clause #55 (by clausification #[54]): ∀ (a : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (∀ (B C : Iota),
% 167.31/167.54 Not (And (in (skS.0 3 a) (cartesian_product2 B C)) (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a))))
% 167.31/167.54 False
% 167.31/167.54 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (Not
% 167.31/167.54 (∀ (C : Iota),
% 167.31/167.54 Not
% 167.31/167.54 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) C))
% 167.31/167.54 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)))))
% 167.31/167.54 True
% 167.31/167.54 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (∀ (C : Iota),
% 167.31/167.54 Not
% 167.31/167.54 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) C))
% 167.31/167.54 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a))))
% 167.31/167.54 False
% 167.31/167.54 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (Not
% 167.31/167.54 (Not
% 167.31/167.54 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 167.31/167.54 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)))))
% 167.31/167.54 True
% 167.31/167.54 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (Not
% 167.31/167.54 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 167.31/167.54 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a))))
% 167.31/167.54 False
% 167.31/167.54 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota),
% 167.31/167.54 Eq
% 167.31/167.54 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 167.31/167.54 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)))
% 167.31/167.54 True
% 167.31/167.54 Clause #61 (by clausification #[60]): ∀ (a : Iota), Eq (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)) True
% 167.31/167.54 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) True
% 167.31/167.54 Clause #63 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (∀ (E : Iota), Ne (ordered_pair a E) (skS.0 3 a_1)) True
% 167.31/167.54 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), Eq (Ne (ordered_pair a a_1) (skS.0 3 a_2)) True
% 167.31/167.54 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), Ne (ordered_pair a a_1) (skS.0 3 a_2)
% 167.31/167.54 Clause #76 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 167.31/167.54 Or
% 167.31/167.54 (Eq
% 167.31/167.54 (∀ (D : Iota),
% 167.31/167.54 Iff (in D a) (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq D (ordered_pair E F))))
% 167.59/167.84 True)
% 167.59/167.84 (Ne a (cartesian_product2 a_1 a_2))
% 167.59/167.84 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota),
% 167.59/167.84 Or (Ne a (cartesian_product2 a_1 a_2))
% 167.59/167.84 (Eq (Iff (in a_3 a) (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq a_3 (ordered_pair E F))))
% 167.59/167.84 True)
% 167.59/167.84 Clause #79 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota),
% 167.59/167.84 Or (Ne a (cartesian_product2 a_1 a_2))
% 167.59/167.84 (Or (Eq (in a_3 a) False)
% 167.59/167.84 (Eq (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq a_3 (ordered_pair E F))) True))
% 167.59/167.84 Clause #319 (by clausification #[79]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 167.59/167.84 Or (Ne a (cartesian_product2 a_1 a_2))
% 167.59/167.84 (Or (Eq (in a_3 a) False)
% 167.59/167.84 (Eq
% 167.59/167.84 (Exists fun F =>
% 167.59/167.84 And (And (in (skS.0 8 a_1 a_2 a_3 a_4) a_1) (in F a_2)) (Eq a_3 (ordered_pair (skS.0 8 a_1 a_2 a_3 a_4) F)))
% 167.59/167.84 True))
% 167.59/167.84 Clause #320 (by clausification #[319]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 167.59/167.84 Or (Ne a (cartesian_product2 a_1 a_2))
% 167.59/167.84 (Or (Eq (in a_3 a) False)
% 167.59/167.84 (Eq
% 167.59/167.84 (And (And (in (skS.0 8 a_1 a_2 a_3 a_4) a_1) (in (skS.0 9 a_1 a_2 a_3 a_4 a_5) a_2))
% 167.59/167.84 (Eq a_3 (ordered_pair (skS.0 8 a_1 a_2 a_3 a_4) (skS.0 9 a_1 a_2 a_3 a_4 a_5))))
% 167.59/167.84 True))
% 167.59/167.84 Clause #321 (by clausification #[320]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 167.59/167.84 Or (Ne a (cartesian_product2 a_1 a_2))
% 167.59/167.84 (Or (Eq (in a_3 a) False) (Eq (Eq a_3 (ordered_pair (skS.0 8 a_1 a_2 a_3 a_4) (skS.0 9 a_1 a_2 a_3 a_4 a_5))) True))
% 167.59/167.84 Clause #323 (by clausification #[321]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 167.59/167.84 Or (Ne a (cartesian_product2 a_1 a_2))
% 167.59/167.84 (Or (Eq (in a_3 a) False) (Eq a_3 (ordered_pair (skS.0 8 a_1 a_2 a_3 a_4) (skS.0 9 a_1 a_2 a_3 a_4 a_5))))
% 167.59/167.84 Clause #324 (by destructive equality resolution #[323]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 167.59/167.84 Or (Eq (in a (cartesian_product2 a_1 a_2)) False)
% 167.59/167.84 (Eq a (ordered_pair (skS.0 8 a_1 a_2 a a_3) (skS.0 9 a_1 a_2 a a_3 a_4)))
% 167.59/167.84 Clause #325 (by superposition #[324, 62]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 167.59/167.84 Or
% 167.59/167.84 (Eq (skS.0 3 a)
% 167.59/167.84 (ordered_pair (skS.0 8 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) (skS.0 3 a) a_3)
% 167.59/167.84 (skS.0 9 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) (skS.0 3 a) a_3 a_4)))
% 167.59/167.84 (Eq False True)
% 167.59/167.84 Clause #17777 (by clausification #[325]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 167.59/167.84 Eq (skS.0 3 a)
% 167.59/167.84 (ordered_pair (skS.0 8 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) (skS.0 3 a) a_3)
% 167.59/167.84 (skS.0 9 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) (skS.0 3 a) a_3 a_4))
% 167.59/167.84 Clause #17778 (by forward contextual literal cutting #[17777, 65]): False
% 167.59/167.84 SZS output end Proof for theBenchmark.p
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