TSTP Solution File: LCL678+1.001 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL678+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n025.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 07:10:46 EDT 2023
% Result : Theorem 3.56s 3.76s
% Output : Proof 3.56s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL678+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 24 20:29:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 3.56/3.76 SZS status Theorem for theBenchmark.p
% 3.56/3.76 SZS output start Proof for theBenchmark.p
% 3.56/3.76 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True
% 3.56/3.76 Clause #2 (by assumption #[]): Eq
% 3.56/3.76 (Not
% 3.56/3.76 (Not
% 3.56/3.76 (Exists fun X =>
% 3.56/3.76 Not
% 3.56/3.76 (Or False
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (Y : Iota),
% 3.56/3.76 Or (Or (Not (r1 X Y)) False)
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))))))))
% 3.56/3.76 True
% 3.56/3.76 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True
% 3.56/3.76 Clause #11 (by clausification #[2]): Eq
% 3.56/3.76 (Not
% 3.56/3.76 (Exists fun X =>
% 3.56/3.76 Not
% 3.56/3.76 (Or False
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (Y : Iota),
% 3.56/3.76 Or (Or (Not (r1 X Y)) False)
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))))))))
% 3.56/3.76 False
% 3.56/3.76 Clause #12 (by clausification #[11]): Eq
% 3.56/3.76 (Exists fun X =>
% 3.56/3.76 Not
% 3.56/3.76 (Or False
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (Y : Iota),
% 3.56/3.76 Or (Or (Not (r1 X Y)) False)
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))))))
% 3.56/3.76 True
% 3.56/3.76 Clause #13 (by clausification #[12]): ∀ (a : Iota),
% 3.56/3.76 Eq
% 3.56/3.76 (Not
% 3.56/3.76 (Or False
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (Y : Iota),
% 3.56/3.76 Or (Or (Not (r1 (skS.0 0 a) Y)) False)
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))))))
% 3.56/3.76 True
% 3.56/3.76 Clause #14 (by clausification #[13]): ∀ (a : Iota),
% 3.56/3.76 Eq
% 3.56/3.76 (Or False
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (Y : Iota),
% 3.56/3.76 Or (Or (Not (r1 (skS.0 0 a) Y)) False)
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))))))
% 3.56/3.76 False
% 3.56/3.76 Clause #15 (by clausification #[14]): ∀ (a : Iota),
% 3.56/3.76 Eq
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (Y : Iota),
% 3.56/3.76 Or (Or (Not (r1 (skS.0 0 a) Y)) False)
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))))
% 3.56/3.76 False
% 3.56/3.76 Clause #17 (by clausification #[15]): ∀ (a : Iota),
% 3.56/3.76 Eq
% 3.56/3.76 (∀ (Y : Iota),
% 3.56/3.76 Or (Or (Not (r1 (skS.0 0 a) Y)) False)
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 Y X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))))
% 3.56/3.76 True
% 3.56/3.76 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 3.56/3.76 Eq
% 3.56/3.76 (Or (Or (Not (r1 (skS.0 0 a) a_1)) False)
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))))
% 3.56/3.76 True
% 3.56/3.76 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota),
% 3.56/3.76 Or (Eq (Or (Not (r1 (skS.0 0 a) a_1)) False) True)
% 3.56/3.76 (Eq
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 3.56/3.76 True)
% 3.56/3.76 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 3.56/3.76 Or
% 3.56/3.76 (Eq
% 3.56/3.76 (Not
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 a X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))))
% 3.56/3.76 True)
% 3.56/3.76 (Or (Eq (Not (r1 (skS.0 0 a_1) a)) True) (Eq False True))
% 3.56/3.76 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota),
% 3.56/3.76 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True)
% 3.56/3.76 (Or (Eq False True)
% 3.56/3.76 (Eq
% 3.56/3.76 (∀ (X : Iota),
% 3.56/3.76 Or (Or (Not (r1 a_1 X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.76 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 3.56/3.76 False))
% 3.56/3.79 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota),
% 3.56/3.79 Or (Eq False True)
% 3.56/3.79 (Or
% 3.56/3.79 (Eq
% 3.56/3.79 (∀ (X : Iota),
% 3.56/3.79 Or (Or (Not (r1 a X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y)))
% 3.56/3.79 (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 3.56/3.79 False)
% 3.56/3.79 (Eq (r1 (skS.0 0 a_1) a) False))
% 3.56/3.79 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 3.56/3.79 Or
% 3.56/3.79 (Eq
% 3.56/3.79 (∀ (X : Iota),
% 3.56/3.79 Or (Or (Not (r1 a X)) (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))) (Not (∀ (Y : Iota), Or (Not (r1 X Y)) (p1 Y))))
% 3.56/3.79 False)
% 3.56/3.79 (Eq (r1 (skS.0 0 a_1) a) False)
% 3.56/3.79 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 3.56/3.79 (Eq
% 3.56/3.79 (Not
% 3.56/3.79 (Or (Or (Not (r1 a_1 (skS.0 1 a_1 a_2))) (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y)))
% 3.56/3.79 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y)))))
% 3.56/3.79 True)
% 3.56/3.79 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 3.56/3.79 (Eq
% 3.56/3.79 (Or (Or (Not (r1 a_1 (skS.0 1 a_1 a_2))) (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y)))
% 3.56/3.79 (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y))))
% 3.56/3.79 False)
% 3.56/3.79 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Not (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y))) False)
% 3.56/3.79 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 3.56/3.79 (Eq (Or (Not (r1 a_1 (skS.0 1 a_1 a_2))) (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y))) False)
% 3.56/3.79 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y)) True)
% 3.56/3.79 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Or (Not (r1 (skS.0 1 a_1 a_2) a_3)) (p1 a_3)) True)
% 3.56/3.79 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (Not (r1 (skS.0 1 a_1 a_2) a_3)) True) (Eq (p1 a_3) True))
% 3.56/3.79 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (p1 a_2) True) (Eq (r1 (skS.0 1 a_1 a_3) a_2) False))
% 3.56/3.79 Clause #32 (by superposition #[31, 3]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 a) True) (Or (Eq (r1 (skS.0 1 (skS.0 0 a_1) a_2) a) False) (Eq False True))
% 3.56/3.79 Clause #33 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 1 a_1 a_2) Y)) (p1 Y)) False)
% 3.56/3.79 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 3.56/3.79 (Eq (Not (Or (Not (r1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3))) (p1 (skS.0 2 a_1 a_2 a_3)))) True)
% 3.56/3.79 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 3.56/3.79 (Eq (Or (Not (r1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3))) (p1 (skS.0 2 a_1 a_2 a_3))) False)
% 3.56/3.79 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (p1 (skS.0 2 a_1 a_2 a_3)) False)
% 3.56/3.79 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.79 Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Not (r1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3))) False)
% 3.56/3.79 Clause #39 (by superposition #[37, 3]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 (skS.0 2 (skS.0 0 a) a_1 a_2)) False) (Eq False True)
% 3.56/3.79 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Eq (p1 (skS.0 2 (skS.0 0 a) a_1 a_2)) False
% 3.56/3.79 Clause #41 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 a) True) (Eq (r1 (skS.0 1 (skS.0 0 a_1) a_2) a) False)
% 3.56/3.79 Clause #51 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (r1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) True)
% 3.56/3.79 Clause #53 (by superposition #[51, 3]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 1 (skS.0 0 a) a_1) (skS.0 2 (skS.0 0 a) a_1 a_2)) True) (Eq False True)
% 3.56/3.79 Clause #59 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 1 (skS.0 0 a) a_1) (skS.0 2 (skS.0 0 a) a_1 a_2)) True
% 3.56/3.79 Clause #60 (by superposition #[59, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq (p1 (skS.0 2 (skS.0 0 a) a_1 a_2)) True) (Eq True False)
% 3.56/3.79 Clause #67 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Eq (p1 (skS.0 2 (skS.0 0 a) a_1 a_2)) True
% 3.56/3.79 Clause #68 (by superposition #[67, 40]): Eq True False
% 3.56/3.79 Clause #69 (by clausification #[68]): False
% 3.56/3.79 SZS output end Proof for theBenchmark.p
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