TSTP Solution File: NUN080+2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN080+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 12:47:22 EDT 2023
% Result : Theorem 4.25s 4.44s
% Output : Proof 4.31s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN080+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 09:03:42 EDT 2023
% 0.14/0.34 % CPUTime :
% 4.25/4.44 SZS status Theorem for theBenchmark.p
% 4.25/4.44 SZS output start Proof for theBenchmark.p
% 4.25/4.44 Clause #0 (by assumption #[]): Eq (Exists fun Y24 => ∀ (X19 : Iota), Or (And (Not (r1 X19)) (Ne X19 Y24)) (And (r1 X19) (Eq X19 Y24))) True
% 4.25/4.44 Clause #1 (by assumption #[]): Eq
% 4.25/4.44 (∀ (X11 : Iota),
% 4.25/4.44 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21)))
% 4.25/4.44 True
% 4.25/4.44 Clause #2 (by assumption #[]): Eq
% 4.25/4.44 (∀ (X13 X14 : Iota),
% 4.25/4.44 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 X13 X14 X15)) (Ne X15 Y22)) (And (r3 X13 X14 X15) (Eq X15 Y22)))
% 4.25/4.44 True
% 4.25/4.44 Clause #11 (by assumption #[]): Eq
% 4.25/4.44 (Not
% 4.25/4.44 (Exists fun Y1 =>
% 4.25/4.44 Exists fun Y2 =>
% 4.25/4.44 Exists fun Y3 =>
% 4.25/4.44 And (Eq Y3 Y2)
% 4.25/4.44 (Exists fun Y4 =>
% 4.25/4.44 And (r3 Y1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))))
% 4.25/4.44 True
% 4.25/4.44 Clause #30 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (X19 : Iota), Or (And (Not (r1 X19)) (Ne X19 (skS.0 2 a))) (And (r1 X19) (Eq X19 (skS.0 2 a)))) True
% 4.25/4.44 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Or (And (Not (r1 a)) (Ne a (skS.0 2 a_1))) (And (r1 a) (Eq a (skS.0 2 a_1)))) True
% 4.25/4.44 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Ne a (skS.0 2 a_1))) True) (Eq (And (r1 a) (Eq a (skS.0 2 a_1))) True)
% 4.25/4.44 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (And (r1 a) (Eq a (skS.0 2 a_1))) True) (Eq (Ne a (skS.0 2 a_1)) True)
% 4.25/4.44 Clause #36 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (Ne a (skS.0 2 a_1)) True) (Eq (r1 a) True)
% 4.25/4.44 Clause #39 (by clausification #[1]): ∀ (a : Iota),
% 4.25/4.44 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True
% 4.25/4.44 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 4.25/4.44 Eq (∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 (skS.0 3 a a_1))) (And (r2 a X12) (Eq X12 (skS.0 3 a a_1)))) True
% 4.25/4.44 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 4.25/4.44 Eq (Or (And (Not (r2 a a_1)) (Ne a_1 (skS.0 3 a a_2))) (And (r2 a a_1) (Eq a_1 (skS.0 3 a a_2)))) True
% 4.25/4.44 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 4.25/4.44 Or (Eq (And (Not (r2 a a_1)) (Ne a_1 (skS.0 3 a a_2))) True) (Eq (And (r2 a a_1) (Eq a_1 (skS.0 3 a a_2))) True)
% 4.25/4.44 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (r2 a a_1) (Eq a_1 (skS.0 3 a a_2))) True) (Eq (Ne a_1 (skS.0 3 a a_2)) True)
% 4.25/4.44 Clause #46 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Eq (Ne a (skS.0 3 a_1 a_2)) True) (Eq (r2 a_1 a) True)
% 4.25/4.44 Clause #49 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Ne a (skS.0 2 a_1))
% 4.25/4.44 Clause #50 (by destructive equality resolution #[49]): ∀ (a : Iota), Eq (r1 (skS.0 2 a)) True
% 4.25/4.44 Clause #51 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Ne a_1 (skS.0 3 a a_2))
% 4.25/4.44 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True
% 4.25/4.44 Clause #62 (by clausification #[2]): ∀ (a : Iota),
% 4.25/4.44 Eq
% 4.25/4.44 (∀ (X14 : Iota),
% 4.25/4.44 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 a X14 X15)) (Ne X15 Y22)) (And (r3 a X14 X15) (Eq X15 Y22)))
% 4.25/4.44 True
% 4.25/4.44 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota),
% 4.25/4.44 Eq (Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 a a_1 X15)) (Ne X15 Y22)) (And (r3 a a_1 X15) (Eq X15 Y22)))
% 4.25/4.44 True
% 4.25/4.44 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 4.25/4.44 Eq
% 4.25/4.44 (∀ (X15 : Iota),
% 4.25/4.44 Or (And (Not (r3 a a_1 X15)) (Ne X15 (skS.0 4 a a_1 a_2))) (And (r3 a a_1 X15) (Eq X15 (skS.0 4 a a_1 a_2))))
% 4.25/4.44 True
% 4.25/4.44 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.25/4.44 Eq (Or (And (Not (r3 a a_1 a_2)) (Ne a_2 (skS.0 4 a a_1 a_3))) (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3)))) True
% 4.25/4.44 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.25/4.44 Or (Eq (And (Not (r3 a a_1 a_2)) (Ne a_2 (skS.0 4 a a_1 a_3))) True)
% 4.25/4.44 (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True)
% 4.25/4.44 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.25/4.44 Or (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True) (Eq (Ne a_2 (skS.0 4 a a_1 a_3)) True)
% 4.31/4.46 Clause #70 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Ne a (skS.0 4 a_1 a_2 a_3)) True) (Eq (r3 a_1 a_2 a) True)
% 4.31/4.46 Clause #92 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Ne a_2 (skS.0 4 a a_1 a_3))
% 4.31/4.46 Clause #93 (by destructive equality resolution #[92]): ∀ (a a_1 a_2 : Iota), Eq (r3 a a_1 (skS.0 4 a a_1 a_2)) True
% 4.31/4.46 Clause #183 (by clausification #[11]): Eq
% 4.31/4.46 (Exists fun Y1 =>
% 4.31/4.46 Exists fun Y2 =>
% 4.31/4.46 Exists fun Y3 =>
% 4.31/4.46 And (Eq Y3 Y2)
% 4.31/4.46 (Exists fun Y4 =>
% 4.31/4.46 And (r3 Y1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))
% 4.31/4.46 False
% 4.31/4.46 Clause #184 (by clausification #[183]): ∀ (a : Iota),
% 4.31/4.46 Eq
% 4.31/4.46 (Exists fun Y2 =>
% 4.31/4.46 Exists fun Y3 =>
% 4.31/4.46 And (Eq Y3 Y2)
% 4.31/4.46 (Exists fun Y4 =>
% 4.31/4.46 And (r3 a Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))
% 4.31/4.46 False
% 4.31/4.46 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota),
% 4.31/4.46 Eq
% 4.31/4.46 (Exists fun Y3 =>
% 4.31/4.46 And (Eq Y3 a)
% 4.31/4.46 (Exists fun Y4 =>
% 4.31/4.46 And (r3 a_1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))
% 4.31/4.46 False
% 4.31/4.46 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 : Iota),
% 4.31/4.46 Eq
% 4.31/4.46 (And (Eq a a_1)
% 4.31/4.46 (Exists fun Y4 => And (r3 a_2 Y4 a) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))
% 4.31/4.46 False
% 4.31/4.46 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota),
% 4.31/4.46 Or (Eq (Eq a a_1) False)
% 4.31/4.46 (Eq (Exists fun Y4 => And (r3 a_2 Y4 a) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))
% 4.31/4.46 False)
% 4.31/4.46 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 : Iota),
% 4.31/4.46 Or
% 4.31/4.46 (Eq (Exists fun Y4 => And (r3 a Y4 a_1) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))
% 4.31/4.46 False)
% 4.31/4.46 (Ne a_1 a_2)
% 4.31/4.46 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.31/4.46 Or (Ne a a_1)
% 4.31/4.46 (Eq (And (r3 a_2 a_3 a) (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))) False)
% 4.31/4.46 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.31/4.46 Or (Ne a a_1)
% 4.31/4.46 (Or (Eq (r3 a_2 a_3 a) False)
% 4.31/4.46 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))) False))
% 4.31/4.46 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.31/4.46 Or (Ne a a_1) (Or (Eq (r3 a_2 a_3 a) False) (Eq (And (r2 a_4 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_4))) False))
% 4.31/4.46 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.31/4.46 Or (Ne a a_1)
% 4.31/4.46 (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_4)) False)))
% 4.31/4.46 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.31/4.46 Or (Ne a a_1) (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Eq (And (r1 a_5) (r2 a_5 a_4)) False)))
% 4.31/4.46 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.31/4.46 Or (Ne a a_1)
% 4.31/4.46 (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False))))
% 4.31/4.46 Clause #195 (by destructive equality resolution #[194]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.31/4.46 Or (Eq (r3 a a_1 a_2) False) (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_3) False)))
% 4.31/4.46 Clause #196 (by superposition #[195, 93]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Or (Eq (r2 a_2 a) False) (Eq False True)))
% 4.31/4.46 Clause #201 (by clausification #[196]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a) False))
% 4.31/4.46 Clause #203 (by superposition #[201, 52]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True))
% 4.31/4.46 Clause #204 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False)
% 4.31/4.46 Clause #206 (by superposition #[204, 50]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 2 a) a_1) False) (Eq False True)
% 4.31/4.46 Clause #209 (by clausification #[206]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 2 a) a_1) False
% 4.31/4.46 Clause #210 (by superposition #[209, 52]): Eq False True
% 4.31/4.46 Clause #211 (by clausification #[210]): False
% 4.31/4.46 SZS output end Proof for theBenchmark.p
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