TSTP Solution File: NUN062+2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN062+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 12:47:17 EDT 2023
% Result : Theorem 7.57s 7.73s
% Output : Proof 7.57s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN062+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 09:03:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 7.57/7.73 SZS status Theorem for theBenchmark.p
% 7.57/7.73 SZS output start Proof for theBenchmark.p
% 7.57/7.73 Clause #1 (by assumption #[]): Eq
% 7.57/7.73 (∀ (X11 : Iota),
% 7.57/7.73 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21)))
% 7.57/7.73 True
% 7.57/7.73 Clause #2 (by assumption #[]): Eq
% 7.57/7.73 (∀ (X13 X14 : Iota),
% 7.57/7.73 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 X13 X14 X15)) (Ne X15 Y22)) (And (r3 X13 X14 X15) (Eq X15 Y22)))
% 7.57/7.73 True
% 7.57/7.73 Clause #10 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 Y10)) (Not (r2 X7 Y10))) True
% 7.57/7.73 Clause #11 (by assumption #[]): Eq
% 7.57/7.73 (Not
% 7.57/7.73 (∀ (X1 : Iota),
% 7.57/7.73 Exists fun Y2 =>
% 7.57/7.73 Exists fun Y1 =>
% 7.57/7.73 And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 X1 Y1 Y3) (Eq Y3 Y2))))
% 7.57/7.73 True
% 7.57/7.73 Clause #12 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 Y10)) (Not (r2 a Y10))) True
% 7.57/7.73 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 a)) (Not (r2 a_1 a))) True
% 7.57/7.73 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 a)) True) (Eq (Not (r2 a_1 a)) True)
% 7.57/7.73 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (r2 a a_1)) True) (Eq (Or (Not (r1 a_2)) (Ne a_2 a_1)) True)
% 7.57/7.73 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (Or (Not (r1 a)) (Ne a a_1)) True) (Eq (r2 a_2 a_1) False)
% 7.57/7.73 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (r1 a_2)) True) (Eq (Ne a_2 a_1) True))
% 7.57/7.73 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Ne a_2 a_1) True) (Eq (r1 a_2) False))
% 7.57/7.73 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Ne a_2 a_1))
% 7.57/7.73 Clause #20 (by destructive equality resolution #[19]): ∀ (a a_1 : Iota), Or (Eq (r2 a a_1) False) (Eq (r1 a_1) False)
% 7.57/7.73 Clause #39 (by clausification #[1]): ∀ (a : Iota),
% 7.57/7.73 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True
% 7.57/7.73 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 7.57/7.73 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
% 7.57/7.73 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 7.57/7.73 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
% 7.57/7.73 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 7.57/7.73 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)
% 7.57/7.73 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)
% 7.57/7.73 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)
% 7.57/7.73 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))
% 7.57/7.73 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True
% 7.57/7.73 Clause #53 (by superposition #[52, 20]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (r1 (skS.0 3 a a_1)) False)
% 7.57/7.73 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 3 a a_1)) False
% 7.57/7.73 Clause #62 (by clausification #[2]): ∀ (a : Iota),
% 7.57/7.73 Eq
% 7.57/7.73 (∀ (X14 : Iota),
% 7.57/7.73 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 a X14 X15)) (Ne X15 Y22)) (And (r3 a X14 X15) (Eq X15 Y22)))
% 7.57/7.73 True
% 7.57/7.73 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota),
% 7.57/7.73 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)))
% 7.57/7.73 True
% 7.57/7.73 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 7.57/7.73 Eq
% 7.57/7.73 (∀ (X15 : Iota),
% 7.57/7.73 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))))
% 7.57/7.73 True
% 7.57/7.73 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.57/7.73 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
% 7.57/7.77 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.57/7.77 Or (Eq (And (Not (r3 a a_1 a_2)) (Ne a_2 (skS.0 4 a a_1 a_3))) True)
% 7.57/7.77 (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True)
% 7.57/7.77 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.57/7.77 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)
% 7.57/7.77 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)
% 7.57/7.77 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))
% 7.57/7.77 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
% 7.57/7.77 Clause #183 (by clausification #[11]): Eq
% 7.57/7.77 (∀ (X1 : Iota),
% 7.57/7.77 Exists fun Y2 =>
% 7.57/7.77 Exists fun Y1 => And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 X1 Y1 Y3) (Eq Y3 Y2)))
% 7.57/7.77 False
% 7.57/7.77 Clause #184 (by clausification #[183]): ∀ (a : Iota),
% 7.57/7.77 Eq
% 7.57/7.77 (Not
% 7.57/7.77 (Exists fun Y2 =>
% 7.57/7.77 Exists fun Y1 =>
% 7.57/7.77 And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 (skS.0 16 a) Y1 Y3) (Eq Y3 Y2))))
% 7.57/7.77 True
% 7.57/7.77 Clause #185 (by clausification #[184]): ∀ (a : Iota),
% 7.57/7.77 Eq
% 7.57/7.77 (Exists fun Y2 =>
% 7.57/7.77 Exists fun Y1 =>
% 7.57/7.77 And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 (skS.0 16 a) Y1 Y3) (Eq Y3 Y2)))
% 7.57/7.77 False
% 7.57/7.77 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota),
% 7.57/7.77 Eq
% 7.57/7.77 (Exists fun Y1 =>
% 7.57/7.77 And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 (skS.0 16 a) Y1 Y3) (Eq Y3 a_1)))
% 7.57/7.77 False
% 7.57/7.77 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota),
% 7.57/7.77 Eq (And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne a Y4)) (Exists fun Y3 => And (r3 (skS.0 16 a_1) a Y3) (Eq Y3 a_2))) False
% 7.57/7.77 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 : Iota),
% 7.57/7.77 Or (Eq (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne a Y4)) False)
% 7.57/7.77 (Eq (Exists fun Y3 => And (r3 (skS.0 16 a_1) a Y3) (Eq Y3 a_2)) False)
% 7.57/7.77 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.57/7.77 Or (Eq (Exists fun Y3 => And (r3 (skS.0 16 a) a_1 Y3) (Eq Y3 a_2)) False)
% 7.57/7.77 (Eq (Not (Or (Not (r1 (skS.0 17 a_1 a_3))) (Ne a_1 (skS.0 17 a_1 a_3)))) True)
% 7.57/7.77 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.57/7.77 Or (Eq (Not (Or (Not (r1 (skS.0 17 a a_1))) (Ne a (skS.0 17 a a_1)))) True)
% 7.57/7.77 (Eq (And (r3 (skS.0 16 a_2) a a_3) (Eq a_3 a_4)) False)
% 7.57/7.77 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.57/7.77 Or (Eq (And (r3 (skS.0 16 a) a_1 a_2) (Eq a_2 a_3)) False)
% 7.57/7.77 (Eq (Or (Not (r1 (skS.0 17 a_1 a_4))) (Ne a_1 (skS.0 17 a_1 a_4))) False)
% 7.57/7.77 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.57/7.77 Or (Eq (Or (Not (r1 (skS.0 17 a a_1))) (Ne a (skS.0 17 a a_1))) False)
% 7.57/7.77 (Or (Eq (r3 (skS.0 16 a_2) a a_3) False) (Eq (Eq a_3 a_4) False))
% 7.57/7.77 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.57/7.77 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (Eq a_2 a_3) False) (Eq (Ne a_1 (skS.0 17 a_1 a_4)) False))
% 7.57/7.77 Clause #194 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.57/7.77 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (Eq a_2 a_3) False) (Eq (Not (r1 (skS.0 17 a_1 a_4))) False))
% 7.57/7.77 Clause #195 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.57/7.77 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (Ne a_1 (skS.0 17 a_1 a_3)) False) (Ne a_2 a_4))
% 7.57/7.77 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Ne a_2 a_3) (Eq a_1 (skS.0 17 a_1 a_4)))
% 7.57/7.77 Clause #197 (by destructive equality resolution #[196]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Eq a_1 (skS.0 17 a_1 a_3))
% 7.57/7.77 Clause #198 (by superposition #[197, 93]): ∀ (a a_1 : Iota), Or (Eq a (skS.0 17 a a_1)) (Eq False True)
% 7.57/7.77 Clause #203 (by clausification #[198]): ∀ (a a_1 : Iota), Eq a (skS.0 17 a a_1)
% 7.57/7.77 Clause #341 (by clausification #[194]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.57/7.78 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (Not (r1 (skS.0 17 a_1 a_3))) False) (Ne a_2 a_4))
% 7.57/7.78 Clause #342 (by clausification #[341]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.57/7.78 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Ne a_2 a_3) (Eq (r1 (skS.0 17 a_1 a_4)) True))
% 7.57/7.78 Clause #343 (by destructive equality resolution #[342]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Eq (r1 (skS.0 17 a_1 a_3)) True)
% 7.57/7.78 Clause #344 (by forward demodulation #[343, 203]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Eq (r1 a_1) True)
% 7.57/7.78 Clause #348 (by superposition #[344, 93]): ∀ (a : Iota), Or (Eq (r1 a) True) (Eq False True)
% 7.57/7.78 Clause #353 (by clausification #[348]): ∀ (a : Iota), Eq (r1 a) True
% 7.57/7.78 Clause #356 (by superposition #[353, 54]): Eq True False
% 7.57/7.78 Clause #360 (by clausification #[356]): False
% 7.57/7.78 SZS output end Proof for theBenchmark.p
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