TSTP Solution File: NUN081+2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN081+2 : TPTP v8.1.2. Released v7.3.0.
% 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 12:47:22 EDT 2023
% Result : Theorem 4.22s 4.45s
% Output : Proof 4.32s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN081+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 10:17:06 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.22/4.45 SZS status Theorem for theBenchmark.p
% 4.22/4.45 SZS output start Proof for theBenchmark.p
% 4.22/4.45 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
% 4.22/4.45 Clause #1 (by assumption #[]): Eq
% 4.22/4.45 (∀ (X11 : Iota),
% 4.22/4.45 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21)))
% 4.22/4.45 True
% 4.22/4.45 Clause #7 (by assumption #[]): Eq (∀ (X4 : Iota), Exists fun Y9 => And (Exists fun Y16 => And (r1 Y16) (r3 X4 Y16 Y9)) (Eq Y9 X4)) True
% 4.22/4.45 Clause #11 (by assumption #[]): Eq
% 4.22/4.45 (Not
% 4.22/4.45 (Exists fun Y1 =>
% 4.22/4.45 Exists fun Y2 =>
% 4.22/4.45 Exists fun Y3 =>
% 4.22/4.45 And (r3 Y1 Y2 Y3)
% 4.22/4.45 (Exists fun Y4 =>
% 4.22/4.45 And (Eq Y3 Y4)
% 4.22/4.45 (Exists fun Y5 =>
% 4.22/4.45 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))))
% 4.22/4.45 True
% 4.22/4.45 Clause #21 (by clausification #[7]): ∀ (a : Iota), Eq (Exists fun Y9 => And (Exists fun Y16 => And (r1 Y16) (r3 a Y16 Y9)) (Eq Y9 a)) True
% 4.22/4.45 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (And (Exists fun Y16 => And (r1 Y16) (r3 a Y16 (skS.0 0 a a_1))) (Eq (skS.0 0 a a_1) a)) True
% 4.22/4.45 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a a_1) a) True
% 4.22/4.45 Clause #24 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Exists fun Y16 => And (r1 Y16) (r3 a Y16 (skS.0 0 a a_1))) True
% 4.22/4.45 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (skS.0 0 a a_1) a
% 4.22/4.45 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 1 a a_1 a_2)) (r3 a (skS.0 1 a a_1 a_2) (skS.0 0 a a_1))) True
% 4.22/4.45 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (r3 a (skS.0 1 a a_1 a_2) (skS.0 0 a a_1)) True
% 4.22/4.45 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 1 a a_1 a_2)) True
% 4.22/4.45 Clause #29 (by forward demodulation #[27, 25]): ∀ (a a_1 a_2 : Iota), Eq (r3 a (skS.0 1 a a_1 a_2) a) True
% 4.22/4.45 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
% 4.22/4.45 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
% 4.22/4.45 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)
% 4.22/4.45 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)
% 4.22/4.45 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (And (r1 a) (Eq a (skS.0 2 a_1))) True) (Eq (Not (r1 a)) True)
% 4.22/4.45 Clause #36 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (Ne a (skS.0 2 a_1)) True) (Eq (r1 a) True)
% 4.22/4.45 Clause #39 (by clausification #[1]): ∀ (a : Iota),
% 4.22/4.45 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True
% 4.22/4.45 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 4.22/4.45 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
% 4.22/4.45 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.45 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
% 4.22/4.45 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.45 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)
% 4.22/4.45 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)
% 4.22/4.45 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)
% 4.22/4.45 Clause #49 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Ne a (skS.0 2 a_1))
% 4.22/4.45 Clause #50 (by destructive equality resolution #[49]): ∀ (a : Iota), Eq (r1 (skS.0 2 a)) True
% 4.22/4.45 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))
% 4.22/4.45 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True
% 4.32/4.48 Clause #55 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 a)) True) (Eq (Eq a (skS.0 2 a_1)) True)
% 4.32/4.48 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (Eq a (skS.0 2 a_1)) True) (Eq (r1 a) False)
% 4.32/4.48 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq a (skS.0 2 a_1))
% 4.32/4.48 Clause #59 (by superposition #[58, 28]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 1 a a_1 a_2) (skS.0 2 a_3)) (Eq False True)
% 4.32/4.48 Clause #74 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 1 a a_1 a_2) (skS.0 2 a_3)
% 4.32/4.48 Clause #75 (by superposition #[74, 29]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 2 a_1) a) True
% 4.32/4.48 Clause #183 (by clausification #[11]): Eq
% 4.32/4.48 (Exists fun Y1 =>
% 4.32/4.48 Exists fun Y2 =>
% 4.32/4.48 Exists fun Y3 =>
% 4.32/4.48 And (r3 Y1 Y2 Y3)
% 4.32/4.48 (Exists fun Y4 =>
% 4.32/4.48 And (Eq Y3 Y4)
% 4.32/4.48 (Exists fun Y5 =>
% 4.32/4.48 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))
% 4.32/4.48 False
% 4.32/4.48 Clause #184 (by clausification #[183]): ∀ (a : Iota),
% 4.32/4.48 Eq
% 4.32/4.48 (Exists fun Y2 =>
% 4.32/4.48 Exists fun Y3 =>
% 4.32/4.48 And (r3 a Y2 Y3)
% 4.32/4.48 (Exists fun Y4 =>
% 4.32/4.48 And (Eq Y3 Y4)
% 4.32/4.48 (Exists fun Y5 =>
% 4.32/4.48 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))
% 4.32/4.48 False
% 4.32/4.48 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota),
% 4.32/4.48 Eq
% 4.32/4.48 (Exists fun Y3 =>
% 4.32/4.48 And (r3 a a_1 Y3)
% 4.32/4.48 (Exists fun Y4 =>
% 4.32/4.48 And (Eq Y3 Y4)
% 4.32/4.48 (Exists fun Y5 =>
% 4.32/4.48 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))
% 4.32/4.48 False
% 4.32/4.48 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 : Iota),
% 4.32/4.48 Eq
% 4.32/4.48 (And (r3 a a_1 a_2)
% 4.32/4.48 (Exists fun Y4 =>
% 4.32/4.48 And (Eq a_2 Y4)
% 4.32/4.48 (Exists fun Y5 =>
% 4.32/4.48 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))
% 4.32/4.48 False
% 4.32/4.48 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota),
% 4.32/4.48 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.48 (Eq
% 4.32/4.48 (Exists fun Y4 =>
% 4.32/4.48 And (Eq a_2 Y4)
% 4.32/4.48 (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))
% 4.32/4.48 False)
% 4.32/4.48 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.32/4.48 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.48 (Eq
% 4.32/4.48 (And (Eq a_2 a_3)
% 4.32/4.48 (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))
% 4.32/4.48 False)
% 4.32/4.48 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.32/4.48 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.48 (Or (Eq (Eq a_2 a_3) False)
% 4.32/4.48 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))
% 4.32/4.48 False))
% 4.32/4.48 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.32/4.48 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.48 (Or
% 4.32/4.48 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))
% 4.32/4.48 False)
% 4.32/4.48 (Ne a_2 a_3))
% 4.32/4.48 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.32/4.48 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.48 (Or (Ne a_2 a_3)
% 4.32/4.48 (Eq (And (r2 a_4 a_3) (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))) False))
% 4.32/4.48 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.32/4.48 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.48 (Or (Ne a_2 a_3)
% 4.32/4.48 (Or (Eq (r2 a_4 a_3) False)
% 4.32/4.48 (Eq (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))) False)))
% 4.32/4.48 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.32/4.48 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.48 (Or (Ne a_2 a_3)
% 4.32/4.48 (Or (Eq (r2 a_4 a_3) False) (Eq (And (r2 a_5 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 a_5))) False)))
% 4.32/4.48 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.32/4.48 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.48 (Or (Ne a_2 a_3)
% 4.32/4.48 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Eq (Exists fun Y7 => And (r1 Y7) (r2 Y7 a_5)) False))))
% 4.32/4.48 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 4.32/4.49 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.49 (Or (Ne a_2 a_3) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Eq (And (r1 a_6) (r2 a_6 a_5)) False))))
% 4.32/4.49 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 4.32/4.49 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.49 (Or (Ne a_2 a_3)
% 4.32/4.49 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Or (Eq (r1 a_6) False) (Eq (r2 a_6 a_5) False)))))
% 4.32/4.49 Clause #197 (by destructive equality resolution #[196]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.32/4.49 Or (Eq (r3 a a_1 a_2) False)
% 4.32/4.49 (Or (Eq (r2 a_3 a_2) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False))))
% 4.32/4.49 Clause #200 (by superposition #[197, 75]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.32/4.49 Or (Eq (r2 a a_1) False)
% 4.32/4.49 (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_2) False) (Eq False True))))
% 4.32/4.49 Clause #201 (by clausification #[200]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.32/4.49 Or (Eq (r2 a a_1) False) (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Eq (r2 a_3 a_2) False)))
% 4.32/4.49 Clause #203 (by superposition #[201, 52]): ∀ (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)))
% 4.32/4.49 Clause #204 (by clausification #[203]): ∀ (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))
% 4.32/4.49 Clause #206 (by superposition #[204, 52]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True))
% 4.32/4.49 Clause #207 (by clausification #[206]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False)
% 4.32/4.49 Clause #209 (by superposition #[207, 50]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 2 a) a_1) False) (Eq False True)
% 4.32/4.49 Clause #212 (by clausification #[209]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 2 a) a_1) False
% 4.32/4.49 Clause #213 (by superposition #[212, 52]): Eq False True
% 4.32/4.49 Clause #214 (by clausification #[213]): False
% 4.32/4.49 SZS output end Proof for theBenchmark.p
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