TSTP Solution File: NUN067+1 by Duper---1.0
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% File : Duper---1.0
% Problem : NUN067+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 12:47:18 EDT 2023
% Result : Theorem 3.58s 3.76s
% Output : Proof 3.58s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUN067+1 : TPTP v8.1.2. Released v7.3.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n031.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 10:04:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.58/3.76 SZS status Theorem for theBenchmark.p
% 3.58/3.76 SZS output start Proof for theBenchmark.p
% 3.58/3.76 Clause #1 (by assumption #[]): Eq
% 3.58/3.76 (∀ (X11 : Iota),
% 3.58/3.76 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21))))
% 3.58/3.76 True
% 3.58/3.76 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True
% 3.58/3.76 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True
% 3.58/3.76 Clause #7 (by assumption #[]): Eq (∀ (X26 X27 : Iota), Or (Or (Not (id X26 X27)) (And (Not (r1 X26)) (Not (r1 X27)))) (And (r1 X26) (r1 X27))) True
% 3.58/3.76 Clause #17 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 X7 Y10))) True
% 3.58/3.76 Clause #18 (by assumption #[]): Eq (Not (Exists fun Y1 => ∀ (Y2 : Iota), Or (Not (id Y1 Y2)) (Not (r1 Y2)))) True
% 3.58/3.76 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True
% 3.58/3.76 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True
% 3.58/3.76 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True
% 3.58/3.76 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True)
% 3.58/3.76 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False)
% 3.58/3.76 Clause #25 (by clausification #[18]): Eq (Exists fun Y1 => ∀ (Y2 : Iota), Or (Not (id Y1 Y2)) (Not (r1 Y2))) False
% 3.58/3.76 Clause #26 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Y2 : Iota), Or (Not (id a Y2)) (Not (r1 Y2))) False
% 3.58/3.76 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Not (Or (Not (id a (skS.0 0 a a_1))) (Not (r1 (skS.0 0 a a_1))))) True
% 3.58/3.76 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Or (Not (id a (skS.0 0 a a_1))) (Not (r1 (skS.0 0 a a_1)))) False
% 3.58/3.76 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 0 a a_1))) False
% 3.58/3.76 Clause #30 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Not (id a (skS.0 0 a a_1))) False
% 3.58/3.76 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a a_1)) True
% 3.58/3.76 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (id a (skS.0 0 a a_1)) True
% 3.58/3.76 Clause #33 (by superposition #[32, 23]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a a_1) a) True) (Eq True False)
% 3.58/3.76 Clause #45 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a a_1) a) True
% 3.58/3.76 Clause #49 (by clausification #[1]): ∀ (a : Iota),
% 3.58/3.76 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True
% 3.58/3.76 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 3.58/3.76 Eq
% 3.58/3.76 (∀ (X12 : Iota), Or (And (id X12 (skS.0 2 a a_1)) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 (skS.0 2 a a_1)))))
% 3.58/3.76 True
% 3.58/3.76 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 3.58/3.76 Eq (Or (And (id a (skS.0 2 a_1 a_2)) (r2 a_1 a)) (And (Not (r2 a_1 a)) (Not (id a (skS.0 2 a_1 a_2))))) True
% 3.58/3.76 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 3.58/3.76 Or (Eq (And (id a (skS.0 2 a_1 a_2)) (r2 a_1 a)) True) (Eq (And (Not (r2 a_1 a)) (Not (id a (skS.0 2 a_1 a_2)))) True)
% 3.58/3.76 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (Not (r2 a a_1)) (Not (id a_1 (skS.0 2 a a_2)))) True) (Eq (r2 a a_1) True)
% 3.58/3.76 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (Not (id a_1 (skS.0 2 a a_2))) True)
% 3.58/3.76 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (id a_1 (skS.0 2 a a_2)) False)
% 3.58/3.76 Clause #59 (by superposition #[57, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 2 a a_1)) True) (Eq False True)
% 3.58/3.76 Clause #61 (by clausification #[59]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 2 a a_1)) True
% 3.58/3.76 Clause #108 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 a Y10))) True
% 3.58/3.76 Clause #109 (by clausification #[108]): ∀ (a a_1 : Iota), Eq (Or (∀ (Y20 : Iota), Or (Not (id Y20 a)) (Not (r1 Y20))) (Not (r2 a_1 a))) True
% 3.58/3.76 Clause #110 (by clausification #[109]): ∀ (a a_1 : Iota), Or (Eq (∀ (Y20 : Iota), Or (Not (id Y20 a)) (Not (r1 Y20))) True) (Eq (Not (r2 a_1 a)) True)
% 3.58/3.78 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (r2 a a_1)) True) (Eq (Or (Not (id a_2 a_1)) (Not (r1 a_2))) True)
% 3.58/3.78 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), Or (Eq (Or (Not (id a a_1)) (Not (r1 a))) True) (Eq (r2 a_2 a_1) False)
% 3.58/3.78 Clause #113 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (id a_2 a_1)) True) (Eq (Not (r1 a_2)) True))
% 3.58/3.78 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (r1 a_2)) True) (Eq (id a_2 a_1) False))
% 3.58/3.78 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (id a_2 a_1) False) (Eq (r1 a_2) False))
% 3.58/3.78 Clause #116 (by superposition #[115, 61]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 2 a_1 a_2)) False) (Or (Eq (r1 a) False) (Eq False True))
% 3.58/3.78 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 2 a_1 a_2)) False) (Eq (r1 a) False)
% 3.58/3.78 Clause #119 (by superposition #[117, 19]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 2 a a_1)) False) (Eq False True)
% 3.58/3.78 Clause #120 (by clausification #[119]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 2 a a_1)) False
% 3.58/3.78 Clause #121 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (X27 : Iota), Or (Or (Not (id a X27)) (And (Not (r1 a)) (Not (r1 X27)))) (And (r1 a) (r1 X27))) True
% 3.58/3.78 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (id a a_1)) (And (Not (r1 a)) (Not (r1 a_1)))) (And (r1 a) (r1 a_1))) True
% 3.58/3.78 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (Or (Not (id a a_1)) (And (Not (r1 a)) (Not (r1 a_1)))) True) (Eq (And (r1 a) (r1 a_1)) True)
% 3.58/3.78 Clause #124 (by clausification #[123]): ∀ (a a_1 : Iota),
% 3.58/3.78 Or (Eq (And (r1 a) (r1 a_1)) True) (Or (Eq (Not (id a a_1)) True) (Eq (And (Not (r1 a)) (Not (r1 a_1))) True))
% 3.58/3.78 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Or (Eq (And (Not (r1 a)) (Not (r1 a_1))) True) (Eq (r1 a_1) True))
% 3.58/3.78 Clause #127 (by clausification #[125]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (r1 a_1))) True) (Or (Eq (r1 a_1) True) (Eq (id a a_1) False))
% 3.58/3.78 Clause #129 (by clausification #[127]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (id a_1 a) False) (Eq (Not (r1 a_1)) True))
% 3.58/3.78 Clause #131 (by clausification #[129]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (id a_1 a) False) (Eq (r1 a_1) False))
% 3.58/3.78 Clause #133 (by superposition #[131, 45]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (r1 (skS.0 0 a a_1)) False) (Eq False True))
% 3.58/3.78 Clause #135 (by clausification #[133]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (r1 (skS.0 0 a a_1)) False)
% 3.58/3.78 Clause #136 (by superposition #[135, 31]): ∀ (a : Iota), Or (Eq (r1 a) True) (Eq False True)
% 3.58/3.78 Clause #137 (by clausification #[136]): ∀ (a : Iota), Eq (r1 a) True
% 3.58/3.78 Clause #143 (by superposition #[137, 120]): Eq True False
% 3.58/3.78 Clause #144 (by clausification #[143]): False
% 3.58/3.78 SZS output end Proof for theBenchmark.p
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