TSTP Solution File: NUN085+2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n011.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 12:47:23 EDT 2023
% Result : Theorem 24.07s 24.40s
% Output : Proof 24.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 09:34:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 24.07/24.40 SZS status Theorem for theBenchmark.p
% 24.07/24.40 SZS output start Proof for theBenchmark.p
% 24.07/24.40 Clause #1 (by assumption #[]): Eq
% 24.07/24.40 (∀ (X11 : Iota),
% 24.07/24.40 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21)))
% 24.07/24.40 True
% 24.07/24.40 Clause #2 (by assumption #[]): Eq
% 24.07/24.40 (∀ (X13 X14 : Iota),
% 24.07/24.40 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 X13 X14 X15)) (Ne X15 Y22)) (And (r3 X13 X14 X15) (Eq X15 Y22)))
% 24.07/24.40 True
% 24.07/24.40 Clause #4 (by assumption #[]): Eq
% 24.07/24.40 (∀ (X1 X8 : Iota),
% 24.07/24.40 Exists fun Y4 =>
% 24.07/24.40 And (Exists fun Y5 => And (Exists fun Y15 => And (r2 X8 Y15) (r3 X1 Y15 Y5)) (Eq Y5 Y4))
% 24.07/24.40 (Exists fun Y7 => And (r2 Y7 Y4) (r3 X1 X8 Y7)))
% 24.07/24.40 True
% 24.07/24.40 Clause #10 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 Y10)) (Not (r2 X7 Y10))) True
% 24.07/24.40 Clause #11 (by assumption #[]): Eq
% 24.07/24.40 (Not
% 24.07/24.40 (∀ (Y1 : Iota),
% 24.07/24.40 Or
% 24.07/24.40 (∀ (Y2 : Iota),
% 24.07/24.40 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 Y1))) (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))))
% 24.07/24.40 (∀ (Y5 : Iota), Or (Ne Y1 Y5) (Not (r1 Y5)))))
% 24.07/24.40 True
% 24.07/24.40 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
% 24.07/24.40 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
% 24.07/24.40 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)
% 24.07/24.40 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)
% 24.07/24.40 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)
% 24.07/24.40 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))
% 24.07/24.40 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))
% 24.07/24.40 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))
% 24.07/24.40 Clause #20 (by destructive equality resolution #[19]): ∀ (a a_1 : Iota), Or (Eq (r2 a a_1) False) (Eq (r1 a_1) False)
% 24.07/24.40 Clause #39 (by clausification #[1]): ∀ (a : Iota),
% 24.07/24.40 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True
% 24.07/24.40 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 24.07/24.40 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
% 24.07/24.40 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 24.07/24.40 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
% 24.07/24.40 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 24.07/24.40 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)
% 24.07/24.40 Clause #44 (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 (Not (r2 a a_1)) True)
% 24.07/24.40 Clause #62 (by clausification #[2]): ∀ (a : Iota),
% 24.07/24.40 Eq
% 24.07/24.40 (∀ (X14 : Iota),
% 24.07/24.40 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 a X14 X15)) (Ne X15 Y22)) (And (r3 a X14 X15) (Eq X15 Y22)))
% 24.07/24.40 True
% 24.07/24.40 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota),
% 24.07/24.40 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)))
% 24.07/24.40 True
% 24.07/24.40 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 24.07/24.40 Eq
% 24.07/24.40 (∀ (X15 : Iota),
% 24.07/24.40 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))))
% 24.07/24.40 True
% 24.07/24.40 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota),
% 24.07/24.40 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
% 24.07/24.40 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota),
% 24.07/24.40 Or (Eq (And (Not (r3 a a_1 a_2)) (Ne a_2 (skS.0 4 a a_1 a_3))) True)
% 24.19/24.43 (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True)
% 24.19/24.43 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True) (Eq (Not (r3 a a_1 a_2)) True)
% 24.19/24.43 Clause #94 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (r2 a a_1)) True) (Eq (Eq a_1 (skS.0 3 a a_2)) True)
% 24.19/24.43 Clause #96 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a (skS.0 3 a_1 a_2)) True) (Eq (r2 a_1 a) False)
% 24.19/24.43 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Eq a_1 (skS.0 3 a a_2))
% 24.19/24.43 Clause #100 (by clausification #[4]): ∀ (a : Iota),
% 24.19/24.43 Eq
% 24.19/24.43 (∀ (X8 : Iota),
% 24.19/24.43 Exists fun Y4 =>
% 24.19/24.43 And (Exists fun Y5 => And (Exists fun Y15 => And (r2 X8 Y15) (r3 a Y15 Y5)) (Eq Y5 Y4))
% 24.19/24.43 (Exists fun Y7 => And (r2 Y7 Y4) (r3 a X8 Y7)))
% 24.19/24.43 True
% 24.19/24.43 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota),
% 24.19/24.43 Eq
% 24.19/24.43 (Exists fun Y4 =>
% 24.19/24.43 And (Exists fun Y5 => And (Exists fun Y15 => And (r2 a Y15) (r3 a_1 Y15 Y5)) (Eq Y5 Y4))
% 24.19/24.43 (Exists fun Y7 => And (r2 Y7 Y4) (r3 a_1 a Y7)))
% 24.19/24.43 True
% 24.19/24.43 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota),
% 24.19/24.43 Eq
% 24.19/24.43 (And (Exists fun Y5 => And (Exists fun Y15 => And (r2 a Y15) (r3 a_1 Y15 Y5)) (Eq Y5 (skS.0 6 a a_1 a_2)))
% 24.19/24.43 (Exists fun Y7 => And (r2 Y7 (skS.0 6 a a_1 a_2)) (r3 a_1 a Y7)))
% 24.19/24.43 True
% 24.19/24.43 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), Eq (Exists fun Y7 => And (r2 Y7 (skS.0 6 a a_1 a_2)) (r3 a_1 a Y7)) True
% 24.19/24.43 Clause #104 (by clausification #[102]): ∀ (a a_1 a_2 : Iota),
% 24.19/24.43 Eq (Exists fun Y5 => And (Exists fun Y15 => And (r2 a Y15) (r3 a_1 Y15 Y5)) (Eq Y5 (skS.0 6 a a_1 a_2))) True
% 24.19/24.43 Clause #105 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota),
% 24.19/24.43 Eq (And (r2 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2)) (r3 a_1 a (skS.0 7 a a_1 a_2 a_3))) True
% 24.19/24.43 Clause #107 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r2 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2)) True
% 24.19/24.43 Clause #125 (by superposition #[107, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (r1 (skS.0 6 a a_1 a_2)) False)
% 24.19/24.43 Clause #136 (by clausification #[125]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 6 a a_1 a_2)) False
% 24.19/24.43 Clause #183 (by clausification #[11]): Eq
% 24.19/24.43 (∀ (Y1 : Iota),
% 24.19/24.43 Or
% 24.19/24.43 (∀ (Y2 : Iota),
% 24.19/24.43 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 Y1))) (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))))
% 24.19/24.43 (∀ (Y5 : Iota), Or (Ne Y1 Y5) (Not (r1 Y5))))
% 24.19/24.43 False
% 24.19/24.43 Clause #184 (by clausification #[183]): ∀ (a : Iota),
% 24.19/24.43 Eq
% 24.19/24.43 (Not
% 24.19/24.43 (Or
% 24.19/24.43 (∀ (Y2 : Iota),
% 24.19/24.43 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 (skS.0 16 a))))
% 24.19/24.43 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))))
% 24.19/24.43 (∀ (Y5 : Iota), Or (Ne (skS.0 16 a) Y5) (Not (r1 Y5)))))
% 24.19/24.43 True
% 24.19/24.43 Clause #185 (by clausification #[184]): ∀ (a : Iota),
% 24.19/24.43 Eq
% 24.19/24.43 (Or
% 24.19/24.43 (∀ (Y2 : Iota),
% 24.19/24.43 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 (skS.0 16 a))))
% 24.19/24.43 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))))
% 24.19/24.43 (∀ (Y5 : Iota), Or (Ne (skS.0 16 a) Y5) (Not (r1 Y5))))
% 24.19/24.43 False
% 24.19/24.43 Clause #186 (by clausification #[185]): ∀ (a : Iota), Eq (∀ (Y5 : Iota), Or (Ne (skS.0 16 a) Y5) (Not (r1 Y5))) False
% 24.19/24.43 Clause #187 (by clausification #[185]): ∀ (a : Iota),
% 24.19/24.43 Eq
% 24.19/24.43 (∀ (Y2 : Iota),
% 24.19/24.43 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 (skS.0 16 a))))
% 24.19/24.43 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))))
% 24.19/24.43 False
% 24.19/24.43 Clause #188 (by clausification #[186]): ∀ (a a_1 : Iota), Eq (Not (Or (Ne (skS.0 16 a) (skS.0 17 a a_1)) (Not (r1 (skS.0 17 a a_1))))) True
% 24.19/24.43 Clause #189 (by clausification #[188]): ∀ (a a_1 : Iota), Eq (Or (Ne (skS.0 16 a) (skS.0 17 a a_1)) (Not (r1 (skS.0 17 a a_1)))) False
% 24.19/24.43 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 17 a a_1))) False
% 24.19/24.43 Clause #191 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 16 a) (skS.0 17 a a_1)) False
% 24.19/24.43 Clause #192 (by clausification #[190]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 17 a a_1)) True
% 24.19/24.43 Clause #198 (by clausification #[191]): ∀ (a a_1 : Iota), Eq (skS.0 16 a) (skS.0 17 a a_1)
% 24.19/24.46 Clause #199 (by backward demodulation #[198, 192]): ∀ (a : Iota), Eq (r1 (skS.0 16 a)) True
% 24.19/24.46 Clause #202 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Not (r3 a a_1 a_2)) True) (Eq (Eq a_2 (skS.0 4 a a_1 a_3)) True)
% 24.19/24.46 Clause #204 (by clausification #[202]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Eq a (skS.0 4 a_1 a_2 a_3)) True) (Eq (r3 a_1 a_2 a) False)
% 24.19/24.46 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) False) (Eq a_2 (skS.0 4 a a_1 a_3))
% 24.19/24.46 Clause #218 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota),
% 24.19/24.46 Eq
% 24.19/24.46 (And (Exists fun Y15 => And (r2 a Y15) (r3 a_1 Y15 (skS.0 18 a a_1 a_2 a_3)))
% 24.19/24.46 (Eq (skS.0 18 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2)))
% 24.19/24.46 True
% 24.19/24.46 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (skS.0 18 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2)) True
% 24.19/24.46 Clause #220 (by clausification #[218]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Exists fun Y15 => And (r2 a Y15) (r3 a_1 Y15 (skS.0 18 a a_1 a_2 a_3))) True
% 24.19/24.46 Clause #221 (by clausification #[219]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 18 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2)
% 24.19/24.46 Clause #235 (by clausification #[220]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 24.19/24.46 Eq (And (r2 a (skS.0 19 a a_1 a_2 a_3 a_4)) (r3 a_1 (skS.0 19 a a_1 a_2 a_3 a_4) (skS.0 18 a a_1 a_2 a_3))) True
% 24.19/24.46 Clause #236 (by clausification #[235]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (r3 a (skS.0 19 a_1 a a_2 a_3 a_4) (skS.0 18 a_1 a a_2 a_3)) True
% 24.19/24.46 Clause #237 (by clausification #[235]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (r2 a (skS.0 19 a a_1 a_2 a_3 a_4)) True
% 24.19/24.46 Clause #238 (by forward demodulation #[236, 221]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (r3 a (skS.0 19 a_1 a a_2 a_3 a_4) (skS.0 6 a_1 a a_2)) True
% 24.19/24.46 Clause #241 (by superposition #[237, 97]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq True False) (Eq (skS.0 19 a a_1 a_2 a_3 a_4) (skS.0 3 a a_5))
% 24.19/24.46 Clause #259 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (skS.0 19 a a_1 a_2 a_3 a_4) (skS.0 3 a a_5)
% 24.19/24.46 Clause #260 (by superposition #[259, 238]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r3 a (skS.0 3 a_1 a_2) (skS.0 6 a_1 a a_3)) True
% 24.19/24.46 Clause #264 (by superposition #[260, 205]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq True False) (Eq (skS.0 6 a a_1 a_2) (skS.0 4 a_1 (skS.0 3 a a_3) a_4))
% 24.19/24.46 Clause #330 (by clausification #[187]): ∀ (a a_1 : Iota),
% 24.19/24.46 Eq
% 24.19/24.46 (Not
% 24.19/24.46 (Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 (skS.0 23 a a_1) (skS.0 16 a))))
% 24.19/24.46 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 23 a a_1))))))
% 24.19/24.46 True
% 24.19/24.46 Clause #331 (by clausification #[330]): ∀ (a a_1 : Iota),
% 24.19/24.46 Eq
% 24.19/24.46 (Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 (skS.0 23 a a_1) (skS.0 16 a))))
% 24.19/24.46 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 23 a a_1)))))
% 24.19/24.46 False
% 24.19/24.46 Clause #332 (by clausification #[331]): ∀ (a a_1 : Iota), Eq (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 23 a a_1)))) False
% 24.19/24.46 Clause #333 (by clausification #[331]): ∀ (a a_1 : Iota), Eq (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 (skS.0 23 a a_1) (skS.0 16 a)))) False
% 24.19/24.46 Clause #334 (by clausification #[332]): ∀ (a a_1 a_2 : Iota),
% 24.19/24.46 Eq (Not (Or (Not (r1 (skS.0 24 a a_1 a_2))) (Not (r2 (skS.0 24 a a_1 a_2) (skS.0 23 a a_1))))) True
% 24.19/24.46 Clause #335 (by clausification #[334]): ∀ (a a_1 a_2 : Iota), Eq (Or (Not (r1 (skS.0 24 a a_1 a_2))) (Not (r2 (skS.0 24 a a_1 a_2) (skS.0 23 a a_1)))) False
% 24.19/24.46 Clause #336 (by clausification #[335]): ∀ (a a_1 a_2 : Iota), Eq (Not (r2 (skS.0 24 a a_1 a_2) (skS.0 23 a a_1))) False
% 24.19/24.46 Clause #338 (by clausification #[336]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 24 a a_1 a_2) (skS.0 23 a a_1)) True
% 24.19/24.46 Clause #340 (by superposition #[338, 97]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (skS.0 23 a a_1) (skS.0 3 (skS.0 24 a a_1 a_2) a_3))
% 24.19/24.46 Clause #397 (by clausification #[333]): ∀ (a a_1 a_2 : Iota),
% 24.19/24.46 Eq (Not (Or (Not (r1 (skS.0 25 a a_1 a_2))) (Not (r3 (skS.0 25 a a_1 a_2) (skS.0 23 a a_1) (skS.0 16 a))))) True
% 24.19/24.46 Clause #398 (by clausification #[397]): ∀ (a a_1 a_2 : Iota),
% 24.19/24.46 Eq (Or (Not (r1 (skS.0 25 a a_1 a_2))) (Not (r3 (skS.0 25 a a_1 a_2) (skS.0 23 a a_1) (skS.0 16 a)))) False
% 24.19/24.47 Clause #399 (by clausification #[398]): ∀ (a a_1 a_2 : Iota), Eq (Not (r3 (skS.0 25 a a_1 a_2) (skS.0 23 a a_1) (skS.0 16 a))) False
% 24.19/24.47 Clause #401 (by clausification #[399]): ∀ (a a_1 a_2 : Iota), Eq (r3 (skS.0 25 a a_1 a_2) (skS.0 23 a a_1) (skS.0 16 a)) True
% 24.19/24.47 Clause #402 (by superposition #[401, 205]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (skS.0 16 a) (skS.0 4 (skS.0 25 a a_1 a_2) (skS.0 23 a a_1) a_3))
% 24.19/24.47 Clause #498 (by clausification #[264]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (skS.0 6 a a_1 a_2) (skS.0 4 a_1 (skS.0 3 a a_3) a_4)
% 24.19/24.47 Clause #500 (by superposition #[498, 136]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r1 (skS.0 4 a (skS.0 3 a_1 a_2) a_3)) False
% 24.19/24.47 Clause #938 (by clausification #[340]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 23 a a_1) (skS.0 3 (skS.0 24 a a_1 a_2) a_3)
% 24.19/24.47 Clause #942 (by superposition #[938, 500]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r1 (skS.0 4 a (skS.0 23 a_1 a_2) a_3)) False
% 24.19/24.47 Clause #1237 (by clausification #[402]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 16 a) (skS.0 4 (skS.0 25 a a_1 a_2) (skS.0 23 a a_1) a_3)
% 24.19/24.47 Clause #1238 (by superposition #[1237, 942]): ∀ (a : Iota), Eq (r1 (skS.0 16 a)) False
% 24.19/24.47 Clause #1245 (by superposition #[1238, 199]): Eq False True
% 24.19/24.47 Clause #1246 (by clausification #[1245]): False
% 24.19/24.47 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------