%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN085+2 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 : Fri Oct 3 07:57:51 PM UTC 2025 % Result : Theorem 23.26s 23.48s % Output : Proof 23.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUN085+2 : TPTP v9.2.0. Released v7.3.0. % 0.08/0.13 % Command : duper %s % 0.12/0.34 % Computer : n005.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 11:32:53 EDT 2025 % 0.12/0.34 % CPUTime : % 23.26/23.48 SZS status Theorem for theBenchmark.p % 23.26/23.48 SZS output start Proof for theBenchmark.p % 23.26/23.48 Clause #1 (by assumption #[]): Eq % 23.26/23.48 (∀ (X11 : Iota), % 23.26/23.48 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21))) % 23.26/23.48 True % 23.26/23.48 Clause #2 (by assumption #[]): Eq % 23.26/23.48 (∀ (X13 X14 : Iota), % 23.26/23.48 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 X13 X14 X15)) (Ne X15 Y22)) (And (r3 X13 X14 X15) (Eq X15 Y22))) % 23.26/23.48 True % 23.26/23.48 Clause #4 (by assumption #[]): Eq % 23.26/23.48 (∀ (X1 X8 : Iota), % 23.26/23.48 Exists fun Y4 => % 23.26/23.48 And (Exists fun Y5 => And (Exists fun Y15 => And (r2 X8 Y15) (r3 X1 Y15 Y5)) (Eq Y5 Y4)) % 23.26/23.48 (Exists fun Y7 => And (r2 Y7 Y4) (r3 X1 X8 Y7))) % 23.26/23.48 True % 23.26/23.48 Clause #10 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 Y10)) (Not (r2 X7 Y10))) True % 23.26/23.48 Clause #11 (by assumption #[]): Eq % 23.26/23.48 (Not % 23.26/23.48 (∀ (Y1 : Iota), % 23.26/23.48 Or % 23.26/23.48 (∀ (Y2 : Iota), % 23.26/23.48 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 Y1))) (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2)))) % 23.26/23.48 (∀ (Y5 : Iota), Or (Ne Y1 Y5) (Not (r1 Y5))))) % 23.26/23.48 True % 23.26/23.48 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 % 23.26/23.48 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 % 23.26/23.48 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) % 23.26/23.48 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) % 23.26/23.48 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) % 23.26/23.48 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)) % 23.26/23.48 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)) % 23.26/23.48 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)) % 23.26/23.48 Clause #20 (by destructive equality resolution #[19]): ∀ (a a_1 : Iota), Or (Eq (r2 a a_1) False) (Eq (r1 a_1) False) % 23.26/23.48 Clause #39 (by clausification #[1]): ∀ (a : Iota), % 23.26/23.48 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True % 23.26/23.48 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 23.26/23.48 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 % 23.26/23.48 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 23.26/23.48 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 % 23.26/23.48 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 23.26/23.48 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) % 23.26/23.48 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) % 23.26/23.48 Clause #62 (by clausification #[2]): ∀ (a : Iota), % 23.26/23.48 Eq % 23.26/23.48 (∀ (X14 : Iota), % 23.26/23.48 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 a X14 X15)) (Ne X15 Y22)) (And (r3 a X14 X15) (Eq X15 Y22))) % 23.26/23.48 True % 23.26/23.48 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 23.26/23.48 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))) % 23.26/23.48 True % 23.26/23.48 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 23.26/23.48 Eq % 23.26/23.48 (∀ (X15 : Iota), % 23.26/23.48 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)))) % 23.26/23.48 True % 23.26/23.48 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), % 23.26/23.48 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 % 23.26/23.48 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 23.26/23.48 Or (Eq (And (Not (r3 a a_1 a_2)) (Ne a_2 (skS.0 4 a a_1 a_3))) True) % 23.33/23.51 (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True) % 23.33/23.51 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) % 23.33/23.51 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) % 23.33/23.51 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) % 23.33/23.51 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)) % 23.33/23.51 Clause #100 (by clausification #[4]): ∀ (a : Iota), % 23.33/23.51 Eq % 23.33/23.51 (∀ (X8 : Iota), % 23.33/23.51 Exists fun Y4 => % 23.33/23.51 And (Exists fun Y5 => And (Exists fun Y15 => And (r2 X8 Y15) (r3 a Y15 Y5)) (Eq Y5 Y4)) % 23.33/23.51 (Exists fun Y7 => And (r2 Y7 Y4) (r3 a X8 Y7))) % 23.33/23.51 True % 23.33/23.51 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), % 23.33/23.51 Eq % 23.33/23.51 (Exists fun Y4 => % 23.33/23.51 And (Exists fun Y5 => And (Exists fun Y15 => And (r2 a Y15) (r3 a_1 Y15 Y5)) (Eq Y5 Y4)) % 23.33/23.51 (Exists fun Y7 => And (r2 Y7 Y4) (r3 a_1 a Y7))) % 23.33/23.51 True % 23.33/23.51 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), % 23.33/23.51 Eq % 23.33/23.51 (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))) % 23.33/23.51 (Exists fun Y7 => And (r2 Y7 (skS.0 6 a a_1 a_2)) (r3 a_1 a Y7))) % 23.33/23.51 True % 23.33/23.51 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 % 23.33/23.51 Clause #104 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 23.33/23.51 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 % 23.33/23.51 Clause #105 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 23.33/23.51 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 % 23.33/23.51 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 % 23.33/23.51 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) % 23.33/23.51 Clause #136 (by clausification #[125]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 6 a a_1 a_2)) False % 23.33/23.51 Clause #183 (by clausification #[11]): Eq % 23.33/23.51 (∀ (Y1 : Iota), % 23.33/23.51 Or % 23.33/23.51 (∀ (Y2 : Iota), % 23.33/23.51 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 Y1))) (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2)))) % 23.33/23.51 (∀ (Y5 : Iota), Or (Ne Y1 Y5) (Not (r1 Y5)))) % 23.33/23.51 False % 23.33/23.51 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 23.33/23.51 Eq % 23.33/23.51 (Not % 23.33/23.51 (Or % 23.33/23.51 (∀ (Y2 : Iota), % 23.33/23.51 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 (skS.0 16 a)))) % 23.33/23.51 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2)))) % 23.33/23.51 (∀ (Y5 : Iota), Or (Ne (skS.0 16 a) Y5) (Not (r1 Y5))))) % 23.33/23.51 True % 23.33/23.51 Clause #185 (by clausification #[184]): ∀ (a : Iota), % 23.33/23.51 Eq % 23.33/23.51 (Or % 23.33/23.51 (∀ (Y2 : Iota), % 23.33/23.51 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 (skS.0 16 a)))) % 23.33/23.51 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2)))) % 23.33/23.51 (∀ (Y5 : Iota), Or (Ne (skS.0 16 a) Y5) (Not (r1 Y5)))) % 23.33/23.51 False % 23.33/23.51 Clause #186 (by clausification #[185]): ∀ (a : Iota), Eq (∀ (Y5 : Iota), Or (Ne (skS.0 16 a) Y5) (Not (r1 Y5))) False % 23.33/23.51 Clause #187 (by clausification #[185]): ∀ (a : Iota), % 23.33/23.51 Eq % 23.33/23.51 (∀ (Y2 : Iota), % 23.33/23.51 Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 Y2 (skS.0 16 a)))) % 23.33/23.51 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2)))) % 23.33/23.51 False % 23.33/23.51 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 % 23.33/23.51 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 % 23.33/23.51 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 17 a a_1))) False % 23.33/23.51 Clause #191 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 16 a) (skS.0 17 a a_1)) False % 23.33/23.51 Clause #192 (by clausification #[190]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 17 a a_1)) True % 23.33/23.51 Clause #198 (by clausification #[191]): ∀ (a a_1 : Iota), Eq (skS.0 16 a) (skS.0 17 a a_1) % 23.33/23.53 Clause #199 (by backward demodulation #[198, 192]): ∀ (a : Iota), Eq (r1 (skS.0 16 a)) True % 23.33/23.53 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) % 23.33/23.53 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) % 23.33/23.53 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)) % 23.33/23.53 Clause #218 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), % 23.33/23.53 Eq % 23.33/23.53 (And (Exists fun Y15 => And (r2 a Y15) (r3 a_1 Y15 (skS.0 18 a a_1 a_2 a_3))) % 23.33/23.53 (Eq (skS.0 18 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2))) % 23.33/23.53 True % 23.33/23.53 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 % 23.33/23.53 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 % 23.33/23.53 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) % 23.33/23.53 Clause #235 (by clausification #[220]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 23.33/23.53 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 % 23.33/23.53 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 % 23.33/23.53 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 % 23.33/23.53 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 % 23.33/23.53 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)) % 23.33/23.53 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) % 23.33/23.53 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 % 23.33/23.53 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)) % 23.33/23.53 Clause #330 (by clausification #[187]): ∀ (a a_1 : Iota), % 23.33/23.53 Eq % 23.33/23.53 (Not % 23.33/23.53 (Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 (skS.0 23 a a_1) (skS.0 16 a)))) % 23.33/23.53 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 23 a a_1)))))) % 23.33/23.53 True % 23.33/23.53 Clause #331 (by clausification #[330]): ∀ (a a_1 : Iota), % 23.33/23.53 Eq % 23.33/23.53 (Or (∀ (Y3 : Iota), Or (Not (r1 Y3)) (Not (r3 Y3 (skS.0 23 a a_1) (skS.0 16 a)))) % 23.33/23.53 (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 23 a a_1))))) % 23.33/23.53 False % 23.33/23.53 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 % 23.33/23.53 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 % 23.33/23.53 Clause #334 (by clausification #[332]): ∀ (a a_1 a_2 : Iota), % 23.33/23.53 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 % 23.33/23.53 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 % 23.33/23.53 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 % 23.33/23.53 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 % 23.33/23.53 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)) % 23.33/23.53 Clause #397 (by clausification #[333]): ∀ (a a_1 a_2 : Iota), % 23.33/23.53 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 % 23.33/23.53 Clause #398 (by clausification #[397]): ∀ (a a_1 a_2 : Iota), % 23.33/23.53 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 % 23.33/23.55 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 % 23.33/23.55 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 % 23.33/23.55 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)) % 23.33/23.55 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) % 23.33/23.55 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 % 23.33/23.55 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) % 23.33/23.55 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 % 23.33/23.55 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) % 23.33/23.55 Clause #1238 (by superposition #[1237, 942]): ∀ (a : Iota), Eq (r1 (skS.0 16 a)) False % 23.33/23.55 Clause #1245 (by superposition #[1238, 199]): Eq False True % 23.33/23.55 Clause #1246 (by clausification #[1245]): False % 23.33/23.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------