%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN076+2 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 07:57:49 PM UTC 2025 % Result : Theorem 38.14s 38.31s % Output : Proof 38.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUN076+2 : TPTP v9.2.0. Released v7.3.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n022.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 11:35:08 EDT 2025 % 0.12/0.34 % CPUTime : % 38.14/38.31 SZS status Theorem for theBenchmark.p % 38.14/38.31 SZS output start Proof for theBenchmark.p % 38.14/38.31 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 % 38.14/38.31 Clause #1 (by assumption #[]): Eq % 38.14/38.31 (∀ (X11 : Iota), % 38.14/38.31 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21))) % 38.14/38.31 True % 38.14/38.31 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 % 38.14/38.31 Clause #8 (by assumption #[]): Eq % 38.14/38.31 (∀ (X5 : Iota), % 38.14/38.31 Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 X5 Y17 Y8)) (Exists fun Y18 => And (r1 Y18) (Eq Y8 Y18))) % 38.14/38.31 True % 38.14/38.31 Clause #9 (by assumption #[]): Eq % 38.14/38.31 (∀ (X6 : Iota), % 38.14/38.31 Or (Exists fun Y19 => And (r1 Y19) (Eq X6 Y19)) (Exists fun Y1 => Exists fun Y11 => And (r2 Y1 Y11) (Eq X6 Y11))) % 38.14/38.31 True % 38.14/38.31 Clause #10 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 Y10)) (Not (r2 X7 Y10))) True % 38.14/38.31 Clause #11 (by assumption #[]): Eq % 38.14/38.31 (Not % 38.14/38.31 (Exists fun Y1 => % 38.14/38.31 Exists fun Y2 => % 38.14/38.31 Exists fun Y3 => % 38.14/38.31 And % 38.14/38.31 (Exists fun Y4 => % 38.14/38.31 And (Eq Y4 Y1) % 38.14/38.31 (Exists fun Y6 => % 38.14/38.31 And (r4 Y6 Y2 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 38.14/38.31 (Exists fun Y5 => And (r3 Y2 Y3 Y5) (Eq Y5 Y1)))) % 38.14/38.31 True % 38.14/38.31 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 % 38.14/38.31 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 % 38.14/38.31 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) % 38.14/38.31 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) % 38.14/38.31 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) % 38.14/38.31 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)) % 38.14/38.31 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)) % 38.14/38.31 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)) % 38.14/38.31 Clause #20 (by destructive equality resolution #[19]): ∀ (a a_1 : Iota), Or (Eq (r2 a a_1) False) (Eq (r1 a_1) False) % 38.14/38.31 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 % 38.14/38.31 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 % 38.14/38.31 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a a_1) a) True % 38.14/38.31 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 % 38.14/38.31 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (skS.0 0 a a_1) a % 38.14/38.31 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 % 38.14/38.31 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 % 38.14/38.31 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 1 a a_1 a_2)) True % 38.14/38.31 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 % 38.14/38.31 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 % 38.14/38.31 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 % 38.14/38.31 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) % 38.14/38.34 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) % 38.14/38.34 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) % 38.14/38.34 Clause #36 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (Ne a (skS.0 2 a_1)) True) (Eq (r1 a) True) % 38.14/38.34 Clause #39 (by clausification #[1]): ∀ (a : Iota), % 38.14/38.34 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True % 38.14/38.34 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 38.14/38.34 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 % 38.14/38.34 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 38.14/38.34 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 % 38.14/38.34 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 38.14/38.34 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) % 38.14/38.34 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) % 38.14/38.34 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) % 38.14/38.34 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) % 38.14/38.34 Clause #49 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Ne a (skS.0 2 a_1)) % 38.14/38.34 Clause #50 (by destructive equality resolution #[49]): ∀ (a : Iota), Eq (r1 (skS.0 2 a)) True % 38.14/38.34 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)) % 38.14/38.34 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 38.14/38.34 Clause #55 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 a)) True) (Eq (Eq a (skS.0 2 a_1)) True) % 38.14/38.34 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (Eq a (skS.0 2 a_1)) True) (Eq (r1 a) False) % 38.14/38.34 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq a (skS.0 2 a_1)) % 38.14/38.34 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) % 38.14/38.34 Clause #60 (by superposition #[58, 50]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) (skS.0 2 a_1)) (Eq False True) % 38.14/38.34 Clause #73 (by clausification #[60]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 2 a_1) % 38.14/38.34 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) % 38.14/38.34 Clause #75 (by superposition #[74, 29]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 2 a_1) a) True % 38.14/38.34 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) % 38.14/38.34 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) % 38.14/38.34 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)) % 38.14/38.34 Clause #148 (by clausification #[8]): ∀ (a : Iota), % 38.14/38.34 Eq (Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 Y8)) (Exists fun Y18 => And (r1 Y18) (Eq Y8 Y18))) % 38.14/38.34 True % 38.14/38.34 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota), % 38.14/38.34 Eq % 38.14/38.34 (And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1))) % 38.14/38.34 (Exists fun Y18 => And (r1 Y18) (Eq (skS.0 10 a a_1) Y18))) % 38.14/38.34 True % 38.14/38.34 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (Exists fun Y18 => And (r1 Y18) (Eq (skS.0 10 a a_1) Y18)) True % 38.14/38.34 Clause #151 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1))) True % 38.14/38.34 Clause #152 (by clausification #[150]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 11 a a_1 a_2)) (Eq (skS.0 10 a a_1) (skS.0 11 a a_1 a_2))) True % 38.14/38.34 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 10 a a_1) (skS.0 11 a a_1 a_2)) True % 38.14/38.34 Clause #154 (by clausification #[152]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 11 a a_1 a_2)) True % 38.19/38.37 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 10 a a_1) (skS.0 11 a a_1 a_2) % 38.19/38.37 Clause #156 (by forward demodulation #[154, 155]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 10 a a_1)) True % 38.19/38.37 Clause #157 (by superposition #[156, 58]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (skS.0 10 a a_1) (skS.0 2 a_2)) % 38.19/38.37 Clause #158 (by clausification #[157]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 10 a a_1) (skS.0 2 a_2) % 38.19/38.37 Clause #161 (by superposition #[158, 158]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 10 a a_1) (skS.0 10 a_2 a_3) % 38.19/38.37 Clause #162 (by clausification #[9]): ∀ (a : Iota), % 38.19/38.37 Eq (Or (Exists fun Y19 => And (r1 Y19) (Eq a Y19)) (Exists fun Y1 => Exists fun Y11 => And (r2 Y1 Y11) (Eq a Y11))) % 38.19/38.37 True % 38.19/38.37 Clause #163 (by clausification #[162]): ∀ (a : Iota), % 38.19/38.37 Or (Eq (Exists fun Y19 => And (r1 Y19) (Eq a Y19)) True) % 38.19/38.37 (Eq (Exists fun Y1 => Exists fun Y11 => And (r2 Y1 Y11) (Eq a Y11)) True) % 38.19/38.37 Clause #164 (by clausification #[163]): ∀ (a a_1 : Iota), % 38.19/38.37 Or (Eq (Exists fun Y1 => Exists fun Y11 => And (r2 Y1 Y11) (Eq a Y11)) True) % 38.19/38.37 (Eq (And (r1 (skS.0 12 a a_1)) (Eq a (skS.0 12 a a_1))) True) % 38.19/38.37 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 : Iota), % 38.19/38.37 Or (Eq (And (r1 (skS.0 12 a a_1)) (Eq a (skS.0 12 a a_1))) True) % 38.19/38.37 (Eq (Exists fun Y11 => And (r2 (skS.0 13 a a_2) Y11) (Eq a Y11)) True) % 38.19/38.37 Clause #166 (by clausification #[165]): ∀ (a a_1 a_2 : Iota), % 38.19/38.37 Or (Eq (Exists fun Y11 => And (r2 (skS.0 13 a a_1) Y11) (Eq a Y11)) True) (Eq (Eq a (skS.0 12 a a_2)) True) % 38.19/38.37 Clause #167 (by clausification #[165]): ∀ (a a_1 a_2 : Iota), % 38.19/38.37 Or (Eq (Exists fun Y11 => And (r2 (skS.0 13 a a_1) Y11) (Eq a Y11)) True) (Eq (r1 (skS.0 12 a a_2)) True) % 38.19/38.37 Clause #168 (by clausification #[166]): ∀ (a a_1 a_2 a_3 : Iota), % 38.19/38.37 Or (Eq (Eq a (skS.0 12 a a_1)) True) % 38.19/38.37 (Eq (And (r2 (skS.0 13 a a_2) (skS.0 14 a a_2 a_3)) (Eq a (skS.0 14 a a_2 a_3))) True) % 38.19/38.37 Clause #169 (by clausification #[168]): ∀ (a a_1 a_2 a_3 : Iota), % 38.19/38.37 Or (Eq (And (r2 (skS.0 13 a a_1) (skS.0 14 a a_1 a_2)) (Eq a (skS.0 14 a a_1 a_2))) True) (Eq a (skS.0 12 a a_3)) % 38.19/38.37 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a (skS.0 12 a a_1)) (Eq (Eq a (skS.0 14 a a_2 a_3)) True) % 38.19/38.37 Clause #171 (by clausification #[169]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a (skS.0 12 a a_1)) (Eq (r2 (skS.0 13 a a_2) (skS.0 14 a a_2 a_3)) True) % 38.19/38.37 Clause #172 (by clausification #[170]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a (skS.0 12 a a_1)) (Eq a (skS.0 14 a a_2 a_3)) % 38.19/38.37 Clause #173 (by clausification #[151]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 15 a a_1 a_2)) (r4 a (skS.0 15 a a_1 a_2) (skS.0 10 a a_1))) True % 38.19/38.37 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 : Iota), Eq (r4 a (skS.0 15 a a_1 a_2) (skS.0 10 a a_1)) True % 38.19/38.37 Clause #175 (by clausification #[173]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 15 a a_1 a_2)) True % 38.19/38.37 Clause #177 (by superposition #[174, 161]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (r4 a (skS.0 15 a a_1 a_2) (skS.0 10 a_3 a_4)) True % 38.19/38.37 Clause #178 (by superposition #[175, 58]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (skS.0 15 a a_1 a_2) (skS.0 2 a_3)) % 38.19/38.37 Clause #179 (by clausification #[178]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 15 a a_1 a_2) (skS.0 2 a_3) % 38.19/38.37 Clause #182 (by superposition #[179, 179]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (skS.0 15 a a_1 a_2) (skS.0 15 a_3 a_4 a_5) % 38.19/38.37 Clause #183 (by clausification #[11]): Eq % 38.19/38.37 (Exists fun Y1 => % 38.19/38.37 Exists fun Y2 => % 38.19/38.37 Exists fun Y3 => % 38.19/38.37 And % 38.19/38.37 (Exists fun Y4 => % 38.19/38.37 And (Eq Y4 Y1) % 38.19/38.37 (Exists fun Y6 => % 38.19/38.37 And (r4 Y6 Y2 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 38.19/38.37 (Exists fun Y5 => And (r3 Y2 Y3 Y5) (Eq Y5 Y1))) % 38.19/38.37 False % 38.19/38.37 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 38.19/38.37 Eq % 38.19/38.37 (Exists fun Y2 => % 38.19/38.37 Exists fun Y3 => % 38.19/38.37 And % 38.19/38.37 (Exists fun Y4 => % 38.19/38.37 And (Eq Y4 a) % 38.19/38.37 (Exists fun Y6 => % 38.19/38.37 And (r4 Y6 Y2 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 38.19/38.39 (Exists fun Y5 => And (r3 Y2 Y3 Y5) (Eq Y5 a))) % 38.19/38.39 False % 38.19/38.39 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), % 38.19/38.39 Eq % 38.19/38.39 (Exists fun Y3 => % 38.19/38.39 And % 38.19/38.39 (Exists fun Y4 => % 38.19/38.39 And (Eq Y4 a) % 38.19/38.39 (Exists fun Y6 => % 38.19/38.39 And (r4 Y6 a_1 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 38.19/38.39 (Exists fun Y5 => And (r3 a_1 Y3 Y5) (Eq Y5 a))) % 38.19/38.39 False % 38.19/38.39 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 : Iota), % 38.19/38.39 Eq % 38.19/38.39 (And % 38.19/38.39 (Exists fun Y4 => % 38.19/38.39 And (Eq Y4 a) % 38.19/38.39 (Exists fun Y6 => % 38.19/38.39 And (r4 Y6 a_1 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 38.19/38.39 (Exists fun Y5 => And (r3 a_1 a_2 Y5) (Eq Y5 a))) % 38.19/38.39 False % 38.19/38.39 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota), % 38.19/38.39 Or % 38.19/38.39 (Eq % 38.19/38.39 (Exists fun Y4 => % 38.19/38.39 And (Eq Y4 a) % 38.19/38.39 (Exists fun Y6 => % 38.19/38.39 And (r4 Y6 a_1 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 38.19/38.39 False) % 38.19/38.39 (Eq (Exists fun Y5 => And (r3 a_1 a_2 Y5) (Eq Y5 a)) False) % 38.19/38.39 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 a_3 : Iota), % 38.19/38.39 Or (Eq (Exists fun Y5 => And (r3 a a_1 Y5) (Eq Y5 a_2)) False) % 38.19/38.39 (Eq % 38.19/38.39 (And (Eq a_3 a_2) % 38.19/38.39 (Exists fun Y6 => % 38.19/38.39 And (r4 Y6 a a_3) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 38.19/38.39 False) % 38.19/38.39 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 38.19/38.39 Or % 38.19/38.39 (Eq % 38.19/38.39 (And (Eq a a_1) % 38.19/38.39 (Exists fun Y6 => % 38.19/38.39 And (r4 Y6 a_2 a) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 38.19/38.39 False) % 38.19/38.39 (Eq (And (r3 a_2 a_3 a_4) (Eq a_4 a_1)) False) % 38.19/38.39 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 38.19/38.39 Or (Eq (And (r3 a a_1 a_2) (Eq a_2 a_3)) False) % 38.19/38.39 (Or (Eq (Eq a_4 a_3) False) % 38.19/38.39 (Eq % 38.19/38.39 (Exists fun Y6 => And (r4 Y6 a a_4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) % 38.19/38.39 False)) % 38.19/38.39 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 38.19/38.39 Or (Eq (Eq a a_1) False) % 38.19/38.39 (Or % 38.19/38.39 (Eq % 38.19/38.39 (Exists fun Y6 => And (r4 Y6 a_2 a) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) % 38.19/38.39 False) % 38.19/38.39 (Or (Eq (r3 a_2 a_3 a_4) False) (Eq (Eq a_4 a_1) False))) % 38.19/38.39 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 38.19/38.39 Or % 38.19/38.39 (Eq (Exists fun Y6 => And (r4 Y6 a a_1) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) % 38.19/38.39 False) % 38.19/38.39 (Or (Eq (r3 a a_2 a_3) False) (Or (Eq (Eq a_3 a_4) False) (Ne a_1 a_4))) % 38.19/38.39 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 38.19/38.39 Or (Eq (r3 a a_1 a_2) False) % 38.19/38.39 (Or (Eq (Eq a_2 a_3) False) % 38.19/38.39 (Or (Ne a_4 a_3) % 38.19/38.39 (Eq (And (r4 a_5 a a_4) (Exists fun Y7 => And (r2 Y7 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) False))) % 38.19/38.39 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 38.19/38.39 Or (Eq (r3 a a_1 a_2) False) % 38.19/38.39 (Or (Ne a_3 a_4) % 38.19/38.39 (Or (Eq (And (r4 a_5 a a_3) (Exists fun Y7 => And (r2 Y7 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) False) % 38.19/38.39 (Ne a_2 a_4))) % 38.19/38.39 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 38.19/38.39 Or (Eq (r3 a a_1 a_2) False) % 38.19/38.39 (Or (Ne a_3 a_4) % 38.19/38.39 (Or (Ne a_2 a_4) % 38.19/38.39 (Or (Eq (r4 a_5 a a_3) False) % 38.19/38.39 (Eq (Exists fun Y7 => And (r2 Y7 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))) False)))) % 38.19/38.39 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 38.19/38.39 Or (Eq (r3 a a_1 a_2) False) % 38.19/38.39 (Or (Ne a_3 a_4) % 38.19/38.39 (Or (Ne a_2 a_4) % 38.19/38.39 (Or (Eq (r4 a_5 a a_3) False) (Eq (And (r2 a_6 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 a_6))) False)))) % 38.19/38.39 Clause #197 (by clausification #[196]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 38.19/38.39 Or (Eq (r3 a a_1 a_2) False) % 38.19/38.39 (Or (Ne a_3 a_4) % 38.19/38.39 (Or (Ne a_2 a_4) % 38.19/38.39 (Or (Eq (r4 a_5 a a_3) False) % 38.19/38.39 (Or (Eq (r2 a_6 a_5) False) (Eq (Exists fun Y8 => And (r1 Y8) (r2 Y8 a_6)) False))))) % 38.19/38.39 Clause #198 (by clausification #[197]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 38.19/38.39 Or (Eq (r3 a a_1 a_2) False) % 38.24/38.42 (Or (Ne a_3 a_4) % 38.24/38.42 (Or (Ne a_2 a_4) % 38.24/38.42 (Or (Eq (r4 a_5 a a_3) False) (Or (Eq (r2 a_6 a_5) False) (Eq (And (r1 a_7) (r2 a_7 a_6)) False))))) % 38.24/38.42 Clause #199 (by clausification #[198]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 38.24/38.42 Or (Eq (r3 a a_1 a_2) False) % 38.24/38.42 (Or (Ne a_3 a_4) % 38.24/38.42 (Or (Ne a_2 a_4) % 38.24/38.42 (Or (Eq (r4 a_5 a a_3) False) (Or (Eq (r2 a_6 a_5) False) (Or (Eq (r1 a_7) False) (Eq (r2 a_7 a_6) False)))))) % 38.24/38.42 Clause #200 (by destructive equality resolution #[199]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 38.24/38.42 Or (Eq (r3 a a_1 a_2) False) % 38.24/38.42 (Or (Ne a_2 a_3) % 38.24/38.42 (Or (Eq (r4 a_4 a a_3) False) (Or (Eq (r2 a_5 a_4) False) (Or (Eq (r1 a_6) False) (Eq (r2 a_6 a_5) False))))) % 38.24/38.42 Clause #201 (by destructive equality resolution #[200]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 38.24/38.42 Or (Eq (r3 a a_1 a_2) False) % 38.24/38.42 (Or (Eq (r4 a_3 a a_2) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False)))) % 38.24/38.42 Clause #204 (by superposition #[201, 75]): ∀ (a a_1 a_2 a_3 : Iota), % 38.24/38.42 Or (Eq (r4 a a_1 a_1) False) % 38.24/38.42 (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_2) False) (Eq False True)))) % 38.24/38.42 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota), % 38.24/38.42 Or (Eq (r4 a a_1 a_1) False) (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Eq (r2 a_3 a_2) False))) % 38.24/38.42 Clause #207 (by superposition #[177, 182]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (r4 a (skS.0 15 a_1 a_2 a_3) (skS.0 10 a_4 a_5)) True % 38.24/38.42 Clause #302 (by clausification #[167]): ∀ (a a_1 a_2 a_3 : Iota), % 38.24/38.42 Or (Eq (r1 (skS.0 12 a a_1)) True) % 38.24/38.42 (Eq (And (r2 (skS.0 13 a a_2) (skS.0 20 a a_2 a_3)) (Eq a (skS.0 20 a a_2 a_3))) True) % 38.24/38.42 Clause #303 (by clausification #[302]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 12 a a_1)) True) (Eq (Eq a (skS.0 20 a a_2 a_3)) True) % 38.24/38.42 Clause #304 (by clausification #[302]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 12 a a_1)) True) (Eq (r2 (skS.0 13 a a_2) (skS.0 20 a a_2 a_3)) True) % 38.24/38.42 Clause #305 (by clausification #[303]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r1 (skS.0 12 a a_1)) True) (Eq a (skS.0 20 a a_2 a_3)) % 38.24/38.42 Clause #319 (by superposition #[171, 172]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a (skS.0 12 a a_1)) (Or (Eq a (skS.0 12 a a_2)) (Eq (r2 (skS.0 13 a a_3) a) True)) % 38.24/38.42 Clause #508 (by equality factoring #[319]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Ne a a) (Eq a (skS.0 12 a a_2))) % 38.24/38.42 Clause #509 (by eliminate resolved literals #[508]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Eq a (skS.0 12 a a_2)) % 38.24/38.42 Clause #615 (by superposition #[304, 305]): ∀ (a a_1 a_2 a_3 : Iota), % 38.24/38.42 Or (Eq (r1 (skS.0 12 a a_1)) True) (Or (Eq (r1 (skS.0 12 a a_2)) True) (Eq (r2 (skS.0 13 a a_3) a) True)) % 38.24/38.42 Clause #1660 (by equality factoring #[615]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Ne True True) (Eq (r1 (skS.0 12 a a_2)) True)) % 38.24/38.42 Clause #1661 (by clausification #[1660]): ∀ (a a_1 a_2 : Iota), % 38.24/38.42 Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Eq (r1 (skS.0 12 a a_2)) True) (Or (Eq True False) (Eq True False))) % 38.24/38.42 Clause #1663 (by clausification #[1661]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Eq (r1 (skS.0 12 a a_2)) True) (Eq True False)) % 38.24/38.42 Clause #1664 (by clausification #[1663]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Eq (r1 (skS.0 12 a a_2)) True) % 38.24/38.42 Clause #1693 (by superposition #[1664, 509]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Eq (r2 (skS.0 13 a a_2) a) True) (Eq (r1 a) True)) % 38.24/38.42 Clause #1726 (by equality factoring #[1693]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Ne True True) (Eq (r2 (skS.0 13 a a_1) a) True)) % 38.24/38.42 Clause #1734 (by clausification #[1726]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Eq True False) (Eq True False))) % 38.24/38.42 Clause #1736 (by clausification #[1734]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (r2 (skS.0 13 a a_1) a) True) (Eq True False)) % 38.24/38.42 Clause #1737 (by clausification #[1736]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (r2 (skS.0 13 a a_1) a) True) % 38.24/38.42 Clause #1749 (by superposition #[1737, 97]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) True) (Or (Eq True False) (Eq a (skS.0 3 (skS.0 13 a a_1) a_2))) % 38.30/38.48 Clause #1778 (by clausification #[1749]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) True) (Eq a (skS.0 3 (skS.0 13 a a_1) a_2)) % 38.30/38.48 Clause #1779 (by superposition #[1778, 58]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a (skS.0 3 (skS.0 13 a a_1) a_2)) (Or (Eq True False) (Eq a (skS.0 2 a_3))) % 38.30/38.48 Clause #1852 (by clausification #[1779]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a (skS.0 3 (skS.0 13 a a_1) a_2)) (Eq a (skS.0 2 a_3)) % 38.30/38.48 Clause #1853 (by superposition #[1852, 52]): ∀ (a a_1 a_2 : Iota), Or (Eq a (skS.0 2 a_1)) (Eq (r2 (skS.0 13 a a_2) a) True) % 38.30/38.48 Clause #2455 (by superposition #[1853, 73]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Eq a (skS.0 2 a_2)) % 38.30/38.48 Clause #2553 (by superposition #[2455, 2455]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Eq (r2 (skS.0 13 a_2 a_3) a_2) True) (Eq a_2 a)) % 38.30/38.48 Clause #3649 (by superposition #[2553, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Eq a_2 a) (Or (Eq True False) (Eq (r1 a_2) False))) % 38.30/38.48 Clause #4278 (by clausification #[3649]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Eq a_2 a) (Eq (r1 a_2) False)) % 38.30/38.48 Clause #4281 (by superposition #[4278, 156]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Or (Eq (skS.0 10 a_2 a_3) a) (Eq False True)) % 38.30/38.48 Clause #4299 (by clausification #[4281]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r2 (skS.0 13 a a_1) a) True) (Eq (skS.0 10 a_2 a_3) a) % 38.30/38.48 Clause #4312 (by superposition #[4299, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 10 a a_1) a_2) (Or (Eq True False) (Eq (r1 a_2) False)) % 38.30/38.48 Clause #4632 (by clausification #[4312]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 10 a a_1) a_2) (Eq (r1 a_2) False) % 38.30/38.48 Clause #4635 (by superposition #[4632, 175]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (skS.0 10 a a_1) (skS.0 15 a_2 a_3 a_4)) (Eq False True) % 38.30/38.48 Clause #4665 (by clausification #[4635]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (skS.0 10 a a_1) (skS.0 15 a_2 a_3 a_4) % 38.30/38.48 Clause #4680 (by superposition #[4665, 207]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (r4 a (skS.0 10 a_1 a_2) (skS.0 10 a_3 a_4)) True % 38.30/38.48 Clause #4723 (by superposition #[4680, 205]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a) False))) % 38.30/38.48 Clause #4728 (by clausification #[4723]): ∀ (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)) % 38.30/38.48 Clause #4735 (by superposition #[4728, 52]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True)) % 38.30/38.48 Clause #4743 (by clausification #[4735]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False) % 38.30/38.48 Clause #4745 (by superposition #[4743, 50]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 2 a) a_1) False) (Eq False True) % 38.30/38.48 Clause #4754 (by clausification #[4745]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 2 a) a_1) False % 38.30/38.48 Clause #4755 (by superposition #[4754, 52]): Eq False True % 38.30/38.48 Clause #4759 (by clausification #[4755]): False % 38.30/38.48 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------