%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN070+2 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 07:57:48 PM UTC 2025 % Result : Theorem 6.35s 6.54s % Output : Proof 6.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : NUN070+2 : TPTP v9.2.0. Released v7.3.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n016.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 11:32:23 EDT 2025 % 0.14/0.34 % CPUTime : % 6.35/6.54 SZS status Theorem for theBenchmark.p % 6.35/6.54 SZS output start Proof for theBenchmark.p % 6.35/6.54 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 % 6.35/6.54 Clause #1 (by assumption #[]): Eq % 6.35/6.54 (∀ (X11 : Iota), % 6.35/6.54 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21))) % 6.35/6.54 True % 6.35/6.54 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 % 6.35/6.54 Clause #11 (by assumption #[]): Eq % 6.35/6.54 (Not % 6.35/6.54 (Exists fun Y1 => % 6.35/6.54 And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 Y1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2))) % 6.35/6.54 (Exists fun Y3 => And (Eq Y1 Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))))) % 6.35/6.54 True % 6.35/6.54 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 % 6.35/6.54 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 % 6.35/6.54 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a a_1) a) True % 6.35/6.54 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 % 6.35/6.54 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (skS.0 0 a a_1) a % 6.35/6.54 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 % 6.35/6.54 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 % 6.35/6.54 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 1 a a_1 a_2)) True % 6.35/6.54 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 % 6.35/6.54 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 % 6.35/6.54 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 % 6.35/6.54 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) % 6.35/6.54 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) % 6.35/6.54 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) % 6.35/6.54 Clause #36 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (Ne a (skS.0 2 a_1)) True) (Eq (r1 a) True) % 6.35/6.54 Clause #39 (by clausification #[1]): ∀ (a : Iota), % 6.35/6.54 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True % 6.35/6.54 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 6.35/6.54 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 % 6.35/6.54 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 6.35/6.54 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 % 6.35/6.54 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 6.35/6.54 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) % 6.35/6.54 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) % 6.35/6.54 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) % 6.35/6.54 Clause #49 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Ne a (skS.0 2 a_1)) % 6.35/6.54 Clause #50 (by destructive equality resolution #[49]): ∀ (a : Iota), Eq (r1 (skS.0 2 a)) True % 6.35/6.54 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)) % 6.35/6.54 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 6.35/6.54 Clause #55 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 a)) True) (Eq (Eq a (skS.0 2 a_1)) True) % 6.35/6.57 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (Eq a (skS.0 2 a_1)) True) (Eq (r1 a) False) % 6.35/6.57 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq a (skS.0 2 a_1)) % 6.35/6.57 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) % 6.35/6.57 Clause #60 (by superposition #[58, 50]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) (skS.0 2 a_1)) (Eq False True) % 6.35/6.57 Clause #73 (by clausification #[60]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 2 a_1) % 6.35/6.57 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) % 6.35/6.57 Clause #75 (by superposition #[74, 29]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 2 a_1) a) True % 6.35/6.57 Clause #76 (by superposition #[74, 73]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 2 a) (skS.0 1 a_1 a_2 a_3) % 6.35/6.57 Clause #78 (by superposition #[76, 75]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r3 a (skS.0 1 a_1 a_2 a_3) a) True % 6.35/6.57 Clause #183 (by clausification #[11]): Eq % 6.35/6.57 (Exists fun Y1 => % 6.35/6.57 And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 Y1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2))) % 6.35/6.57 (Exists fun Y3 => And (Eq Y1 Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3)))) % 6.35/6.57 False % 6.35/6.57 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 6.35/6.57 Eq % 6.35/6.57 (And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2))) % 6.35/6.57 (Exists fun Y3 => And (Eq a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3)))) % 6.35/6.57 False % 6.35/6.57 Clause #185 (by clausification #[184]): ∀ (a : Iota), % 6.35/6.57 Or % 6.35/6.57 (Eq (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2))) % 6.35/6.57 False) % 6.35/6.57 (Eq (Exists fun Y3 => And (Eq a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))) False) % 6.35/6.57 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), % 6.35/6.57 Or (Eq (Exists fun Y3 => And (Eq a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))) False) % 6.35/6.57 (Eq (And (Exists fun Y4 => And (r1 Y4) (r3 a_1 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 a_1))) False) % 6.35/6.57 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota), % 6.35/6.57 Or (Eq (And (Exists fun Y4 => And (r1 Y4) (r3 a Y4 a_1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 a))) False) % 6.35/6.57 (Eq (And (Eq a_1 a_2) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2))) False) % 6.35/6.57 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 : Iota), % 6.35/6.57 Or (Eq (And (Eq a a_1) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_1))) False) % 6.35/6.57 (Or (Eq (Exists fun Y4 => And (r1 Y4) (r3 a_2 Y4 a)) False) (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a_2)) False)) % 6.35/6.57 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 : Iota), % 6.35/6.57 Or (Eq (Exists fun Y4 => And (r1 Y4) (r3 a Y4 a_1)) False) % 6.35/6.57 (Or (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a)) False) % 6.35/6.57 (Or (Eq (Eq a_1 a_2) False) (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2)) False))) % 6.35/6.57 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 : Iota), % 6.35/6.57 Or (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a)) False) % 6.35/6.57 (Or (Eq (Eq a_1 a_2) False) % 6.35/6.57 (Or (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2)) False) (Eq (And (r1 a_3) (r3 a a_3 a_1)) False))) % 6.35/6.57 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.57 Or (Eq (Eq a a_1) False) % 6.35/6.57 (Or (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_1)) False) % 6.35/6.57 (Or (Eq (And (r1 a_2) (r3 a_3 a_2 a)) False) (Eq (And (r1 a_4) (r2 a_4 a_3)) False))) % 6.35/6.57 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.57 Or (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a)) False) % 6.35/6.57 (Or (Eq (And (r1 a_1) (r3 a_2 a_1 a_3)) False) (Or (Eq (And (r1 a_4) (r2 a_4 a_2)) False) (Ne a_3 a))) % 6.35/6.57 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.35/6.57 Or (Eq (And (r1 a) (r3 a_1 a a_2)) False) % 6.35/6.57 (Or (Eq (And (r1 a_3) (r2 a_3 a_1)) False) (Or (Ne a_2 a_4) (Eq (And (r1 a_5) (r2 a_5 a_4)) False))) % 6.35/6.57 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.35/6.57 Or (Eq (And (r1 a) (r2 a a_1)) False) % 6.35/6.57 (Or (Ne a_2 a_3) (Or (Eq (And (r1 a_4) (r2 a_4 a_3)) False) (Or (Eq (r1 a_5) False) (Eq (r3 a_1 a_5 a_2) False)))) % 6.44/6.59 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.44/6.59 Or (Ne a a_1) % 6.44/6.59 (Or (Eq (And (r1 a_2) (r2 a_2 a_1)) False) % 6.44/6.59 (Or (Eq (r1 a_3) False) (Or (Eq (r3 a_4 a_3 a) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False))))) % 6.44/6.59 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.44/6.59 Or (Ne a a_1) % 6.44/6.59 (Or (Eq (r1 a_2) False) % 6.44/6.59 (Or (Eq (r3 a_3 a_2 a) False) % 6.44/6.59 (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_1) False)))))) % 6.44/6.59 Clause #197 (by destructive equality resolution #[196]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.44/6.59 Or (Eq (r1 a) False) % 6.44/6.59 (Or (Eq (r3 a_1 a a_2) False) % 6.44/6.59 (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_2) False))))) % 6.44/6.59 Clause #198 (by superposition #[197, 28]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.44/6.59 Or (Eq (r3 a (skS.0 1 a_1 a_2 a_3) a_4) False) % 6.44/6.59 (Or (Eq (r1 a_5) False) % 6.44/6.59 (Or (Eq (r2 a_5 a) False) (Or (Eq (r1 a_6) False) (Or (Eq (r2 a_6 a_4) False) (Eq False True))))) % 6.44/6.59 Clause #328 (by clausification #[198]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.44/6.59 Or (Eq (r3 a (skS.0 1 a_1 a_2 a_3) a_4) False) % 6.44/6.59 (Or (Eq (r1 a_5) False) (Or (Eq (r2 a_5 a) False) (Or (Eq (r1 a_6) False) (Eq (r2 a_6 a_4) False)))) % 6.44/6.59 Clause #332 (by superposition #[328, 78]): ∀ (a a_1 a_2 : Iota), % 6.44/6.59 Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Or (Eq (r2 a_2 a_1) False) (Eq False True)))) % 6.44/6.59 Clause #333 (by clausification #[332]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a_1) False))) % 6.44/6.59 Clause #335 (by superposition #[333, 50]): ∀ (a a_1 a_2 : Iota), % 6.44/6.59 Or (Eq (r2 (skS.0 2 a) a_1) False) (Or (Eq (r1 a_2) False) (Or (Eq (r2 a_2 a_1) False) (Eq False True))) % 6.44/6.59 Clause #339 (by clausification #[335]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 2 a) a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a_1) False)) % 6.44/6.59 Clause #340 (by superposition #[339, 52]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a (skS.0 3 (skS.0 2 a_1) a_2)) False) (Eq False True)) % 6.44/6.59 Clause #351 (by clausification #[340]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Eq (r2 a (skS.0 3 (skS.0 2 a_1) a_2)) False) % 6.44/6.59 Clause #353 (by superposition #[351, 50]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 2 a) (skS.0 3 (skS.0 2 a_1) a_2)) False) (Eq False True) % 6.44/6.59 Clause #373 (by clausification #[353]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 2 a) (skS.0 3 (skS.0 2 a_1) a_2)) False % 6.44/6.59 Clause #374 (by superposition #[373, 52]): Eq False True % 6.44/6.59 Clause #375 (by clausification #[374]): False % 6.44/6.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------