%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN060+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 07:57:47 PM UTC 2025 % Result : Theorem 5.11s 5.34s % Output : Proof 5.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : NUN060+2 : TPTP v9.2.0. Released v7.3.0. % 0.08/0.15 % Command : duper %s % 0.14/0.36 % Computer : n005.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 : Thu Oct 2 11:31:38 EDT 2025 % 0.14/0.37 % CPUTime : % 5.11/5.34 SZS status Theorem for theBenchmark.p % 5.11/5.34 SZS output start Proof for theBenchmark.p % 5.11/5.34 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 % 5.11/5.34 Clause #1 (by assumption #[]): Eq % 5.11/5.34 (∀ (X11 : Iota), % 5.11/5.34 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21))) % 5.11/5.34 True % 5.11/5.34 Clause #2 (by assumption #[]): Eq % 5.11/5.34 (∀ (X13 X14 : Iota), % 5.11/5.34 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 X13 X14 X15)) (Ne X15 Y22)) (And (r3 X13 X14 X15) (Eq X15 Y22))) % 5.11/5.34 True % 5.11/5.34 Clause #11 (by assumption #[]): Eq % 5.11/5.34 (Not % 5.11/5.34 (Exists fun Y1 => % 5.11/5.34 Exists fun Y2 => % 5.11/5.34 Exists fun Y3 => % 5.11/5.34 And (Eq Y3 Y1) % 5.11/5.34 (Exists fun Y4 => % 5.11/5.34 And (r3 Y2 Y4 Y3) % 5.11/5.34 (Exists fun Y5 => % 5.11/5.34 And (r2 Y5 Y4) % 5.11/5.34 (Exists fun Y6 => % 5.11/5.34 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))))))) % 5.11/5.34 True % 5.11/5.34 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 % 5.11/5.34 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 % 5.11/5.34 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) % 5.11/5.34 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) % 5.11/5.34 Clause #36 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (Ne a (skS.0 2 a_1)) True) (Eq (r1 a) True) % 5.11/5.34 Clause #39 (by clausification #[1]): ∀ (a : Iota), % 5.11/5.34 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True % 5.11/5.34 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 5.11/5.34 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 % 5.11/5.34 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 5.11/5.34 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 % 5.11/5.34 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 5.11/5.34 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) % 5.11/5.34 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) % 5.11/5.34 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) % 5.11/5.34 Clause #49 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Ne a (skS.0 2 a_1)) % 5.11/5.34 Clause #50 (by destructive equality resolution #[49]): ∀ (a : Iota), Eq (r1 (skS.0 2 a)) True % 5.11/5.34 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)) % 5.11/5.34 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 5.11/5.34 Clause #62 (by clausification #[2]): ∀ (a : Iota), % 5.11/5.34 Eq % 5.11/5.34 (∀ (X14 : Iota), % 5.11/5.34 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 a X14 X15)) (Ne X15 Y22)) (And (r3 a X14 X15) (Eq X15 Y22))) % 5.11/5.34 True % 5.11/5.34 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 5.11/5.34 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))) % 5.11/5.34 True % 5.11/5.34 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 5.11/5.34 Eq % 5.11/5.34 (∀ (X15 : Iota), % 5.11/5.34 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)))) % 5.11/5.34 True % 5.11/5.34 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), % 5.11/5.34 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 % 5.11/5.34 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 5.11/5.34 Or (Eq (And (Not (r3 a a_1 a_2)) (Ne a_2 (skS.0 4 a a_1 a_3))) True) % 5.11/5.34 (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True) % 5.11/5.37 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 5.11/5.37 Or (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True) (Eq (Ne a_2 (skS.0 4 a a_1 a_3)) True) % 5.11/5.37 Clause #70 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Ne a (skS.0 4 a_1 a_2 a_3)) True) (Eq (r3 a_1 a_2 a) True) % 5.11/5.37 Clause #92 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Ne a_2 (skS.0 4 a a_1 a_3)) % 5.11/5.37 Clause #93 (by destructive equality resolution #[92]): ∀ (a a_1 a_2 : Iota), Eq (r3 a a_1 (skS.0 4 a a_1 a_2)) True % 5.11/5.37 Clause #183 (by clausification #[11]): Eq % 5.11/5.37 (Exists fun Y1 => % 5.11/5.37 Exists fun Y2 => % 5.11/5.37 Exists fun Y3 => % 5.11/5.37 And (Eq Y3 Y1) % 5.11/5.37 (Exists fun Y4 => % 5.11/5.37 And (r3 Y2 Y4 Y3) % 5.11/5.37 (Exists fun Y5 => % 5.11/5.37 And (r2 Y5 Y4) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))))) % 5.11/5.37 False % 5.11/5.37 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 5.11/5.37 Eq % 5.11/5.37 (Exists fun Y2 => % 5.11/5.37 Exists fun Y3 => % 5.11/5.37 And (Eq Y3 a) % 5.11/5.37 (Exists fun Y4 => % 5.11/5.37 And (r3 Y2 Y4 Y3) % 5.11/5.37 (Exists fun Y5 => % 5.11/5.37 And (r2 Y5 Y4) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))))) % 5.11/5.37 False % 5.11/5.37 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), % 5.11/5.37 Eq % 5.11/5.37 (Exists fun Y3 => % 5.11/5.37 And (Eq Y3 a) % 5.11/5.37 (Exists fun Y4 => % 5.11/5.37 And (r3 a_1 Y4 Y3) % 5.11/5.37 (Exists fun Y5 => % 5.11/5.37 And (r2 Y5 Y4) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))))) % 5.11/5.37 False % 5.11/5.37 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 : Iota), % 5.11/5.37 Eq % 5.11/5.37 (And (Eq a a_1) % 5.11/5.37 (Exists fun Y4 => % 5.11/5.37 And (r3 a_2 Y4 a) % 5.11/5.37 (Exists fun Y5 => % 5.11/5.37 And (r2 Y5 Y4) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))))) % 5.11/5.37 False % 5.11/5.37 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota), % 5.11/5.37 Or (Eq (Eq a a_1) False) % 5.11/5.37 (Eq % 5.11/5.37 (Exists fun Y4 => % 5.11/5.37 And (r3 a_2 Y4 a) % 5.11/5.37 (Exists fun Y5 => % 5.11/5.37 And (r2 Y5 Y4) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))))) % 5.11/5.37 False) % 5.11/5.37 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 : Iota), % 5.11/5.37 Or % 5.11/5.37 (Eq % 5.11/5.37 (Exists fun Y4 => % 5.11/5.37 And (r3 a Y4 a_1) % 5.11/5.37 (Exists fun Y5 => % 5.11/5.37 And (r2 Y5 Y4) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))))) % 5.11/5.37 False) % 5.11/5.37 (Ne a_1 a_2) % 5.11/5.37 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota), % 5.11/5.37 Or (Ne a a_1) % 5.11/5.37 (Eq % 5.11/5.37 (And (r3 a_2 a_3 a) % 5.11/5.37 (Exists fun Y5 => % 5.11/5.37 And (r2 Y5 a_3) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))))) % 5.11/5.37 False) % 5.11/5.37 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 : Iota), % 5.11/5.37 Or (Ne a a_1) % 5.11/5.37 (Or (Eq (r3 a_2 a_3 a) False) % 5.11/5.37 (Eq % 5.11/5.37 (Exists fun Y5 => % 5.11/5.37 And (r2 Y5 a_3) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 Y5) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 5.11/5.37 False)) % 5.11/5.37 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.11/5.37 Or (Ne a a_1) % 5.11/5.37 (Or (Eq (r3 a_2 a_3 a) False) % 5.11/5.37 (Eq % 5.11/5.37 (And (r2 a_4 a_3) % 5.11/5.37 (Exists fun Y6 => % 5.11/5.37 And (r2 Y6 a_4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 5.11/5.37 False)) % 5.11/5.37 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.11/5.37 Or (Ne a a_1) % 5.11/5.37 (Or (Eq (r3 a_2 a_3 a) False) % 5.11/5.37 (Or (Eq (r2 a_4 a_3) False) % 5.11/5.37 (Eq % 5.11/5.37 (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) % 5.11/5.37 False))) % 5.11/5.37 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.20/5.40 Or (Ne a a_1) % 5.20/5.40 (Or (Eq (r3 a_2 a_3 a) False) % 5.20/5.40 (Or (Eq (r2 a_4 a_3) False) % 5.20/5.40 (Eq (And (r2 a_5 a_4) (Exists fun Y7 => And (r2 Y7 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) False))) % 5.20/5.40 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.20/5.40 Or (Ne a a_1) % 5.20/5.40 (Or (Eq (r3 a_2 a_3 a) False) % 5.20/5.40 (Or (Eq (r2 a_4 a_3) False) % 5.20/5.40 (Or (Eq (r2 a_5 a_4) False) % 5.20/5.40 (Eq (Exists fun Y7 => And (r2 Y7 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))) False)))) % 5.20/5.40 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 5.20/5.40 Or (Ne a a_1) % 5.20/5.40 (Or (Eq (r3 a_2 a_3 a) False) % 5.20/5.40 (Or (Eq (r2 a_4 a_3) False) % 5.20/5.40 (Or (Eq (r2 a_5 a_4) False) (Eq (And (r2 a_6 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 a_6))) False)))) % 5.20/5.40 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 5.20/5.40 Or (Ne a a_1) % 5.20/5.40 (Or (Eq (r3 a_2 a_3 a) False) % 5.20/5.40 (Or (Eq (r2 a_4 a_3) False) % 5.20/5.40 (Or (Eq (r2 a_5 a_4) False) % 5.20/5.40 (Or (Eq (r2 a_6 a_5) False) (Eq (Exists fun Y8 => And (r1 Y8) (r2 Y8 a_6)) False))))) % 5.20/5.40 Clause #197 (by clausification #[196]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 5.20/5.40 Or (Ne a a_1) % 5.20/5.40 (Or (Eq (r3 a_2 a_3 a) False) % 5.20/5.40 (Or (Eq (r2 a_4 a_3) False) % 5.20/5.40 (Or (Eq (r2 a_5 a_4) False) (Or (Eq (r2 a_6 a_5) False) (Eq (And (r1 a_7) (r2 a_7 a_6)) False))))) % 5.20/5.40 Clause #198 (by clausification #[197]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 5.20/5.40 Or (Ne a a_1) % 5.20/5.40 (Or (Eq (r3 a_2 a_3 a) False) % 5.20/5.40 (Or (Eq (r2 a_4 a_3) False) % 5.20/5.40 (Or (Eq (r2 a_5 a_4) False) (Or (Eq (r2 a_6 a_5) False) (Or (Eq (r1 a_7) False) (Eq (r2 a_7 a_6) False)))))) % 5.20/5.40 Clause #199 (by destructive equality resolution #[198]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 5.20/5.40 Or (Eq (r3 a a_1 a_2) False) % 5.20/5.40 (Or (Eq (r2 a_3 a_1) False) % 5.20/5.40 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Or (Eq (r1 a_6) False) (Eq (r2 a_6 a_5) False))))) % 5.20/5.40 Clause #200 (by superposition #[199, 93]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.20/5.40 Or (Eq (r2 a a_1) False) % 5.20/5.40 (Or (Eq (r2 a_2 a) False) % 5.20/5.40 (Or (Eq (r2 a_3 a_2) False) (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_3) False) (Eq False True))))) % 5.20/5.40 Clause #205 (by clausification #[200]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.20/5.40 Or (Eq (r2 a a_1) False) % 5.20/5.40 (Or (Eq (r2 a_2 a) False) (Or (Eq (r2 a_3 a_2) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_3) False)))) % 5.20/5.40 Clause #207 (by superposition #[205, 52]): ∀ (a a_1 a_2 a_3 : Iota), % 5.20/5.40 Or (Eq (r2 a a_1) False) % 5.20/5.40 (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_2) False) (Eq False True)))) % 5.20/5.40 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 a_3 : Iota), % 5.20/5.40 Or (Eq (r2 a a_1) False) (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Eq (r2 a_3 a_2) False))) % 5.20/5.40 Clause #210 (by superposition #[208, 52]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Or (Eq (r2 a_2 a) False) (Eq False True))) % 5.20/5.40 Clause #211 (by clausification #[210]): ∀ (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)) % 5.20/5.40 Clause #213 (by superposition #[211, 52]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True)) % 5.20/5.40 Clause #214 (by clausification #[213]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False) % 5.20/5.40 Clause #216 (by superposition #[214, 50]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 2 a) a_1) False) (Eq False True) % 5.20/5.40 Clause #230 (by clausification #[216]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 2 a) a_1) False % 5.20/5.40 Clause #231 (by superposition #[230, 52]): Eq False True % 5.20/5.40 Clause #232 (by clausification #[231]): False % 5.20/5.40 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------