%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN080+2 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 07:57:50 PM UTC 2025 % Result : Theorem 4.27s 4.52s % Output : Proof 4.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUN080+2 : TPTP v9.2.0. Released v7.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n017.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 : Thu Oct 2 11:37:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.27/4.52 SZS status Theorem for theBenchmark.p % 4.27/4.52 SZS output start Proof for theBenchmark.p % 4.27/4.52 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 % 4.27/4.52 Clause #1 (by assumption #[]): Eq % 4.27/4.52 (∀ (X11 : Iota), % 4.27/4.52 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21))) % 4.27/4.52 True % 4.27/4.52 Clause #2 (by assumption #[]): Eq % 4.27/4.52 (∀ (X13 X14 : Iota), % 4.27/4.52 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 X13 X14 X15)) (Ne X15 Y22)) (And (r3 X13 X14 X15) (Eq X15 Y22))) % 4.27/4.52 True % 4.27/4.52 Clause #11 (by assumption #[]): Eq % 4.27/4.52 (Not % 4.27/4.52 (Exists fun Y1 => % 4.27/4.52 Exists fun Y2 => % 4.27/4.52 Exists fun Y3 => % 4.27/4.52 And (Eq Y3 Y2) % 4.27/4.52 (Exists fun Y4 => % 4.27/4.52 And (r3 Y1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))) % 4.27/4.52 True % 4.27/4.52 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 % 4.27/4.52 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 % 4.27/4.52 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) % 4.27/4.52 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) % 4.27/4.52 Clause #36 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (Ne a (skS.0 2 a_1)) True) (Eq (r1 a) True) % 4.27/4.52 Clause #39 (by clausification #[1]): ∀ (a : Iota), % 4.27/4.52 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True % 4.27/4.52 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 4.27/4.52 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 % 4.27/4.52 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.27/4.52 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 % 4.27/4.52 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 4.27/4.52 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) % 4.27/4.52 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) % 4.27/4.52 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) % 4.27/4.52 Clause #49 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Ne a (skS.0 2 a_1)) % 4.27/4.52 Clause #50 (by destructive equality resolution #[49]): ∀ (a : Iota), Eq (r1 (skS.0 2 a)) True % 4.27/4.52 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)) % 4.27/4.52 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 4.27/4.52 Clause #62 (by clausification #[2]): ∀ (a : Iota), % 4.27/4.52 Eq % 4.27/4.52 (∀ (X14 : Iota), % 4.27/4.52 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 a X14 X15)) (Ne X15 Y22)) (And (r3 a X14 X15) (Eq X15 Y22))) % 4.27/4.52 True % 4.27/4.52 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 4.27/4.52 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))) % 4.27/4.52 True % 4.27/4.52 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 4.27/4.52 Eq % 4.27/4.52 (∀ (X15 : Iota), % 4.27/4.52 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)))) % 4.27/4.52 True % 4.27/4.52 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.52 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 % 4.27/4.52 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.52 Or (Eq (And (Not (r3 a a_1 a_2)) (Ne a_2 (skS.0 4 a a_1 a_3))) True) % 4.27/4.52 (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True) % 4.27/4.52 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.52 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) % 4.33/4.55 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) % 4.33/4.55 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)) % 4.33/4.55 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 % 4.33/4.55 Clause #183 (by clausification #[11]): Eq % 4.33/4.55 (Exists fun Y1 => % 4.33/4.55 Exists fun Y2 => % 4.33/4.55 Exists fun Y3 => % 4.33/4.55 And (Eq Y3 Y2) % 4.33/4.55 (Exists fun Y4 => % 4.33/4.55 And (r3 Y1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))) % 4.33/4.55 False % 4.33/4.55 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 4.33/4.55 Eq % 4.33/4.55 (Exists fun Y2 => % 4.33/4.55 Exists fun Y3 => % 4.33/4.55 And (Eq Y3 Y2) % 4.33/4.55 (Exists fun Y4 => % 4.33/4.55 And (r3 a Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))) % 4.33/4.55 False % 4.33/4.55 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), % 4.33/4.55 Eq % 4.33/4.55 (Exists fun Y3 => % 4.33/4.55 And (Eq Y3 a) % 4.33/4.55 (Exists fun Y4 => % 4.33/4.55 And (r3 a_1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))) % 4.33/4.55 False % 4.33/4.55 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 : Iota), % 4.33/4.55 Eq % 4.33/4.55 (And (Eq a a_1) % 4.33/4.55 (Exists fun Y4 => And (r3 a_2 Y4 a) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))) % 4.33/4.55 False % 4.33/4.55 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota), % 4.33/4.55 Or (Eq (Eq a a_1) False) % 4.33/4.55 (Eq (Exists fun Y4 => And (r3 a_2 Y4 a) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))) % 4.33/4.55 False) % 4.33/4.55 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 : Iota), % 4.33/4.55 Or % 4.33/4.55 (Eq (Exists fun Y4 => And (r3 a Y4 a_1) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))) % 4.33/4.55 False) % 4.33/4.55 (Ne a_1 a_2) % 4.33/4.55 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.55 Or (Ne a a_1) % 4.33/4.55 (Eq (And (r3 a_2 a_3 a) (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))) False) % 4.33/4.55 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.55 Or (Ne a a_1) % 4.33/4.55 (Or (Eq (r3 a_2 a_3 a) False) % 4.33/4.55 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))) False)) % 4.33/4.55 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.33/4.55 Or (Ne a a_1) (Or (Eq (r3 a_2 a_3 a) False) (Eq (And (r2 a_4 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_4))) False)) % 4.33/4.55 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.33/4.55 Or (Ne a a_1) % 4.33/4.55 (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_4)) False))) % 4.33/4.55 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.33/4.55 Or (Ne a a_1) (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Eq (And (r1 a_5) (r2 a_5 a_4)) False))) % 4.33/4.55 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.33/4.55 Or (Ne a a_1) % 4.33/4.55 (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False)))) % 4.33/4.55 Clause #195 (by destructive equality resolution #[194]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.33/4.55 Or (Eq (r3 a a_1 a_2) False) (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_3) False))) % 4.33/4.55 Clause #196 (by superposition #[195, 93]): ∀ (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))) % 4.33/4.55 Clause #201 (by clausification #[196]): ∀ (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)) % 4.33/4.55 Clause #203 (by superposition #[201, 52]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True)) % 4.33/4.55 Clause #204 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False) % 4.33/4.55 Clause #206 (by superposition #[204, 50]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 2 a) a_1) False) (Eq False True) % 4.33/4.55 Clause #209 (by clausification #[206]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 2 a) a_1) False % 4.33/4.55 Clause #210 (by superposition #[209, 52]): Eq False True % 4.33/4.55 Clause #211 (by clausification #[210]): False % 4.33/4.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------