%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN081+2 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 4.32s 4.50s % Output : Proof 4.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUN081+2 : TPTP v9.2.0. Released v7.3.0. % 0.04/0.13 % Command : duper %s % 0.12/0.34 % Computer : n021.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 11:42:08 EDT 2025 % 0.12/0.34 % CPUTime : % 4.32/4.50 SZS status Theorem for theBenchmark.p % 4.32/4.50 SZS output start Proof for theBenchmark.p % 4.32/4.50 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 % 4.32/4.50 Clause #1 (by assumption #[]): Eq % 4.32/4.50 (∀ (X11 : Iota), % 4.32/4.50 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21))) % 4.32/4.50 True % 4.32/4.50 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 % 4.32/4.50 Clause #11 (by assumption #[]): Eq % 4.32/4.50 (Not % 4.32/4.50 (Exists fun Y1 => % 4.32/4.50 Exists fun Y2 => % 4.32/4.50 Exists fun Y3 => % 4.32/4.50 And (r3 Y1 Y2 Y3) % 4.32/4.50 (Exists fun Y4 => % 4.32/4.50 And (Eq Y3 Y4) % 4.32/4.50 (Exists fun Y5 => % 4.32/4.50 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))) % 4.32/4.50 True % 4.32/4.50 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 % 4.32/4.50 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 % 4.32/4.50 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a a_1) a) True % 4.32/4.50 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 % 4.32/4.50 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (skS.0 0 a a_1) a % 4.32/4.50 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 % 4.32/4.50 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 % 4.32/4.50 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 1 a a_1 a_2)) True % 4.32/4.50 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 % 4.32/4.50 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 % 4.32/4.50 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 % 4.32/4.50 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) % 4.32/4.50 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) % 4.32/4.50 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) % 4.32/4.50 Clause #36 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (Ne a (skS.0 2 a_1)) True) (Eq (r1 a) True) % 4.32/4.50 Clause #39 (by clausification #[1]): ∀ (a : Iota), % 4.32/4.50 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True % 4.32/4.50 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 4.32/4.50 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 % 4.32/4.50 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.32/4.50 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 % 4.32/4.50 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 4.32/4.50 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) % 4.32/4.50 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) % 4.32/4.50 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) % 4.32/4.50 Clause #49 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Ne a (skS.0 2 a_1)) % 4.32/4.50 Clause #50 (by destructive equality resolution #[49]): ∀ (a : Iota), Eq (r1 (skS.0 2 a)) True % 4.32/4.50 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)) % 4.32/4.50 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 4.36/4.53 Clause #55 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 a)) True) (Eq (Eq a (skS.0 2 a_1)) True) % 4.36/4.53 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (Eq a (skS.0 2 a_1)) True) (Eq (r1 a) False) % 4.36/4.53 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq a (skS.0 2 a_1)) % 4.36/4.53 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) % 4.36/4.53 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) % 4.36/4.53 Clause #75 (by superposition #[74, 29]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 2 a_1) a) True % 4.36/4.53 Clause #183 (by clausification #[11]): Eq % 4.36/4.53 (Exists fun Y1 => % 4.36/4.53 Exists fun Y2 => % 4.36/4.53 Exists fun Y3 => % 4.36/4.53 And (r3 Y1 Y2 Y3) % 4.36/4.53 (Exists fun Y4 => % 4.36/4.53 And (Eq Y3 Y4) % 4.36/4.53 (Exists fun Y5 => % 4.36/4.53 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))) % 4.36/4.53 False % 4.36/4.53 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 4.36/4.53 Eq % 4.36/4.53 (Exists fun Y2 => % 4.36/4.53 Exists fun Y3 => % 4.36/4.53 And (r3 a Y2 Y3) % 4.36/4.53 (Exists fun Y4 => % 4.36/4.53 And (Eq Y3 Y4) % 4.36/4.53 (Exists fun Y5 => % 4.36/4.53 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))) % 4.36/4.53 False % 4.36/4.53 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), % 4.36/4.53 Eq % 4.36/4.53 (Exists fun Y3 => % 4.36/4.53 And (r3 a a_1 Y3) % 4.36/4.53 (Exists fun Y4 => % 4.36/4.53 And (Eq Y3 Y4) % 4.36/4.53 (Exists fun Y5 => % 4.36/4.53 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))) % 4.36/4.53 False % 4.36/4.53 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 : Iota), % 4.36/4.53 Eq % 4.36/4.53 (And (r3 a a_1 a_2) % 4.36/4.53 (Exists fun Y4 => % 4.36/4.53 And (Eq a_2 Y4) % 4.36/4.53 (Exists fun Y5 => % 4.36/4.53 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))) % 4.36/4.53 False % 4.36/4.53 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota), % 4.36/4.53 Or (Eq (r3 a a_1 a_2) False) % 4.36/4.53 (Eq % 4.36/4.53 (Exists fun Y4 => % 4.36/4.53 And (Eq a_2 Y4) % 4.36/4.53 (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))) % 4.36/4.53 False) % 4.36/4.53 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.53 Or (Eq (r3 a a_1 a_2) False) % 4.36/4.53 (Eq % 4.36/4.53 (And (Eq a_2 a_3) % 4.36/4.53 (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))) % 4.36/4.53 False) % 4.36/4.53 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.53 Or (Eq (r3 a a_1 a_2) False) % 4.36/4.53 (Or (Eq (Eq a_2 a_3) False) % 4.36/4.53 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))) % 4.36/4.53 False)) % 4.36/4.53 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.53 Or (Eq (r3 a a_1 a_2) False) % 4.36/4.53 (Or % 4.36/4.53 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))) % 4.36/4.53 False) % 4.36/4.53 (Ne a_2 a_3)) % 4.36/4.53 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.36/4.53 Or (Eq (r3 a a_1 a_2) False) % 4.36/4.53 (Or (Ne a_2 a_3) % 4.36/4.53 (Eq (And (r2 a_4 a_3) (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))) False)) % 4.36/4.53 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.36/4.53 Or (Eq (r3 a a_1 a_2) False) % 4.36/4.53 (Or (Ne a_2 a_3) % 4.36/4.53 (Or (Eq (r2 a_4 a_3) False) % 4.36/4.53 (Eq (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))) False))) % 4.36/4.53 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.36/4.53 Or (Eq (r3 a a_1 a_2) False) % 4.36/4.53 (Or (Ne a_2 a_3) % 4.36/4.53 (Or (Eq (r2 a_4 a_3) False) (Eq (And (r2 a_5 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 a_5))) False))) % 4.36/4.53 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.36/4.53 Or (Eq (r3 a a_1 a_2) False) % 4.36/4.53 (Or (Ne a_2 a_3) % 4.36/4.53 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Eq (Exists fun Y7 => And (r1 Y7) (r2 Y7 a_5)) False)))) % 4.36/4.53 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.37/4.54 Or (Eq (r3 a a_1 a_2) False) % 4.37/4.54 (Or (Ne a_2 a_3) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Eq (And (r1 a_6) (r2 a_6 a_5)) False)))) % 4.37/4.54 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.37/4.54 Or (Eq (r3 a a_1 a_2) False) % 4.37/4.54 (Or (Ne a_2 a_3) % 4.37/4.54 (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))))) % 4.37/4.54 Clause #197 (by destructive equality resolution #[196]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.37/4.54 Or (Eq (r3 a a_1 a_2) False) % 4.37/4.54 (Or (Eq (r2 a_3 a_2) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False)))) % 4.37/4.54 Clause #200 (by superposition #[197, 75]): ∀ (a a_1 a_2 a_3 : Iota), % 4.37/4.54 Or (Eq (r2 a a_1) False) % 4.37/4.54 (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_2) False) (Eq False True)))) % 4.37/4.54 Clause #201 (by clausification #[200]): ∀ (a a_1 a_2 a_3 : Iota), % 4.37/4.54 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))) % 4.37/4.54 Clause #203 (by superposition #[201, 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))) % 4.37/4.54 Clause #204 (by clausification #[203]): ∀ (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)) % 4.37/4.54 Clause #206 (by superposition #[204, 52]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True)) % 4.37/4.54 Clause #207 (by clausification #[206]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False) % 4.37/4.54 Clause #209 (by superposition #[207, 50]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 2 a) a_1) False) (Eq False True) % 4.37/4.54 Clause #212 (by clausification #[209]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 2 a) a_1) False % 4.37/4.54 Clause #213 (by superposition #[212, 52]): Eq False True % 4.37/4.54 Clause #214 (by clausification #[213]): False % 4.37/4.54 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------