%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN062+2 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 6.35s 6.55s % Output : Proof 6.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUN062+2 : TPTP v9.2.0. Released v7.3.0. % 0.06/0.14 % Command : duper %s % 0.14/0.34 % Computer : n028.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 11:38:38 EDT 2025 % 0.14/0.34 % CPUTime : % 6.35/6.55 SZS status Theorem for theBenchmark.p % 6.35/6.55 SZS output start Proof for theBenchmark.p % 6.35/6.55 Clause #1 (by assumption #[]): Eq % 6.35/6.55 (∀ (X11 : Iota), % 6.35/6.55 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21))) % 6.35/6.55 True % 6.35/6.55 Clause #2 (by assumption #[]): Eq % 6.35/6.55 (∀ (X13 X14 : Iota), % 6.35/6.55 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 X13 X14 X15)) (Ne X15 Y22)) (And (r3 X13 X14 X15) (Eq X15 Y22))) % 6.35/6.55 True % 6.35/6.55 Clause #10 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 Y10)) (Not (r2 X7 Y10))) True % 6.35/6.55 Clause #11 (by assumption #[]): Eq % 6.35/6.55 (Not % 6.35/6.55 (∀ (X1 : Iota), % 6.35/6.55 Exists fun Y2 => % 6.35/6.55 Exists fun Y1 => % 6.35/6.55 And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 X1 Y1 Y3) (Eq Y3 Y2)))) % 6.35/6.55 True % 6.35/6.55 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 % 6.35/6.55 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 % 6.35/6.55 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) % 6.35/6.55 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) % 6.35/6.55 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) % 6.35/6.55 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)) % 6.35/6.55 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)) % 6.35/6.55 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)) % 6.35/6.55 Clause #20 (by destructive equality resolution #[19]): ∀ (a a_1 : Iota), Or (Eq (r2 a a_1) False) (Eq (r1 a_1) False) % 6.35/6.55 Clause #39 (by clausification #[1]): ∀ (a : Iota), % 6.35/6.55 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True % 6.35/6.55 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 6.35/6.55 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 % 6.35/6.55 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 6.35/6.55 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 % 6.35/6.55 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 6.35/6.55 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) % 6.35/6.55 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) % 6.35/6.55 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) % 6.35/6.55 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)) % 6.35/6.55 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 6.35/6.55 Clause #53 (by superposition #[52, 20]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (r1 (skS.0 3 a a_1)) False) % 6.35/6.55 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 3 a a_1)) False % 6.35/6.55 Clause #62 (by clausification #[2]): ∀ (a : Iota), % 6.35/6.55 Eq % 6.35/6.55 (∀ (X14 : Iota), % 6.35/6.55 Exists fun Y22 => ∀ (X15 : Iota), Or (And (Not (r3 a X14 X15)) (Ne X15 Y22)) (And (r3 a X14 X15) (Eq X15 Y22))) % 6.35/6.55 True % 6.35/6.55 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 6.35/6.55 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))) % 6.35/6.55 True % 6.35/6.55 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 6.35/6.55 Eq % 6.35/6.55 (∀ (X15 : Iota), % 6.35/6.55 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)))) % 6.35/6.55 True % 6.35/6.55 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), % 6.35/6.55 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 % 6.35/6.58 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 6.35/6.58 Or (Eq (And (Not (r3 a a_1 a_2)) (Ne a_2 (skS.0 4 a a_1 a_3))) True) % 6.35/6.58 (Eq (And (r3 a a_1 a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True) % 6.35/6.58 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 6.35/6.58 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) % 6.35/6.58 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) % 6.35/6.58 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)) % 6.35/6.58 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 % 6.35/6.58 Clause #183 (by clausification #[11]): Eq % 6.35/6.58 (∀ (X1 : Iota), % 6.35/6.58 Exists fun Y2 => % 6.35/6.58 Exists fun Y1 => And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 X1 Y1 Y3) (Eq Y3 Y2))) % 6.35/6.58 False % 6.35/6.58 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 6.35/6.58 Eq % 6.35/6.58 (Not % 6.35/6.58 (Exists fun Y2 => % 6.35/6.58 Exists fun Y1 => % 6.35/6.58 And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 (skS.0 16 a) Y1 Y3) (Eq Y3 Y2)))) % 6.35/6.58 True % 6.35/6.58 Clause #185 (by clausification #[184]): ∀ (a : Iota), % 6.35/6.58 Eq % 6.35/6.58 (Exists fun Y2 => % 6.35/6.58 Exists fun Y1 => % 6.35/6.58 And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 (skS.0 16 a) Y1 Y3) (Eq Y3 Y2))) % 6.35/6.58 False % 6.35/6.58 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), % 6.35/6.58 Eq % 6.35/6.58 (Exists fun Y1 => % 6.35/6.58 And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne Y1 Y4)) (Exists fun Y3 => And (r3 (skS.0 16 a) Y1 Y3) (Eq Y3 a_1))) % 6.35/6.58 False % 6.35/6.58 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota), % 6.35/6.58 Eq (And (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne a Y4)) (Exists fun Y3 => And (r3 (skS.0 16 a_1) a Y3) (Eq Y3 a_2))) False % 6.35/6.58 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 : Iota), % 6.35/6.58 Or (Eq (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Ne a Y4)) False) % 6.35/6.58 (Eq (Exists fun Y3 => And (r3 (skS.0 16 a_1) a Y3) (Eq Y3 a_2)) False) % 6.35/6.58 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota), % 6.35/6.58 Or (Eq (Exists fun Y3 => And (r3 (skS.0 16 a) a_1 Y3) (Eq Y3 a_2)) False) % 6.35/6.58 (Eq (Not (Or (Not (r1 (skS.0 17 a_1 a_3))) (Ne a_1 (skS.0 17 a_1 a_3)))) True) % 6.35/6.58 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.58 Or (Eq (Not (Or (Not (r1 (skS.0 17 a a_1))) (Ne a (skS.0 17 a a_1)))) True) % 6.35/6.58 (Eq (And (r3 (skS.0 16 a_2) a a_3) (Eq a_3 a_4)) False) % 6.35/6.58 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.58 Or (Eq (And (r3 (skS.0 16 a) a_1 a_2) (Eq a_2 a_3)) False) % 6.35/6.58 (Eq (Or (Not (r1 (skS.0 17 a_1 a_4))) (Ne a_1 (skS.0 17 a_1 a_4))) False) % 6.35/6.58 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.58 Or (Eq (Or (Not (r1 (skS.0 17 a a_1))) (Ne a (skS.0 17 a a_1))) False) % 6.35/6.58 (Or (Eq (r3 (skS.0 16 a_2) a a_3) False) (Eq (Eq a_3 a_4) False)) % 6.35/6.58 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.58 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (Eq a_2 a_3) False) (Eq (Ne a_1 (skS.0 17 a_1 a_4)) False)) % 6.35/6.58 Clause #194 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.58 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (Eq a_2 a_3) False) (Eq (Not (r1 (skS.0 17 a_1 a_4))) False)) % 6.35/6.58 Clause #195 (by clausification #[193]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.58 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (Ne a_1 (skS.0 17 a_1 a_3)) False) (Ne a_2 a_4)) % 6.35/6.58 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Ne a_2 a_3) (Eq a_1 (skS.0 17 a_1 a_4))) % 6.35/6.58 Clause #197 (by destructive equality resolution #[196]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Eq a_1 (skS.0 17 a_1 a_3)) % 6.35/6.58 Clause #198 (by superposition #[197, 93]): ∀ (a a_1 : Iota), Or (Eq a (skS.0 17 a a_1)) (Eq False True) % 6.35/6.58 Clause #203 (by clausification #[198]): ∀ (a a_1 : Iota), Eq a (skS.0 17 a a_1) % 6.35/6.58 Clause #341 (by clausification #[194]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.58 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (Not (r1 (skS.0 17 a_1 a_3))) False) (Ne a_2 a_4)) % 6.35/6.58 Clause #342 (by clausification #[341]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.35/6.58 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Ne a_2 a_3) (Eq (r1 (skS.0 17 a_1 a_4)) True)) % 6.35/6.58 Clause #343 (by destructive equality resolution #[342]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Eq (r1 (skS.0 17 a_1 a_3)) True) % 6.35/6.58 Clause #344 (by forward demodulation #[343, 203]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Eq (r1 a_1) True) % 6.35/6.58 Clause #348 (by superposition #[344, 93]): ∀ (a : Iota), Or (Eq (r1 a) True) (Eq False True) % 6.35/6.58 Clause #353 (by clausification #[348]): ∀ (a : Iota), Eq (r1 a) True % 6.35/6.58 Clause #356 (by superposition #[353, 54]): Eq True False % 6.35/6.58 Clause #360 (by clausification #[356]): False % 6.35/6.58 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------