%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN080+1 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 4.31s 4.58s % Output : Proof 4.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUN080+1 : TPTP v9.2.0. Released v7.3.0. % 0.08/0.14 % Command : duper %s % 0.14/0.35 % Computer : n001.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 11:39:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.31/4.58 SZS status Theorem for theBenchmark.p % 4.31/4.58 SZS output start Proof for theBenchmark.p % 4.31/4.58 Clause #0 (by assumption #[]): Eq (Exists fun Y24 => ∀ (X19 : Iota), Or (And (id X19 Y24) (r1 X19)) (And (Not (r1 X19)) (Not (id X19 Y24)))) True % 4.31/4.58 Clause #1 (by assumption #[]): Eq % 4.31/4.58 (∀ (X11 : Iota), % 4.31/4.58 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21)))) % 4.31/4.58 True % 4.31/4.58 Clause #2 (by assumption #[]): Eq % 4.31/4.58 (∀ (X13 X14 : Iota), % 4.31/4.58 Exists fun Y22 => % 4.31/4.58 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 X13 X14 X15)) (And (Not (r3 X13 X14 X15)) (Not (id X15 Y22)))) % 4.31/4.58 True % 4.31/4.58 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 4.31/4.58 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True % 4.31/4.58 Clause #14 (by assumption #[]): Eq (∀ (X4 : Iota), Exists fun Y9 => And (id Y9 X4) (Exists fun Y16 => And (r1 Y16) (r3 X4 Y16 Y9))) True % 4.31/4.58 Clause #18 (by assumption #[]): Eq % 4.31/4.58 (Not % 4.31/4.58 (Exists fun Y1 => % 4.31/4.58 Exists fun Y2 => % 4.31/4.58 Exists fun Y3 => % 4.31/4.58 And (id Y3 Y2) % 4.31/4.58 (Exists fun Y4 => % 4.31/4.58 And (r3 Y1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))) % 4.31/4.58 True % 4.31/4.58 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 4.31/4.58 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True % 4.31/4.58 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True % 4.31/4.58 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True) % 4.31/4.58 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False) % 4.31/4.58 Clause #34 (by clausification #[0]): ∀ (a : Iota), % 4.31/4.58 Eq (∀ (X19 : Iota), Or (And (id X19 (skS.0 0 a)) (r1 X19)) (And (Not (r1 X19)) (Not (id X19 (skS.0 0 a))))) True % 4.31/4.58 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Or (And (id a (skS.0 0 a_1)) (r1 a)) (And (Not (r1 a)) (Not (id a (skS.0 0 a_1))))) True % 4.31/4.58 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (And (id a (skS.0 0 a_1)) (r1 a)) True) (Eq (And (Not (r1 a)) (Not (id a (skS.0 0 a_1)))) True) % 4.31/4.58 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (id a (skS.0 0 a_1)))) True) (Eq (r1 a) True) % 4.31/4.58 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True) % 4.31/4.58 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False) % 4.31/4.58 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True) % 4.31/4.58 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True % 4.31/4.58 Clause #53 (by clausification #[14]): ∀ (a : Iota), Eq (Exists fun Y9 => And (id Y9 a) (Exists fun Y16 => And (r1 Y16) (r3 a Y16 Y9))) True % 4.31/4.58 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (And (id (skS.0 1 a a_1) a) (Exists fun Y16 => And (r1 Y16) (r3 a Y16 (skS.0 1 a a_1)))) True % 4.31/4.58 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True % 4.31/4.58 Clause #61 (by superposition #[56, 23]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 1 a a_1)) True) (Eq True False) % 4.31/4.58 Clause #63 (by clausification #[1]): ∀ (a : Iota), % 4.31/4.58 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True % 4.31/4.58 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 4.31/4.58 Eq % 4.31/4.58 (∀ (X12 : Iota), Or (And (id X12 (skS.0 3 a a_1)) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 (skS.0 3 a a_1))))) % 4.31/4.58 True % 4.31/4.58 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 4.31/4.58 Eq (Or (And (id a (skS.0 3 a_1 a_2)) (r2 a_1 a)) (And (Not (r2 a_1 a)) (Not (id a (skS.0 3 a_1 a_2))))) True % 4.31/4.58 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 4.31/4.58 Or (Eq (And (id a (skS.0 3 a_1 a_2)) (r2 a_1 a)) True) (Eq (And (Not (r2 a_1 a)) (Not (id a (skS.0 3 a_1 a_2)))) True) % 4.31/4.58 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (Not (r2 a a_1)) (Not (id a_1 (skS.0 3 a a_2)))) True) (Eq (r2 a a_1) True) % 4.31/4.58 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (Not (id a_1 (skS.0 3 a a_2))) True) % 4.42/4.60 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (id a_1 (skS.0 3 a a_2)) False) % 4.42/4.60 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True) % 4.42/4.60 Clause #75 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (id a (skS.0 1 a a_1)) True % 4.42/4.60 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 4.42/4.60 Clause #80 (by clausification #[2]): ∀ (a : Iota), % 4.42/4.60 Eq % 4.42/4.60 (∀ (X14 : Iota), % 4.42/4.60 Exists fun Y22 => % 4.42/4.60 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 a X14 X15)) (And (Not (r3 a X14 X15)) (Not (id X15 Y22)))) % 4.42/4.60 True % 4.42/4.60 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), % 4.42/4.60 Eq % 4.42/4.60 (Exists fun Y22 => % 4.42/4.60 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 a a_1 X15)) (And (Not (r3 a a_1 X15)) (Not (id X15 Y22)))) % 4.42/4.60 True % 4.42/4.60 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), % 4.42/4.60 Eq % 4.42/4.60 (∀ (X15 : Iota), % 4.42/4.60 Or (And (id X15 (skS.0 4 a a_1 a_2)) (r3 a a_1 X15)) % 4.42/4.60 (And (Not (r3 a a_1 X15)) (Not (id X15 (skS.0 4 a a_1 a_2))))) % 4.42/4.60 True % 4.42/4.60 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota), % 4.42/4.60 Eq % 4.42/4.60 (Or (And (id a (skS.0 4 a_1 a_2 a_3)) (r3 a_1 a_2 a)) (And (Not (r3 a_1 a_2 a)) (Not (id a (skS.0 4 a_1 a_2 a_3))))) % 4.42/4.60 True % 4.42/4.60 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), % 4.42/4.60 Or (Eq (And (id a (skS.0 4 a_1 a_2 a_3)) (r3 a_1 a_2 a)) True) % 4.42/4.60 (Eq (And (Not (r3 a_1 a_2 a)) (Not (id a (skS.0 4 a_1 a_2 a_3)))) True) % 4.42/4.60 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 a_3 : Iota), % 4.42/4.60 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (id a_2 (skS.0 4 a a_1 a_3)))) True) (Eq (r3 a a_1 a_2) True) % 4.42/4.60 Clause #87 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Eq (Not (id a_2 (skS.0 4 a a_1 a_3))) True) % 4.42/4.60 Clause #89 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Eq (id a_2 (skS.0 4 a a_1 a_3)) False) % 4.42/4.60 Clause #91 (by superposition #[89, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 a a_1 (skS.0 4 a a_1 a_2)) True) (Eq False True) % 4.42/4.60 Clause #97 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), Eq (r3 a a_1 (skS.0 4 a a_1 a_2)) True % 4.42/4.60 Clause #372 (by clausification #[18]): Eq % 4.42/4.60 (Exists fun Y1 => % 4.42/4.60 Exists fun Y2 => % 4.42/4.60 Exists fun Y3 => % 4.42/4.60 And (id Y3 Y2) % 4.42/4.60 (Exists fun Y4 => % 4.42/4.60 And (r3 Y1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))) % 4.42/4.60 False % 4.42/4.60 Clause #373 (by clausification #[372]): ∀ (a : Iota), % 4.42/4.60 Eq % 4.42/4.60 (Exists fun Y2 => % 4.42/4.60 Exists fun Y3 => % 4.42/4.60 And (id Y3 Y2) % 4.42/4.60 (Exists fun Y4 => % 4.42/4.60 And (r3 a Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))) % 4.42/4.60 False % 4.42/4.60 Clause #374 (by clausification #[373]): ∀ (a a_1 : Iota), % 4.42/4.60 Eq % 4.42/4.60 (Exists fun Y3 => % 4.42/4.60 And (id Y3 a) % 4.42/4.60 (Exists fun Y4 => % 4.42/4.60 And (r3 a_1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))) % 4.42/4.60 False % 4.42/4.60 Clause #375 (by clausification #[374]): ∀ (a a_1 a_2 : Iota), % 4.42/4.60 Eq % 4.42/4.60 (And (id a a_1) % 4.42/4.60 (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))))) % 4.42/4.60 False % 4.42/4.60 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 : Iota), % 4.42/4.60 Or (Eq (id a a_1) False) % 4.42/4.60 (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)))) % 4.42/4.60 False) % 4.42/4.60 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 a_3 : Iota), % 4.42/4.60 Or (Eq (id a a_1) False) % 4.42/4.60 (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) % 4.42/4.60 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 : Iota), % 4.42/4.60 Or (Eq (id a a_1) False) % 4.42/4.60 (Or (Eq (r3 a_2 a_3 a) False) % 4.42/4.60 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))) False)) % 4.42/4.60 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.42/4.60 Or (Eq (id a a_1) False) % 4.42/4.60 (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)) % 4.44/4.62 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.44/4.62 Or (Eq (id a a_1) False) % 4.44/4.62 (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))) % 4.44/4.62 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.44/4.62 Or (Eq (id a a_1) False) % 4.44/4.62 (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))) % 4.44/4.62 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.44/4.62 Or (Eq (id a a_1) False) % 4.44/4.62 (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)))) % 4.44/4.62 Clause #386 (by superposition #[382, 75]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.44/4.62 Or (Eq (r3 a a_1 a_2) False) % 4.44/4.62 (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_3) False) (Eq False True)))) % 4.44/4.62 Clause #389 (by clausification #[386]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.44/4.62 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))) % 4.44/4.62 Clause #391 (by superposition #[389, 97]): ∀ (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))) % 4.44/4.62 Clause #392 (by clausification #[391]): ∀ (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)) % 4.44/4.62 Clause #395 (by superposition #[392, 78]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True)) % 4.44/4.62 Clause #396 (by clausification #[395]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False) % 4.44/4.62 Clause #397 (by superposition #[396, 44]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) False) (Eq False True) % 4.44/4.62 Clause #407 (by clausification #[397]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 0 a) a_1) False % 4.44/4.62 Clause #408 (by superposition #[407, 78]): Eq False True % 4.44/4.62 Clause #409 (by clausification #[408]): False % 4.44/4.62 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------