%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN069+1 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 07:57:48 PM UTC 2025 % Result : Theorem 3.53s 3.72s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUN069+1 : TPTP v9.2.0. Released v7.3.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n020.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 11:34:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.53/3.72 SZS status Theorem for theBenchmark.p % 3.53/3.72 SZS output start Proof for theBenchmark.p % 3.53/3.72 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 % 3.53/3.72 Clause #1 (by assumption #[]): Eq % 3.53/3.72 (∀ (X11 : Iota), % 3.53/3.72 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21)))) % 3.53/3.72 True % 3.53/3.72 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 3.53/3.72 Clause #18 (by assumption #[]): Eq (Not (Exists fun Y1 => And (id Y1 Y1) (Exists fun Y2 => And (r1 Y2) (r2 Y2 Y1)))) True % 3.53/3.72 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 3.53/3.72 Clause #34 (by clausification #[0]): ∀ (a : Iota), % 3.53/3.72 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 % 3.53/3.72 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 % 3.53/3.72 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) % 3.53/3.72 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) % 3.53/3.72 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True) % 3.53/3.72 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False) % 3.53/3.72 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True) % 3.53/3.72 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True % 3.53/3.72 Clause #53 (by clausification #[18]): Eq (Exists fun Y1 => And (id Y1 Y1) (Exists fun Y2 => And (r1 Y2) (r2 Y2 Y1))) False % 3.53/3.72 Clause #54 (by clausification #[53]): ∀ (a : Iota), Eq (And (id a a) (Exists fun Y2 => And (r1 Y2) (r2 Y2 a))) False % 3.53/3.72 Clause #55 (by clausification #[54]): ∀ (a : Iota), Or (Eq (id a a) False) (Eq (Exists fun Y2 => And (r1 Y2) (r2 Y2 a)) False) % 3.53/3.72 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (id a a) False) (Eq (And (r1 a_1) (r2 a_1 a)) False) % 3.53/3.72 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (id a a) False) (Or (Eq (r1 a_1) False) (Eq (r2 a_1 a) False)) % 3.53/3.72 Clause #58 (by superposition #[57, 19]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True)) % 3.53/3.72 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False) % 3.53/3.72 Clause #60 (by superposition #[59, 44]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) False) (Eq False True) % 3.53/3.72 Clause #61 (by clausification #[1]): ∀ (a : Iota), % 3.53/3.72 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True % 3.53/3.72 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), % 3.53/3.72 Eq % 3.53/3.72 (∀ (X12 : Iota), Or (And (id X12 (skS.0 1 a a_1)) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 (skS.0 1 a a_1))))) % 3.53/3.72 True % 3.53/3.72 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 3.53/3.72 Eq (Or (And (id a (skS.0 1 a_1 a_2)) (r2 a_1 a)) (And (Not (r2 a_1 a)) (Not (id a (skS.0 1 a_1 a_2))))) True % 3.53/3.72 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 3.53/3.72 Or (Eq (And (id a (skS.0 1 a_1 a_2)) (r2 a_1 a)) True) (Eq (And (Not (r2 a_1 a)) (Not (id a (skS.0 1 a_1 a_2)))) True) % 3.53/3.72 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (Not (r2 a a_1)) (Not (id a_1 (skS.0 1 a a_2)))) True) (Eq (r2 a a_1) True) % 3.53/3.72 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (Not (id a_1 (skS.0 1 a a_2))) True) % 3.53/3.72 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (id a_1 (skS.0 1 a a_2)) False) % 3.53/3.72 Clause #70 (by superposition #[69, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 1 a a_1)) True) (Eq False True) % 3.53/3.72 Clause #72 (by clausification #[60]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 0 a) a_1) False % 3.53/3.72 Clause #73 (by clausification #[70]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 1 a a_1)) True % 3.53/3.72 Clause #74 (by superposition #[73, 72]): Eq True False % 3.53/3.72 Clause #76 (by clausification #[74]): False % 3.53/3.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------