%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN067+1 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 3.68s 3.85s % Output : Proof 3.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUN067+1 : TPTP v9.2.0. Released v7.3.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n029.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 11:41:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.68/3.85 SZS status Theorem for theBenchmark.p % 3.68/3.85 SZS output start Proof for theBenchmark.p % 3.68/3.85 Clause #1 (by assumption #[]): Eq % 3.68/3.85 (∀ (X11 : Iota), % 3.68/3.85 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21)))) % 3.68/3.85 True % 3.68/3.85 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 3.68/3.85 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True % 3.68/3.85 Clause #7 (by assumption #[]): Eq (∀ (X26 X27 : Iota), Or (Or (Not (id X26 X27)) (And (Not (r1 X26)) (Not (r1 X27)))) (And (r1 X26) (r1 X27))) True % 3.68/3.85 Clause #17 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 X7 Y10))) True % 3.68/3.85 Clause #18 (by assumption #[]): Eq (Not (Exists fun Y1 => ∀ (Y2 : Iota), Or (Not (id Y1 Y2)) (Not (r1 Y2)))) True % 3.68/3.85 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 3.68/3.85 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True % 3.68/3.85 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True % 3.68/3.85 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True) % 3.68/3.85 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False) % 3.68/3.85 Clause #25 (by clausification #[18]): Eq (Exists fun Y1 => ∀ (Y2 : Iota), Or (Not (id Y1 Y2)) (Not (r1 Y2))) False % 3.68/3.85 Clause #26 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Y2 : Iota), Or (Not (id a Y2)) (Not (r1 Y2))) False % 3.68/3.85 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Not (Or (Not (id a (skS.0 0 a a_1))) (Not (r1 (skS.0 0 a a_1))))) True % 3.68/3.85 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Or (Not (id a (skS.0 0 a a_1))) (Not (r1 (skS.0 0 a a_1)))) False % 3.68/3.85 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 0 a a_1))) False % 3.68/3.85 Clause #30 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Not (id a (skS.0 0 a a_1))) False % 3.68/3.85 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a a_1)) True % 3.68/3.85 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (id a (skS.0 0 a a_1)) True % 3.68/3.85 Clause #33 (by superposition #[32, 23]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a a_1) a) True) (Eq True False) % 3.68/3.85 Clause #45 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a a_1) a) True % 3.68/3.85 Clause #49 (by clausification #[1]): ∀ (a : Iota), % 3.68/3.85 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True % 3.68/3.85 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 3.68/3.85 Eq % 3.68/3.85 (∀ (X12 : Iota), Or (And (id X12 (skS.0 2 a a_1)) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 (skS.0 2 a a_1))))) % 3.68/3.85 True % 3.68/3.85 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 3.68/3.85 Eq (Or (And (id a (skS.0 2 a_1 a_2)) (r2 a_1 a)) (And (Not (r2 a_1 a)) (Not (id a (skS.0 2 a_1 a_2))))) True % 3.68/3.85 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 3.68/3.85 Or (Eq (And (id a (skS.0 2 a_1 a_2)) (r2 a_1 a)) True) (Eq (And (Not (r2 a_1 a)) (Not (id a (skS.0 2 a_1 a_2)))) True) % 3.68/3.85 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (Not (r2 a a_1)) (Not (id a_1 (skS.0 2 a a_2)))) True) (Eq (r2 a a_1) True) % 3.68/3.85 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (Not (id a_1 (skS.0 2 a a_2))) True) % 3.68/3.85 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (id a_1 (skS.0 2 a a_2)) False) % 3.68/3.85 Clause #59 (by superposition #[57, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 2 a a_1)) True) (Eq False True) % 3.68/3.85 Clause #61 (by clausification #[59]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 2 a a_1)) True % 3.68/3.85 Clause #108 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 a Y10))) True % 3.68/3.85 Clause #109 (by clausification #[108]): ∀ (a a_1 : Iota), Eq (Or (∀ (Y20 : Iota), Or (Not (id Y20 a)) (Not (r1 Y20))) (Not (r2 a_1 a))) True % 3.68/3.85 Clause #110 (by clausification #[109]): ∀ (a a_1 : Iota), Or (Eq (∀ (Y20 : Iota), Or (Not (id Y20 a)) (Not (r1 Y20))) True) (Eq (Not (r2 a_1 a)) True) % 3.70/3.87 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (r2 a a_1)) True) (Eq (Or (Not (id a_2 a_1)) (Not (r1 a_2))) True) % 3.70/3.87 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), Or (Eq (Or (Not (id a a_1)) (Not (r1 a))) True) (Eq (r2 a_2 a_1) False) % 3.70/3.87 Clause #113 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (id a_2 a_1)) True) (Eq (Not (r1 a_2)) True)) % 3.70/3.87 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (r1 a_2)) True) (Eq (id a_2 a_1) False)) % 3.70/3.87 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (id a_2 a_1) False) (Eq (r1 a_2) False)) % 3.70/3.87 Clause #116 (by superposition #[115, 61]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 2 a_1 a_2)) False) (Or (Eq (r1 a) False) (Eq False True)) % 3.70/3.87 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 2 a_1 a_2)) False) (Eq (r1 a) False) % 3.70/3.87 Clause #119 (by superposition #[117, 19]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 2 a a_1)) False) (Eq False True) % 3.70/3.87 Clause #120 (by clausification #[119]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 2 a a_1)) False % 3.70/3.87 Clause #121 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (X27 : Iota), Or (Or (Not (id a X27)) (And (Not (r1 a)) (Not (r1 X27)))) (And (r1 a) (r1 X27))) True % 3.70/3.87 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (id a a_1)) (And (Not (r1 a)) (Not (r1 a_1)))) (And (r1 a) (r1 a_1))) True % 3.70/3.87 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (Or (Not (id a a_1)) (And (Not (r1 a)) (Not (r1 a_1)))) True) (Eq (And (r1 a) (r1 a_1)) True) % 3.70/3.87 Clause #124 (by clausification #[123]): ∀ (a a_1 : Iota), % 3.70/3.87 Or (Eq (And (r1 a) (r1 a_1)) True) (Or (Eq (Not (id a a_1)) True) (Eq (And (Not (r1 a)) (Not (r1 a_1))) True)) % 3.70/3.87 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Or (Eq (And (Not (r1 a)) (Not (r1 a_1))) True) (Eq (r1 a_1) True)) % 3.70/3.87 Clause #127 (by clausification #[125]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (r1 a_1))) True) (Or (Eq (r1 a_1) True) (Eq (id a a_1) False)) % 3.70/3.87 Clause #129 (by clausification #[127]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (id a_1 a) False) (Eq (Not (r1 a_1)) True)) % 3.70/3.87 Clause #131 (by clausification #[129]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (id a_1 a) False) (Eq (r1 a_1) False)) % 3.70/3.87 Clause #133 (by superposition #[131, 45]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (r1 (skS.0 0 a a_1)) False) (Eq False True)) % 3.70/3.87 Clause #135 (by clausification #[133]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (r1 (skS.0 0 a a_1)) False) % 3.70/3.87 Clause #136 (by superposition #[135, 31]): ∀ (a : Iota), Or (Eq (r1 a) True) (Eq False True) % 3.70/3.87 Clause #137 (by clausification #[136]): ∀ (a : Iota), Eq (r1 a) True % 3.70/3.87 Clause #143 (by superposition #[137, 120]): Eq True False % 3.70/3.87 Clause #144 (by clausification #[143]): False % 3.70/3.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------