%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM851+2 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 07:57:27 PM UTC 2025 % Result : Theorem 30.93s 31.14s % Output : Proof 31.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM851+2 : TPTP v9.2.0. Released v4.1.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n010.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 : Fri Oct 3 08:56:53 EDT 2025 % 0.12/0.34 % CPUTime : % 30.93/31.14 SZS status Theorem for theBenchmark.p % 30.93/31.14 SZS output start Proof for theBenchmark.p % 30.93/31.14 Clause #0 (by assumption #[]): Eq (Not (Eq (vmul (vplus vd471 vd473) vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469)))) True % 30.93/31.14 Clause #2 (by assumption #[]): Eq (Eq vd470 (vplus vd471 vd473)) True % 30.93/31.14 Clause #5 (by assumption #[]): Eq (∀ (Vd432 Vd433 Vd434 : Iota), Eq (vmul Vd432 (vplus Vd433 Vd434)) (vplus (vmul Vd432 Vd433) (vmul Vd432 Vd434))) % 30.93/31.14 True % 30.93/31.14 Clause #6 (by assumption #[]): Eq (∀ (Vd418 Vd419 : Iota), Eq (vmul Vd418 Vd419) (vmul Vd419 Vd418)) True % 30.93/31.14 Clause #13 (by assumption #[]): Eq % 30.93/31.14 (∀ (Vd120 Vd121 : Iota), % 30.93/31.14 Or (Or (Eq Vd120 Vd121) (Exists fun Vd123 => Eq Vd120 (vplus Vd121 Vd123))) % 30.93/31.14 (Exists fun Vd125 => Eq Vd121 (vplus Vd120 Vd125))) % 30.93/31.14 True % 30.93/31.14 Clause #14 (by assumption #[]): Eq (∀ (Vd120 Vd121 : Iota), Or (Ne Vd120 Vd121) (Not (Exists fun Vd125 => Eq Vd121 (vplus Vd120 Vd125)))) True % 30.93/31.14 Clause #27 (by clausification #[2]): Eq vd470 (vplus vd471 vd473) % 30.93/31.14 Clause #35 (by clausification #[0]): Eq (Eq (vmul (vplus vd471 vd473) vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469))) False % 30.93/31.14 Clause #36 (by clausification #[35]): Ne (vmul (vplus vd471 vd473) vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.14 Clause #37 (by forward demodulation #[36, 27]): Ne (vmul vd470 vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.14 Clause #78 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Vd433 Vd434 : Iota), Eq (vmul a (vplus Vd433 Vd434)) (vplus (vmul a Vd433) (vmul a Vd434))) True % 30.93/31.14 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Eq (∀ (Vd434 : Iota), Eq (vmul a (vplus a_1 Vd434)) (vplus (vmul a a_1) (vmul a Vd434))) True % 30.93/31.14 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), Eq (Eq (vmul a (vplus a_1 a_2)) (vplus (vmul a a_1) (vmul a a_2))) True % 30.93/31.14 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), Eq (vmul a (vplus a_1 a_2)) (vplus (vmul a a_1) (vmul a a_2)) % 30.93/31.14 Clause #103 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Vd419 : Iota), Eq (vmul a Vd419) (vmul Vd419 a)) True % 30.93/31.14 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota), Eq (Eq (vmul a a_1) (vmul a_1 a)) True % 30.93/31.14 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (vmul a a_1) (vmul a_1 a) % 30.93/31.14 Clause #113 (by superposition #[105, 81]): ∀ (a a_1 a_2 : Iota), Eq (vmul a (vplus a_1 a_2)) (vplus (vmul a_1 a) (vmul a a_2)) % 30.93/31.14 Clause #200 (by clausification #[13]): ∀ (a : Iota), % 30.93/31.14 Eq % 30.93/31.14 (∀ (Vd121 : Iota), % 30.93/31.14 Or (Or (Eq a Vd121) (Exists fun Vd123 => Eq a (vplus Vd121 Vd123))) % 30.93/31.14 (Exists fun Vd125 => Eq Vd121 (vplus a Vd125))) % 30.93/31.14 True % 30.93/31.14 Clause #201 (by clausification #[200]): ∀ (a a_1 : Iota), % 30.93/31.14 Eq (Or (Or (Eq a a_1) (Exists fun Vd123 => Eq a (vplus a_1 Vd123))) (Exists fun Vd125 => Eq a_1 (vplus a Vd125))) True % 30.93/31.14 Clause #202 (by clausification #[201]): ∀ (a a_1 : Iota), % 30.93/31.14 Or (Eq (Or (Eq a a_1) (Exists fun Vd123 => Eq a (vplus a_1 Vd123))) True) % 30.93/31.14 (Eq (Exists fun Vd125 => Eq a_1 (vplus a Vd125)) True) % 30.93/31.14 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota), % 30.93/31.14 Or (Eq (Exists fun Vd125 => Eq a (vplus a_1 Vd125)) True) % 30.93/31.14 (Or (Eq (Eq a_1 a) True) (Eq (Exists fun Vd123 => Eq a_1 (vplus a Vd123)) True)) % 30.93/31.14 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota), % 30.93/31.14 Or (Eq (Eq a a_1) True) % 30.93/31.14 (Or (Eq (Exists fun Vd123 => Eq a (vplus a_1 Vd123)) True) (Eq (Eq a_1 (vplus a (skS.0 0 a_1 a a_2))) True)) % 30.93/31.14 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 : Iota), % 30.93/31.14 Or (Eq (Exists fun Vd123 => Eq a (vplus a_1 Vd123)) True) % 30.93/31.14 (Or (Eq (Eq a_1 (vplus a (skS.0 0 a_1 a a_2))) True) (Eq a a_1)) % 30.93/31.14 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 a_3 : Iota), % 30.93/31.14 Or (Eq (Eq a (vplus a_1 (skS.0 0 a a_1 a_2))) True) (Or (Eq a_1 a) (Eq (Eq a_1 (vplus a (skS.0 1 a_1 a a_3))) True)) % 30.93/31.14 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 a_3 : Iota), % 30.93/31.14 Or (Eq a a_1) (Or (Eq (Eq a (vplus a_1 (skS.0 1 a a_1 a_2))) True) (Eq a_1 (vplus a (skS.0 0 a_1 a a_3)))) % 30.93/31.14 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 a_3 : Iota), % 30.93/31.14 Or (Eq a a_1) (Or (Eq a_1 (vplus a (skS.0 0 a_1 a a_2))) (Eq a (vplus a_1 (skS.0 1 a a_1 a_3)))) % 30.93/31.14 Clause #225 (by superposition #[208, 37]): ∀ (a a_1 a_2 : Iota), % 30.93/31.16 Or % 30.93/31.16 (Eq a % 30.93/31.16 (vplus (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (skS.0 0 a (vplus (vmul vd471 vd469) (vmul vd473 vd469)) a_1))) % 30.93/31.16 (Or % 30.93/31.16 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (vplus a (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) a a_2))) % 30.93/31.16 (Ne (vmul vd470 vd469) a)) % 30.93/31.16 Clause #424 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (Vd121 : Iota), Or (Ne a Vd121) (Not (Exists fun Vd125 => Eq Vd121 (vplus a Vd125)))) True % 30.93/31.16 Clause #425 (by clausification #[424]): ∀ (a a_1 : Iota), Eq (Or (Ne a a_1) (Not (Exists fun Vd125 => Eq a_1 (vplus a Vd125)))) True % 30.93/31.16 Clause #426 (by clausification #[425]): ∀ (a a_1 : Iota), Or (Eq (Ne a a_1) True) (Eq (Not (Exists fun Vd125 => Eq a_1 (vplus a Vd125))) True) % 30.93/31.16 Clause #427 (by clausification #[426]): ∀ (a a_1 : Iota), Or (Eq (Not (Exists fun Vd125 => Eq a (vplus a_1 Vd125))) True) (Ne a_1 a) % 30.93/31.16 Clause #428 (by clausification #[427]): ∀ (a a_1 : Iota), Or (Ne a a_1) (Eq (Exists fun Vd125 => Eq a_1 (vplus a Vd125)) False) % 30.93/31.16 Clause #429 (by clausification #[428]): ∀ (a a_1 a_2 : Iota), Or (Ne a a_1) (Eq (Eq a_1 (vplus a a_2)) False) % 30.93/31.16 Clause #430 (by clausification #[429]): ∀ (a a_1 a_2 : Iota), Or (Ne a a_1) (Ne a_1 (vplus a a_2)) % 30.93/31.16 Clause #431 (by destructive equality resolution #[430]): ∀ (a a_1 : Iota), Ne a (vplus a a_1) % 30.93/31.16 Clause #17415 (by destructive equality resolution #[225]): ∀ (a a_1 : Iota), % 30.93/31.16 Or % 30.93/31.16 (Eq (vmul vd470 vd469) % 30.93/31.16 (vplus (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (skS.0 0 (vmul vd470 vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469)) a))) % 30.93/31.16 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 30.93/31.16 Clause #17416 (by forward demodulation #[17415, 105]): ∀ (a a_1 : Iota), % 30.93/31.16 Or % 30.93/31.16 (Eq (vmul vd469 vd470) % 30.93/31.16 (vplus (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (skS.0 0 (vmul vd470 vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469)) a))) % 30.93/31.16 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 30.93/31.16 Clause #17417 (by forward demodulation #[17416, 105]): ∀ (a a_1 : Iota), % 30.93/31.16 Or % 30.93/31.16 (Eq (vmul vd469 vd470) % 30.93/31.16 (vplus (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (skS.0 0 (vmul vd470 vd469) (vplus (vmul vd471 vd469) (vmul vd469 vd473)) a))) % 30.93/31.16 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 30.93/31.16 Clause #17418 (by forward demodulation #[17417, 113]): ∀ (a a_1 : Iota), % 30.93/31.16 Or % 30.93/31.16 (Eq (vmul vd469 vd470) % 30.93/31.16 (vplus (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (skS.0 0 (vmul vd470 vd469) (vmul vd469 (vplus vd471 vd473)) a))) % 30.93/31.16 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 30.93/31.16 Clause #17419 (by forward demodulation #[17418, 27]): ∀ (a a_1 : Iota), % 30.93/31.16 Or % 30.93/31.16 (Eq (vmul vd469 vd470) % 30.93/31.16 (vplus (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (skS.0 0 (vmul vd470 vd469) (vmul vd469 vd470) a))) % 30.93/31.16 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 30.93/31.16 Clause #17420 (by forward demodulation #[17419, 105]): ∀ (a a_1 : Iota), % 30.93/31.16 Or % 30.93/31.16 (Eq (vmul vd469 vd470) % 30.93/31.16 (vplus (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 30.93/31.16 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 30.93/31.16 Clause #17421 (by forward demodulation #[17420, 105]): ∀ (a a_1 : Iota), % 30.93/31.16 Or % 30.93/31.16 (Eq (vmul vd469 vd470) % 30.93/31.16 (vplus (vplus (vmul vd471 vd469) (vmul vd469 vd473)) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 30.93/31.16 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 30.93/31.16 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 31.06/31.27 Clause #17422 (by forward demodulation #[17421, 113]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 (vplus vd471 vd473)) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 31.06/31.27 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 31.06/31.27 Clause #17423 (by forward demodulation #[17422, 27]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 31.06/31.27 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 31.06/31.27 Clause #17424 (by forward demodulation #[17423, 105]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vplus (vmul vd471 vd469) (vmul vd469 vd473)) % 31.06/31.27 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 31.06/31.27 Clause #17425 (by forward demodulation #[17424, 113]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vmul vd469 (vplus vd471 vd473)) % 31.06/31.27 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 31.06/31.27 Clause #17426 (by forward demodulation #[17425, 27]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vmul vd469 vd470) % 31.06/31.27 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469) a_1))) % 31.06/31.27 Clause #17427 (by forward demodulation #[17426, 105]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vmul vd469 vd470) % 31.06/31.27 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd469 vd470) a_1))) % 31.06/31.27 Clause #17428 (by forward demodulation #[17427, 105]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vmul vd469 vd470) % 31.06/31.27 (vplus (vmul vd470 vd469) (skS.0 1 (vplus (vmul vd471 vd469) (vmul vd469 vd473)) (vmul vd469 vd470) a_1))) % 31.06/31.27 Clause #17429 (by forward demodulation #[17428, 113]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vmul vd469 vd470) (vplus (vmul vd470 vd469) (skS.0 1 (vmul vd469 (vplus vd471 vd473)) (vmul vd469 vd470) a_1))) % 31.06/31.27 Clause #17430 (by forward demodulation #[17429, 27]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vmul vd469 vd470) (vplus (vmul vd470 vd469) (skS.0 1 (vmul vd469 vd470) (vmul vd469 vd470) a_1))) % 31.06/31.27 Clause #17431 (by forward demodulation #[17430, 105]): ∀ (a a_1 : Iota), % 31.06/31.27 Or (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 0 (vmul vd469 vd470) (vmul vd469 vd470) a))) % 31.06/31.27 (Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 1 (vmul vd469 vd470) (vmul vd469 vd470) a_1))) % 31.06/31.27 Clause #17432 (by forward contextual literal cutting #[17431, 431]): ∀ (a : Iota), Eq (vmul vd469 vd470) (vplus (vmul vd469 vd470) (skS.0 1 (vmul vd469 vd470) (vmul vd469 vd470) a)) % 31.06/31.27 Clause #17433 (by forward contextual literal cutting #[17432, 431]): False % 31.06/31.27 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------