%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM851+1 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 90.20s 90.42s % Output : Proof 90.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM851+1 : TPTP v9.2.0. Released v4.1.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n019.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 : Fri Oct 3 08:59:38 EDT 2025 % 0.13/0.35 % CPUTime : % 90.20/90.42 SZS status Theorem for theBenchmark.p % 90.20/90.42 SZS output start Proof for theBenchmark.p % 90.20/90.42 Clause #0 (by assumption #[]): Eq (Not (Eq (vmul (vplus vd471 vd473) vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469)))) True % 90.20/90.42 Clause #2 (by assumption #[]): Eq (Eq vd470 (vplus vd471 vd473)) True % 90.20/90.42 Clause #5 (by assumption #[]): Eq (∀ (Vd432 Vd433 Vd434 : Iota), Eq (vmul Vd432 (vplus Vd433 Vd434)) (vplus (vmul Vd432 Vd433) (vmul Vd432 Vd434))) % 90.20/90.42 True % 90.20/90.42 Clause #6 (by assumption #[]): Eq (∀ (Vd418 Vd419 : Iota), Eq (vmul Vd418 Vd419) (vmul Vd419 Vd418)) True % 90.20/90.42 Clause #32 (by assumption #[]): Eq (∀ (Vd203 Vd204 : Iota), Or (Or (Eq Vd203 Vd204) (greater Vd203 Vd204)) (less Vd203 Vd204)) True % 90.20/90.42 Clause #33 (by assumption #[]): Eq (∀ (Vd203 Vd204 : Iota), Or (Ne Vd203 Vd204) (Not (less Vd203 Vd204))) True % 90.20/90.42 Clause #35 (by assumption #[]): Eq (∀ (Vd203 Vd204 : Iota), Or (Ne Vd203 Vd204) (Not (greater Vd203 Vd204))) True % 90.20/90.42 Clause #55 (by clausification #[2]): Eq vd470 (vplus vd471 vd473) % 90.20/90.42 Clause #61 (by clausification #[0]): Eq (Eq (vmul (vplus vd471 vd473) vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469))) False % 90.20/90.42 Clause #62 (by clausification #[61]): Ne (vmul (vplus vd471 vd473) vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 90.20/90.42 Clause #63 (by forward demodulation #[62, 55]): Ne (vmul vd470 vd469) (vplus (vmul vd471 vd469) (vmul vd473 vd469)) % 90.20/90.42 Clause #122 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Vd433 Vd434 : Iota), Eq (vmul a (vplus Vd433 Vd434)) (vplus (vmul a Vd433) (vmul a Vd434))) True % 90.20/90.42 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Eq (∀ (Vd434 : Iota), Eq (vmul a (vplus a_1 Vd434)) (vplus (vmul a a_1) (vmul a Vd434))) True % 90.20/90.42 Clause #124 (by clausification #[123]): ∀ (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 % 90.20/90.42 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), Eq (vmul a (vplus a_1 a_2)) (vplus (vmul a a_1) (vmul a a_2)) % 90.20/90.42 Clause #149 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Vd419 : Iota), Eq (vmul a Vd419) (vmul Vd419 a)) True % 90.20/90.42 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (Eq (vmul a a_1) (vmul a_1 a)) True % 90.20/90.42 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (vmul a a_1) (vmul a_1 a) % 90.20/90.42 Clause #156 (by superposition #[151, 125]): ∀ (a a_1 a_2 : Iota), Eq (vmul a (vplus a_1 a_2)) (vplus (vmul a_1 a) (vmul a a_2)) % 90.20/90.42 Clause #425 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (Vd204 : Iota), Or (Or (Eq a Vd204) (greater a Vd204)) (less a Vd204)) True % 90.20/90.42 Clause #426 (by clausification #[425]): ∀ (a a_1 : Iota), Eq (Or (Or (Eq a a_1) (greater a a_1)) (less a a_1)) True % 90.20/90.42 Clause #427 (by clausification #[426]): ∀ (a a_1 : Iota), Or (Eq (Or (Eq a a_1) (greater a a_1)) True) (Eq (less a a_1) True) % 90.20/90.42 Clause #428 (by clausification #[427]): ∀ (a a_1 : Iota), Or (Eq (less a a_1) True) (Or (Eq (Eq a a_1) True) (Eq (greater a a_1) True)) % 90.20/90.42 Clause #429 (by clausification #[428]): ∀ (a a_1 : Iota), Or (Eq (less a a_1) True) (Or (Eq (greater a a_1) True) (Eq a a_1)) % 90.20/90.42 Clause #466 (by superposition #[429, 63]): ∀ (a : Iota), % 90.20/90.42 Or (Eq (less (vplus (vmul vd471 vd469) (vmul vd473 vd469)) a) True) % 90.20/90.42 (Or (Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) a) True) (Ne (vmul vd470 vd469) a)) % 90.20/90.42 Clause #650 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Vd204 : Iota), Or (Ne a Vd204) (Not (less a Vd204))) True % 90.20/90.42 Clause #651 (by clausification #[650]): ∀ (a a_1 : Iota), Eq (Or (Ne a a_1) (Not (less a a_1))) True % 90.20/90.42 Clause #652 (by clausification #[651]): ∀ (a a_1 : Iota), Or (Eq (Ne a a_1) True) (Eq (Not (less a a_1)) True) % 90.20/90.42 Clause #653 (by clausification #[652]): ∀ (a a_1 : Iota), Or (Eq (Not (less a a_1)) True) (Ne a a_1) % 90.20/90.42 Clause #654 (by clausification #[653]): ∀ (a a_1 : Iota), Or (Ne a a_1) (Eq (less a a_1) False) % 90.20/90.42 Clause #655 (by destructive equality resolution #[654]): ∀ (a : Iota), Eq (less a a) False % 90.20/90.42 Clause #705 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (Vd204 : Iota), Or (Ne a Vd204) (Not (greater a Vd204))) True % 90.20/90.42 Clause #706 (by clausification #[705]): ∀ (a a_1 : Iota), Eq (Or (Ne a a_1) (Not (greater a a_1))) True % 90.44/90.61 Clause #707 (by clausification #[706]): ∀ (a a_1 : Iota), Or (Eq (Ne a a_1) True) (Eq (Not (greater a a_1)) True) % 90.44/90.61 Clause #708 (by clausification #[707]): ∀ (a a_1 : Iota), Or (Eq (Not (greater a a_1)) True) (Ne a a_1) % 90.44/90.61 Clause #709 (by clausification #[708]): ∀ (a a_1 : Iota), Or (Ne a a_1) (Eq (greater a a_1) False) % 90.44/90.61 Clause #710 (by destructive equality resolution #[709]): ∀ (a : Iota), Eq (greater a a) False % 90.44/90.61 Clause #31316 (by destructive equality resolution #[466]): Or (Eq (less (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469)) True) % 90.44/90.61 (Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469)) True) % 90.44/90.61 Clause #31317 (by forward demodulation #[31316, 151]): Or (Eq (less (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd469 vd470)) True) % 90.44/90.61 (Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469)) True) % 90.44/90.61 Clause #31318 (by forward demodulation #[31317, 151]): Or (Eq (less (vplus (vmul vd471 vd469) (vmul vd469 vd473)) (vmul vd469 vd470)) True) % 90.44/90.61 (Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469)) True) % 90.44/90.61 Clause #31319 (by forward demodulation #[31318, 156]): Or (Eq (less (vmul vd469 (vplus vd471 vd473)) (vmul vd469 vd470)) True) % 90.44/90.61 (Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469)) True) % 90.44/90.61 Clause #31320 (by forward demodulation #[31319, 55]): Or (Eq (less (vmul vd469 vd470) (vmul vd469 vd470)) True) % 90.44/90.61 (Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469)) True) % 90.44/90.61 Clause #31321 (by forward demodulation #[31320, 655]): Or (Eq False True) (Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469)) True) % 90.44/90.61 Clause #31322 (by clausification #[31321]): Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd470 vd469)) True % 90.44/90.61 Clause #31323 (by forward demodulation #[31322, 151]): Eq (greater (vplus (vmul vd471 vd469) (vmul vd473 vd469)) (vmul vd469 vd470)) True % 90.44/90.61 Clause #31324 (by forward demodulation #[31323, 151]): Eq (greater (vplus (vmul vd471 vd469) (vmul vd469 vd473)) (vmul vd469 vd470)) True % 90.44/90.61 Clause #31325 (by forward demodulation #[31324, 156]): Eq (greater (vmul vd469 (vplus vd471 vd473)) (vmul vd469 vd470)) True % 90.44/90.61 Clause #31326 (by forward demodulation #[31325, 55]): Eq (greater (vmul vd469 vd470) (vmul vd469 vd470)) True % 90.44/90.61 Clause #31333 (by superposition #[31326, 710]): Eq True False % 90.44/90.61 Clause #31373 (by clausification #[31333]): False % 90.44/90.61 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------