%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM924+1 : TPTP v9.2.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 07:57:33 PM UTC 2025 % Result : Theorem 10.69s 10.87s % Output : Proof 10.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM924+1 : TPTP v9.2.0. Released v5.3.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.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 : Fri Oct 3 07:05:53 EDT 2025 % 0.13/0.34 % CPUTime : % 10.69/10.87 SZS status Theorem for theBenchmark.p % 10.69/10.87 SZS output start Proof for theBenchmark.p % 10.69/10.87 Clause #2 (by assumption #[]): Eq % 10.69/10.87 (ord_less_int % 10.69/10.87 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) t) % 10.69/10.87 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) % 10.69/10.87 zero_zero_int)) % 10.69/10.87 True % 10.69/10.87 Clause #3 (by assumption #[]): Eq % 10.69/10.87 (Eq (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.69/10.87 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) t)) % 10.69/10.87 True % 10.69/10.87 Clause #24 (by assumption #[]): Eq (∀ (K_1 : Iota), Eq (number_number_of_int K_1) K_1) True % 10.69/10.87 Clause #25 (by assumption #[]): Eq (∀ (Z W : Iota), Eq (times_times_int Z W) (times_times_int W Z)) True % 10.69/10.87 Clause #60 (by assumption #[]): Eq (Eq (plus_plus_nat one_one_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls)))) True % 10.69/10.87 Clause #61 (by assumption #[]): Eq (∀ (W : Iota), Eq (times_times_int pls W) pls) True % 10.69/10.87 Clause #97 (by assumption #[]): Eq (∀ (Z W : Iota), Eq (plus_plus_int Z W) (plus_plus_int W Z)) True % 10.69/10.87 Clause #98 (by assumption #[]): Eq (Eq zero_zero_int (number_number_of_int pls)) True % 10.69/10.87 Clause #99 (by assumption #[]): Eq % 10.69/10.87 (Not % 10.69/10.87 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.69/10.87 zero_zero_int)) % 10.69/10.87 True % 10.69/10.87 Clause #104 (by clausification #[98]): Eq zero_zero_int (number_number_of_int pls) % 10.69/10.87 Clause #107 (by clausification #[3]): Eq (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.69/10.87 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) t) % 10.69/10.87 Clause #108 (by backward demodulation #[107, 2]): Eq % 10.69/10.87 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.69/10.87 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) % 10.69/10.87 zero_zero_int)) % 10.69/10.87 True % 10.69/10.87 Clause #109 (by clausification #[24]): ∀ (a : Iota), Eq (Eq (number_number_of_int a) a) True % 10.69/10.87 Clause #110 (by clausification #[109]): ∀ (a : Iota), Eq (number_number_of_int a) a % 10.69/10.87 Clause #112 (by superposition #[110, 104]): Eq zero_zero_int pls % 10.69/10.87 Clause #130 (by clausification #[61]): ∀ (a : Iota), Eq (Eq (times_times_int pls a) pls) True % 10.69/10.87 Clause #131 (by clausification #[130]): ∀ (a : Iota), Eq (times_times_int pls a) pls % 10.69/10.87 Clause #632 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (W : Iota), Eq (times_times_int a W) (times_times_int W a)) True % 10.69/10.87 Clause #633 (by clausification #[632]): ∀ (a a_1 : Iota), Eq (Eq (times_times_int a a_1) (times_times_int a_1 a)) True % 10.69/10.87 Clause #634 (by clausification #[633]): ∀ (a a_1 : Iota), Eq (times_times_int a a_1) (times_times_int a_1 a) % 10.69/10.87 Clause #682 (by clausification #[60]): Eq (plus_plus_nat one_one_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))) % 10.69/10.87 Clause #4357 (by clausification #[97]): ∀ (a : Iota), Eq (∀ (W : Iota), Eq (plus_plus_int a W) (plus_plus_int W a)) True % 10.69/10.87 Clause #4358 (by clausification #[4357]): ∀ (a a_1 : Iota), Eq (Eq (plus_plus_int a a_1) (plus_plus_int a_1 a)) True % 10.69/10.87 Clause #4359 (by clausification #[4358]): ∀ (a a_1 : Iota), Eq (plus_plus_int a a_1) (plus_plus_int a_1 a) % 10.69/10.87 Clause #4452 (by clausification #[99]): Eq (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) zero_zero_int) % 10.69/10.87 False % 10.69/10.87 Clause #4453 (by forward demodulation #[4452, 112]): Eq (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) pls) False % 10.69/10.87 Clause #4454 (by forward demodulation #[4453, 4359]): Eq (ord_less_int (plus_plus_int one_one_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls))))) pls) False % 10.69/10.87 Clause #4455 (by forward demodulation #[4454, 682]): Eq (ord_less_int (plus_plus_int one_one_int (power_power_int s (plus_plus_nat one_one_nat one_one_nat))) pls) False % 10.69/10.87 Clause #4538 (by forward demodulation #[108, 634]): Eq % 10.69/10.87 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.71/10.89 (times_times_int zero_zero_int % 10.71/10.89 (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))) % 10.71/10.89 True % 10.71/10.89 Clause #4539 (by forward demodulation #[4538, 4359]): Eq % 10.71/10.89 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.71/10.89 (times_times_int zero_zero_int % 10.71/10.89 (plus_plus_int one_one_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m)))) % 10.71/10.89 True % 10.71/10.89 Clause #4540 (by forward demodulation #[4539, 634]): Eq % 10.71/10.89 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.71/10.89 (times_times_int zero_zero_int % 10.71/10.89 (plus_plus_int one_one_int (times_times_int m (number_number_of_int (bit0 (bit0 (bit1 pls)))))))) % 10.71/10.89 True % 10.71/10.89 Clause #4541 (by forward demodulation #[4540, 110]): Eq % 10.71/10.89 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.71/10.89 (times_times_int zero_zero_int (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 (bit1 pls))))))) % 10.71/10.89 True % 10.71/10.89 Clause #4542 (by forward demodulation #[4541, 112]): Eq % 10.71/10.89 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 10.71/10.89 (times_times_int pls (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 (bit1 pls))))))) % 10.71/10.89 True % 10.71/10.89 Clause #4543 (by forward demodulation #[4542, 131]): Eq (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) pls) True % 10.71/10.89 Clause #4544 (by forward demodulation #[4543, 4359]): Eq (ord_less_int (plus_plus_int one_one_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls))))) pls) True % 10.71/10.89 Clause #4545 (by forward demodulation #[4544, 682]): Eq (ord_less_int (plus_plus_int one_one_int (power_power_int s (plus_plus_nat one_one_nat one_one_nat))) pls) True % 10.71/10.89 Clause #4546 (by superposition #[4545, 4455]): Eq True False % 10.71/10.89 Clause #4566 (by clausification #[4546]): False % 10.71/10.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------