%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM924^1 : TPTP v9.2.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 12.73s 12.92s % Output : Proof 12.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM924^1 : TPTP v9.2.0. Released v5.3.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n018.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 07:46:08 EDT 2025 % 0.14/0.36 % CPUTime : % 12.73/12.92 SZS status Theorem for theBenchmark.p % 12.73/12.92 SZS output start Proof for theBenchmark.p % 12.73/12.92 Clause #2 (by assumption #[]): Eq % 12.73/12.92 (ord_less_int % 12.73/12.92 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) t) % 12.73/12.92 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) % 12.73/12.92 zero_zero_int)) % 12.73/12.92 True % 12.73/12.92 Clause #3 (by assumption #[]): Eq % 12.73/12.92 (Eq (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.73/12.92 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) t)) % 12.73/12.92 True % 12.73/12.92 Clause #24 (by assumption #[]): Eq (∀ (K : int), Eq (number_number_of_int K) K) True % 12.73/12.92 Clause #25 (by assumption #[]): Eq (∀ (Z W : int), Eq (times_times_int Z W) (times_times_int W Z)) True % 12.73/12.92 Clause #60 (by assumption #[]): Eq (Eq (plus_plus_nat one_one_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls)))) True % 12.73/12.92 Clause #61 (by assumption #[]): Eq (∀ (W : int), Eq (times_times_int pls W) pls) True % 12.73/12.92 Clause #97 (by assumption #[]): Eq (∀ (Z W : int), Eq (plus_plus_int Z W) (plus_plus_int W Z)) True % 12.73/12.92 Clause #98 (by assumption #[]): Eq (Eq zero_zero_int (number_number_of_int pls)) True % 12.73/12.92 Clause #99 (by assumption #[]): Eq % 12.73/12.92 (Not % 12.73/12.92 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.73/12.92 zero_zero_int)) % 12.73/12.92 True % 12.73/12.92 Clause #104 (by clausification #[98]): Eq zero_zero_int (number_number_of_int pls) % 12.73/12.92 Clause #107 (by clausification #[3]): Eq (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.73/12.92 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) t) % 12.73/12.92 Clause #108 (by backward demodulation #[107, 2]): Eq % 12.73/12.92 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.73/12.92 (times_times_int (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int) % 12.73/12.92 zero_zero_int)) % 12.73/12.92 True % 12.73/12.92 Clause #109 (by clausification #[24]): ∀ (a : int), Eq (Eq (number_number_of_int a) a) True % 12.73/12.92 Clause #110 (by clausification #[109]): ∀ (a : int), Eq (number_number_of_int a) a % 12.73/12.92 Clause #112 (by superposition #[110, 104]): Eq zero_zero_int pls % 12.73/12.92 Clause #130 (by clausification #[61]): ∀ (a : int), Eq (Eq (times_times_int pls a) pls) True % 12.73/12.92 Clause #131 (by clausification #[130]): ∀ (a : int), Eq (times_times_int pls a) pls % 12.73/12.92 Clause #632 (by clausification #[25]): ∀ (a : int), Eq (∀ (W : int), Eq (times_times_int a W) (times_times_int W a)) True % 12.73/12.92 Clause #633 (by clausification #[632]): ∀ (a a_1 : int), Eq (Eq (times_times_int a a_1) (times_times_int a_1 a)) True % 12.73/12.92 Clause #634 (by clausification #[633]): ∀ (a a_1 : int), Eq (times_times_int a a_1) (times_times_int a_1 a) % 12.73/12.92 Clause #682 (by clausification #[60]): Eq (plus_plus_nat one_one_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))) % 12.73/12.92 Clause #4239 (by clausification #[97]): ∀ (a : int), Eq (∀ (W : int), Eq (plus_plus_int a W) (plus_plus_int W a)) True % 12.73/12.92 Clause #4240 (by clausification #[4239]): ∀ (a a_1 : int), Eq (Eq (plus_plus_int a a_1) (plus_plus_int a_1 a)) True % 12.73/12.92 Clause #4241 (by clausification #[4240]): ∀ (a a_1 : int), Eq (plus_plus_int a a_1) (plus_plus_int a_1 a) % 12.73/12.92 Clause #4334 (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) % 12.73/12.92 False % 12.73/12.92 Clause #4335 (by forward demodulation #[4334, 112]): Eq (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) pls) False % 12.73/12.92 Clause #4336 (by forward demodulation #[4335, 4241]): Eq (ord_less_int (plus_plus_int one_one_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls))))) pls) False % 12.73/12.92 Clause #4337 (by forward demodulation #[4336, 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 % 12.73/12.92 Clause #4417 (by forward demodulation #[108, 634]): Eq % 12.73/12.92 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.77/12.95 (times_times_int zero_zero_int % 12.77/12.95 (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))) % 12.77/12.95 True % 12.77/12.95 Clause #4418 (by forward demodulation #[4417, 4241]): Eq % 12.77/12.95 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.77/12.95 (times_times_int zero_zero_int % 12.77/12.95 (plus_plus_int one_one_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m)))) % 12.77/12.95 True % 12.77/12.95 Clause #4419 (by forward demodulation #[4418, 634]): Eq % 12.77/12.95 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.77/12.95 (times_times_int zero_zero_int % 12.77/12.95 (plus_plus_int one_one_int (times_times_int m (number_number_of_int (bit0 (bit0 (bit1 pls)))))))) % 12.77/12.95 True % 12.77/12.95 Clause #4420 (by forward demodulation #[4419, 110]): Eq % 12.77/12.95 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.77/12.95 (times_times_int zero_zero_int (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 (bit1 pls))))))) % 12.77/12.95 True % 12.77/12.95 Clause #4421 (by forward demodulation #[4420, 112]): Eq % 12.77/12.95 (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) % 12.77/12.95 (times_times_int pls (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 (bit1 pls))))))) % 12.77/12.95 True % 12.77/12.95 Clause #4422 (by forward demodulation #[4421, 131]): Eq (ord_less_int (plus_plus_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls)))) one_one_int) pls) True % 12.77/12.95 Clause #4423 (by forward demodulation #[4422, 4241]): Eq (ord_less_int (plus_plus_int one_one_int (power_power_int s (number_number_of_nat (bit0 (bit1 pls))))) pls) True % 12.77/12.95 Clause #4424 (by forward demodulation #[4423, 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 % 12.77/12.95 Clause #4425 (by superposition #[4424, 4337]): Eq True False % 12.77/12.95 Clause #4441 (by clausification #[4425]): False % 12.77/12.95 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------