%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM925_5 : TPTP v9.2.0. Released v6.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:57:36 PM UTC 2025 % Result : Theorem 16.35s 16.55s % Output : Proof 16.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : NUM925_5 : TPTP v9.2.0. Released v6.0.0. % 0.10/0.13 % Command : duper %s % 0.12/0.34 % Computer : n024.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 07:19:38 EDT 2025 % 0.12/0.34 % CPUTime : % 16.35/16.55 SZS status Theorem for theBenchmark.p % 16.35/16.55 SZS output start Proof for theBenchmark.p % 16.35/16.55 Clause #0 (by assumption #[]): Eq (ord_less int (zero_zero int) (plus_plus int (one_one int) (semiring_1_of_nat int n))) True % 16.35/16.55 Clause #26 (by assumption #[]): Eq (Not (ord_less int pls pls)) True % 16.35/16.55 Clause #45 (by assumption #[]): Eq % 16.35/16.55 (∀ (A : Type), % 16.35/16.55 linordered_idom A → % 16.35/16.55 ∀ (A1 : A), % 16.35/16.55 Iff (ord_less A (zero_zero A) (power_power A A1 (number_number_of nat (bit0 (bit1 pls))))) % 16.35/16.55 (Ne A1 (zero_zero A))) % 16.35/16.55 True % 16.35/16.55 Clause #68 (by assumption #[]): Eq (Eq pls (zero_zero int)) True % 16.35/16.55 Clause #69 (by assumption #[]): Eq (∀ (K : int), Eq (plus_plus int K pls) K) True % 16.35/16.55 Clause #77 (by assumption #[]): Eq (∀ (K : int), Eq (bit1 K) (plus_plus int (plus_plus int (one_one int) K) K)) True % 16.35/16.55 Clause #99 (by assumption #[]): Eq (linordered_idom int) True % 16.35/16.55 Clause #134 (by assumption #[]): Eq % 16.35/16.55 (Not % 16.35/16.55 (Ne % 16.35/16.55 (power_power int (plus_plus int (one_one int) (semiring_1_of_nat int n)) (number_number_of nat (bit0 (bit1 pls)))) % 16.35/16.55 (zero_zero int))) % 16.35/16.55 True % 16.35/16.55 Clause #168 (by clausification #[68]): Eq pls (zero_zero int) % 16.35/16.55 Clause #169 (by backward demodulation #[168, 0]): Eq (ord_less int pls (plus_plus int (one_one int) (semiring_1_of_nat int n))) True % 16.35/16.55 Clause #175 (by clausification #[26]): Eq (ord_less int pls pls) False % 16.35/16.55 Clause #223 (by clausification #[69]): ∀ (a : int), Eq (Eq (plus_plus int a pls) a) True % 16.35/16.55 Clause #224 (by clausification #[223]): ∀ (a : int), Eq (plus_plus int a pls) a % 16.35/16.55 Clause #582 (by clausification #[45]): ∀ (a : Type), % 16.35/16.55 Eq % 16.35/16.55 (linordered_idom a → % 16.35/16.55 ∀ (A1 : a), % 16.35/16.55 Iff (ord_less a (zero_zero a) (power_power a A1 (number_number_of nat (bit0 (bit1 pls))))) % 16.35/16.55 (Ne A1 (zero_zero a))) % 16.35/16.55 True % 16.35/16.55 Clause #583 (by clausification #[582]): ∀ (a : Type), % 16.35/16.55 Or (Eq (linordered_idom a) False) % 16.35/16.55 (Eq % 16.35/16.55 (∀ (A1 : a), % 16.35/16.55 Iff (ord_less a (zero_zero a) (power_power a A1 (number_number_of nat (bit0 (bit1 pls))))) % 16.35/16.55 (Ne A1 (zero_zero a))) % 16.35/16.55 True) % 16.35/16.55 Clause #584 (by clausification #[583]): ∀ (a : Type) (a_1 : a), % 16.35/16.55 Or (Eq (linordered_idom a) False) % 16.35/16.55 (Eq % 16.35/16.55 (Iff (ord_less a (zero_zero a) (power_power a a_1 (number_number_of nat (bit0 (bit1 pls))))) % 16.35/16.55 (Ne a_1 (zero_zero a))) % 16.35/16.55 True) % 16.35/16.55 Clause #585 (by clausification #[584]): ∀ (a : Type) (a_1 : a), % 16.35/16.55 Or (Eq (linordered_idom a) False) % 16.35/16.55 (Or (Eq (ord_less a (zero_zero a) (power_power a a_1 (number_number_of nat (bit0 (bit1 pls))))) True) % 16.35/16.55 (Eq (Ne a_1 (zero_zero a)) False)) % 16.35/16.55 Clause #587 (by clausification #[585]): ∀ (a : Type) (a_1 : a), % 16.35/16.55 Or (Eq (linordered_idom a) False) % 16.35/16.55 (Or (Eq (ord_less a (zero_zero a) (power_power a a_1 (number_number_of nat (bit0 (bit1 pls))))) True) % 16.35/16.55 (Eq a_1 (zero_zero a))) % 16.35/16.55 Clause #588 (by superposition #[587, 99]): ∀ (a : int), % 16.35/16.55 Or (Eq (ord_less int (zero_zero int) (power_power int a (number_number_of nat (bit0 (bit1 pls))))) True) % 16.35/16.55 (Or (Eq a (zero_zero int)) (Eq False True)) % 16.35/16.55 Clause #591 (by clausification #[77]): ∀ (a : int), Eq (Eq (bit1 a) (plus_plus int (plus_plus int (one_one int) a) a)) True % 16.35/16.55 Clause #592 (by clausification #[591]): ∀ (a : int), Eq (bit1 a) (plus_plus int (plus_plus int (one_one int) a) a) % 16.35/16.55 Clause #593 (by superposition #[592, 224]): Eq (bit1 pls) (plus_plus int (one_one int) pls) % 16.35/16.55 Clause #595 (by superposition #[593, 224]): Eq (bit1 pls) (one_one int) % 16.35/16.55 Clause #601 (by backward demodulation #[595, 169]): Eq (ord_less int pls (plus_plus int (bit1 pls) (semiring_1_of_nat int n))) True % 16.35/16.55 Clause #1108 (by clausification #[134]): Eq % 16.35/16.55 (Ne (power_power int (plus_plus int (one_one int) (semiring_1_of_nat int n)) (number_number_of nat (bit0 (bit1 pls)))) % 16.35/16.55 (zero_zero int)) % 16.35/16.55 False % 16.35/16.55 Clause #1109 (by clausification #[1108]): Eq (power_power int (plus_plus int (one_one int) (semiring_1_of_nat int n)) (number_number_of nat (bit0 (bit1 pls)))) % 16.35/16.55 (zero_zero int) % 16.35/16.55 Clause #1110 (by forward demodulation #[1109, 595]): Eq (power_power int (plus_plus int (bit1 pls) (semiring_1_of_nat int n)) (number_number_of nat (bit0 (bit1 pls)))) % 16.35/16.55 (zero_zero int) % 16.35/16.55 Clause #1111 (by forward demodulation #[1110, 168]): Eq (power_power int (plus_plus int (bit1 pls) (semiring_1_of_nat int n)) (number_number_of nat (bit0 (bit1 pls)))) pls % 16.35/16.56 Clause #2956 (by clausification #[588]): ∀ (a : int), % 16.35/16.56 Or (Eq (ord_less int (zero_zero int) (power_power int a (number_number_of nat (bit0 (bit1 pls))))) True) % 16.35/16.56 (Eq a (zero_zero int)) % 16.35/16.56 Clause #2957 (by forward demodulation #[2956, 168]): ∀ (a : int), % 16.35/16.56 Or (Eq (ord_less int pls (power_power int a (number_number_of nat (bit0 (bit1 pls))))) True) (Eq a (zero_zero int)) % 16.35/16.56 Clause #2958 (by forward demodulation #[2957, 168]): ∀ (a : int), Or (Eq (ord_less int pls (power_power int a (number_number_of nat (bit0 (bit1 pls))))) True) (Eq a pls) % 16.35/16.56 Clause #3193 (by superposition #[2958, 1111]): Or (Eq (ord_less int pls pls) True) (Eq (plus_plus int (bit1 pls) (semiring_1_of_nat int n)) pls) % 16.35/16.56 Clause #3195 (by forward demodulation #[3193, 175]): Or (Eq False True) (Eq (plus_plus int (bit1 pls) (semiring_1_of_nat int n)) pls) % 16.35/16.56 Clause #3196 (by clausification #[3195]): Eq (plus_plus int (bit1 pls) (semiring_1_of_nat int n)) pls % 16.35/16.56 Clause #3198 (by backward demodulation #[3196, 601]): Eq (ord_less int pls pls) True % 16.35/16.56 Clause #3207 (by superposition #[3198, 175]): Eq True False % 16.35/16.56 Clause #3224 (by clausification #[3207]): False % 16.35/16.56 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------