TSTP Solution File: NUM925_2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 : Thu Aug 31 10:58:16 EDT 2023
% Result : Theorem 178.85s 179.04s
% Output : Proof 179.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% 0.16/0.15 % Command : duper %s
% 0.16/0.37 % Computer : n022.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Aug 25 15:07:10 EDT 2023
% 0.16/0.37 % CPUTime :
% 178.85/179.04 SZS status Theorem for theBenchmark.p
% 178.85/179.04 SZS output start Proof for theBenchmark.p
% 178.85/179.04 Clause #0 (by assumption #[]): Eq
% 178.85/179.04 (hBOOL
% 178.85/179.04 (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int)
% 178.85/179.04 (hAPP_int_int (plus_plus_int one_one_int) (hAPP_nat_int semiri1621563631at_int n))))
% 178.85/179.04 True
% 178.85/179.04 Clause #9 (by assumption #[]): Eq (Eq (hAPP_nat_real (power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls)))) zero_zero_real) True
% 178.85/179.04 Clause #25 (by assumption #[]): Eq (Eq (number_number_of_int (bit1 pls)) one_one_int) True
% 178.85/179.04 Clause #37 (by assumption #[]): Eq (Eq (hAPP_nat_int semiri1621563631at_int one_one_nat) one_one_int) True
% 178.85/179.04 Clause #41 (by assumption #[]): Eq (Eq (hAPP_nat_int semiri1621563631at_int zero_zero_nat) zero_zero_int) True
% 178.85/179.04 Clause #60 (by assumption #[]): Eq (∀ (Z_2 W : int), Eq (hAPP_int_int (plus_plus_int Z_2) W) (hAPP_int_int (plus_plus_int W) Z_2)) True
% 178.85/179.04 Clause #71 (by assumption #[]): Eq (Not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) zero_zero_int))) True
% 178.85/179.04 Clause #90 (by assumption #[]): Eq (Eq pls zero_zero_int) True
% 178.85/179.04 Clause #123 (by assumption #[]): Eq
% 178.85/179.04 (∀ (A_66 : real),
% 178.85/179.04 Not
% 178.85/179.04 (hBOOL
% 178.85/179.04 (hAPP_real_bool
% 178.85/179.04 (hAPP_r1134773055l_bool ord_less_real
% 178.85/179.04 (hAPP_nat_real (power_power_real A_66) (number_number_of_nat (bit0 (bit1 pls)))))
% 178.85/179.04 zero_zero_real)))
% 178.85/179.04 True
% 178.85/179.04 Clause #159 (by assumption #[]): Eq (∀ (K : int), Eq (number_number_of_int K) K) True
% 178.85/179.04 Clause #198 (by assumption #[]): Eq
% 178.85/179.04 (∀ (Xa Ya : nat) (P_1 : bool),
% 178.85/179.04 And
% 178.85/179.04 (hBOOL P_1 →
% 178.85/179.04 Eq (hAPP_nat_int semiri1621563631at_int Xa)
% 178.85/179.04 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat P_1 Xa) Ya)))
% 178.85/179.04 (Not (hBOOL P_1) →
% 178.85/179.04 Eq (hAPP_nat_int semiri1621563631at_int Ya)
% 178.85/179.04 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat P_1 Xa) Ya))))
% 178.85/179.04 True
% 178.85/179.04 Clause #202 (by assumption #[]): Eq (Ne one_one_int zero_zero_int) True
% 178.85/179.04 Clause #205 (by assumption #[]): Eq (∀ (N_23 : nat) (A_62 : int), Ne A_62 zero_zero_int → Ne (hAPP_nat_int (power_power_int A_62) N_23) zero_zero_int)
% 178.85/179.04 True
% 178.85/179.04 Clause #481 (by assumption #[]): Eq (∀ (K : int), Eq (succ K) (hAPP_int_int (plus_plus_int K) one_one_int)) True
% 178.85/179.04 Clause #590 (by assumption #[]): Eq (∀ (X Y : nat), Eq (hAPP_nat_nat (if_nat fTrue X) Y) X) True
% 178.85/179.04 Clause #592 (by assumption #[]): Eq (∀ (P : bool), Or (Eq P fTrue) (Eq P fFalse)) True
% 178.85/179.04 Clause #593 (by assumption #[]): Eq
% 178.85/179.04 (Not
% 178.85/179.04 (Ne
% 178.85/179.04 (hAPP_nat_int (power_power_int (hAPP_int_int (plus_plus_int one_one_int) (hAPP_nat_int semiri1621563631at_int n)))
% 178.85/179.04 (number_number_of_nat (bit0 (bit1 pls))))
% 178.85/179.04 zero_zero_int))
% 178.85/179.04 True
% 178.85/179.04 Clause #595 (by clausification #[202]): Ne one_one_int zero_zero_int
% 178.85/179.04 Clause #599 (by clausification #[90]): Eq pls zero_zero_int
% 178.85/179.04 Clause #600 (by backward demodulation #[599, 595]): Ne one_one_int pls
% 178.85/179.04 Clause #601 (by backward demodulation #[599, 0]): Eq
% 178.85/179.04 (hBOOL
% 178.85/179.04 (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls)
% 178.85/179.04 (hAPP_int_int (plus_plus_int one_one_int) (hAPP_nat_int semiri1621563631at_int n))))
% 178.85/179.04 True
% 178.85/179.04 Clause #626 (by clausification #[37]): Eq (hAPP_nat_int semiri1621563631at_int one_one_nat) one_one_int
% 178.85/179.04 Clause #648 (by clausification #[25]): Eq (number_number_of_int (bit1 pls)) one_one_int
% 178.85/179.04 Clause #656 (by clausification #[159]): ∀ (a : int), Eq (Eq (number_number_of_int a) a) True
% 178.85/179.04 Clause #657 (by clausification #[656]): ∀ (a : int), Eq (number_number_of_int a) a
% 178.85/179.04 Clause #658 (by superposition #[657, 648]): Eq (bit1 pls) one_one_int
% 178.85/179.04 Clause #675 (by clausification #[41]): Eq (hAPP_nat_int semiri1621563631at_int zero_zero_nat) zero_zero_int
% 178.85/179.04 Clause #676 (by forward demodulation #[675, 599]): Eq (hAPP_nat_int semiri1621563631at_int zero_zero_nat) pls
% 178.85/179.04 Clause #680 (by clausification #[9]): Eq (hAPP_nat_real (power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls)))) zero_zero_real
% 178.85/179.04 Clause #681 (by forward demodulation #[680, 658]): Eq (hAPP_nat_real (power_power_real zero_zero_real) (number_number_of_nat (bit0 one_one_int))) zero_zero_real
% 178.85/179.04 Clause #716 (by clausification #[71]): Eq (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) zero_zero_int)) False
% 178.85/179.06 Clause #717 (by forward demodulation #[716, 599]): Eq (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) pls)) False
% 178.85/179.06 Clause #1624 (by clausification #[481]): ∀ (a : int), Eq (Eq (succ a) (hAPP_int_int (plus_plus_int a) one_one_int)) True
% 178.85/179.06 Clause #1625 (by clausification #[1624]): ∀ (a : int), Eq (succ a) (hAPP_int_int (plus_plus_int a) one_one_int)
% 178.85/179.06 Clause #1789 (by clausification #[60]): ∀ (a : int), Eq (∀ (W : int), Eq (hAPP_int_int (plus_plus_int a) W) (hAPP_int_int (plus_plus_int W) a)) True
% 178.85/179.06 Clause #1790 (by clausification #[1789]): ∀ (a a_1 : int), Eq (Eq (hAPP_int_int (plus_plus_int a) a_1) (hAPP_int_int (plus_plus_int a_1) a)) True
% 178.85/179.06 Clause #1791 (by clausification #[1790]): ∀ (a a_1 : int), Eq (hAPP_int_int (plus_plus_int a) a_1) (hAPP_int_int (plus_plus_int a_1) a)
% 178.85/179.06 Clause #1794 (by superposition #[1791, 1625]): ∀ (a : int), Eq (succ a) (hAPP_int_int (plus_plus_int one_one_int) a)
% 178.85/179.06 Clause #3156 (by clausification #[123]): ∀ (a : real),
% 178.85/179.06 Eq
% 178.85/179.06 (Not
% 178.85/179.06 (hBOOL
% 178.85/179.06 (hAPP_real_bool
% 178.85/179.06 (hAPP_r1134773055l_bool ord_less_real
% 178.85/179.06 (hAPP_nat_real (power_power_real a) (number_number_of_nat (bit0 (bit1 pls)))))
% 178.85/179.06 zero_zero_real)))
% 178.85/179.06 True
% 178.85/179.06 Clause #3157 (by clausification #[3156]): ∀ (a : real),
% 178.85/179.06 Eq
% 178.85/179.06 (hBOOL
% 178.85/179.06 (hAPP_real_bool
% 178.85/179.06 (hAPP_r1134773055l_bool ord_less_real
% 178.85/179.06 (hAPP_nat_real (power_power_real a) (number_number_of_nat (bit0 (bit1 pls)))))
% 178.85/179.06 zero_zero_real))
% 178.85/179.06 False
% 178.85/179.06 Clause #3158 (by forward demodulation #[3157, 658]): ∀ (a : real),
% 178.85/179.06 Eq
% 178.85/179.06 (hBOOL
% 178.85/179.06 (hAPP_real_bool
% 178.85/179.06 (hAPP_r1134773055l_bool ord_less_real
% 178.85/179.06 (hAPP_nat_real (power_power_real a) (number_number_of_nat (bit0 one_one_int))))
% 178.85/179.06 zero_zero_real))
% 178.85/179.06 False
% 178.85/179.06 Clause #3160 (by superposition #[3158, 681]): Eq (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) zero_zero_real)) False
% 178.85/179.06 Clause #5866 (by clausification #[198]): ∀ (a : nat),
% 178.85/179.06 Eq
% 178.85/179.06 (∀ (Ya : nat) (P_1 : bool),
% 178.85/179.06 And
% 178.85/179.06 (hBOOL P_1 →
% 178.85/179.06 Eq (hAPP_nat_int semiri1621563631at_int a)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat P_1 a) Ya)))
% 178.85/179.06 (Not (hBOOL P_1) →
% 178.85/179.06 Eq (hAPP_nat_int semiri1621563631at_int Ya)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat P_1 a) Ya))))
% 178.85/179.06 True
% 178.85/179.06 Clause #5867 (by clausification #[5866]): ∀ (a a_1 : nat),
% 178.85/179.06 Eq
% 178.85/179.06 (∀ (P_1 : bool),
% 178.85/179.06 And
% 178.85/179.06 (hBOOL P_1 →
% 178.85/179.06 Eq (hAPP_nat_int semiri1621563631at_int a)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat P_1 a) a_1)))
% 178.85/179.06 (Not (hBOOL P_1) →
% 178.85/179.06 Eq (hAPP_nat_int semiri1621563631at_int a_1)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat P_1 a) a_1))))
% 178.85/179.06 True
% 178.85/179.06 Clause #5868 (by clausification #[5867]): ∀ (a : bool) (a_1 a_2 : nat),
% 178.85/179.06 Eq
% 178.85/179.06 (And
% 178.85/179.06 (hBOOL a →
% 178.85/179.06 Eq (hAPP_nat_int semiri1621563631at_int a_1)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat a a_1) a_2)))
% 178.85/179.06 (Not (hBOOL a) →
% 178.85/179.06 Eq (hAPP_nat_int semiri1621563631at_int a_2)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat a a_1) a_2))))
% 178.85/179.06 True
% 178.85/179.06 Clause #5869 (by clausification #[5868]): ∀ (a : bool) (a_1 a_2 : nat),
% 178.85/179.06 Eq
% 178.85/179.06 (Not (hBOOL a) →
% 178.85/179.06 Eq (hAPP_nat_int semiri1621563631at_int a_1)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat a a_2) a_1)))
% 178.85/179.06 True
% 178.85/179.06 Clause #5871 (by clausification #[5869]): ∀ (a : bool) (a_1 a_2 : nat),
% 178.85/179.06 Or (Eq (Not (hBOOL a)) False)
% 178.85/179.06 (Eq
% 178.85/179.06 (Eq (hAPP_nat_int semiri1621563631at_int a_1)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat a a_2) a_1)))
% 178.85/179.06 True)
% 178.85/179.06 Clause #5872 (by clausification #[5871]): ∀ (a : nat) (a_1 : bool) (a_2 : nat),
% 178.85/179.06 Or
% 178.85/179.06 (Eq
% 178.85/179.06 (Eq (hAPP_nat_int semiri1621563631at_int a)
% 178.85/179.06 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat a_1 a_2) a)))
% 178.85/179.06 True)
% 178.85/179.06 (Eq (hBOOL a_1) True)
% 178.85/179.06 Clause #5873 (by clausification #[5872]): ∀ (a : bool) (a_1 a_2 : nat),
% 178.91/179.09 Or (Eq (hBOOL a) True)
% 178.91/179.09 (Eq (hAPP_nat_int semiri1621563631at_int a_1)
% 178.91/179.09 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (if_nat a a_2) a_1)))
% 178.91/179.09 Clause #6054 (by clausification #[205]): ∀ (a : nat), Eq (∀ (A_62 : int), Ne A_62 zero_zero_int → Ne (hAPP_nat_int (power_power_int A_62) a) zero_zero_int) True
% 178.91/179.09 Clause #6055 (by clausification #[6054]): ∀ (a : int) (a_1 : nat), Eq (Ne a zero_zero_int → Ne (hAPP_nat_int (power_power_int a) a_1) zero_zero_int) True
% 178.91/179.09 Clause #6056 (by clausification #[6055]): ∀ (a : int) (a_1 : nat),
% 178.91/179.09 Or (Eq (Ne a zero_zero_int) False) (Eq (Ne (hAPP_nat_int (power_power_int a) a_1) zero_zero_int) True)
% 178.91/179.09 Clause #6057 (by clausification #[6056]): ∀ (a : int) (a_1 : nat), Or (Eq (Ne (hAPP_nat_int (power_power_int a) a_1) zero_zero_int) True) (Eq a zero_zero_int)
% 178.91/179.09 Clause #6058 (by clausification #[6057]): ∀ (a : int) (a_1 : nat), Or (Eq a zero_zero_int) (Ne (hAPP_nat_int (power_power_int a) a_1) zero_zero_int)
% 178.91/179.09 Clause #6059 (by forward demodulation #[6058, 599]): ∀ (a : int) (a_1 : nat), Or (Eq a pls) (Ne (hAPP_nat_int (power_power_int a) a_1) zero_zero_int)
% 178.91/179.09 Clause #6060 (by forward demodulation #[6059, 599]): ∀ (a : int) (a_1 : nat), Or (Eq a pls) (Ne (hAPP_nat_int (power_power_int a) a_1) pls)
% 178.91/179.09 Clause #6277 (by clausification #[590]): ∀ (a : nat), Eq (∀ (Y : nat), Eq (hAPP_nat_nat (if_nat fTrue a) Y) a) True
% 178.91/179.09 Clause #6278 (by clausification #[6277]): ∀ (a a_1 : nat), Eq (Eq (hAPP_nat_nat (if_nat fTrue a) a_1) a) True
% 178.91/179.09 Clause #6279 (by clausification #[6278]): ∀ (a a_1 : nat), Eq (hAPP_nat_nat (if_nat fTrue a) a_1) a
% 178.91/179.09 Clause #6280 (by superposition #[6279, 5873]): ∀ (a a_1 : nat),
% 178.91/179.09 Or (Eq (hBOOL fTrue) True) (Eq (hAPP_nat_int semiri1621563631at_int a) (hAPP_nat_int semiri1621563631at_int a_1))
% 178.91/179.09 Clause #6282 (by superposition #[6280, 676]): ∀ (a : nat), Or (Eq (hBOOL fTrue) True) (Eq (hAPP_nat_int semiri1621563631at_int a) pls)
% 178.91/179.09 Clause #6331 (by superposition #[6282, 626]): Or (Eq (hBOOL fTrue) True) (Eq pls one_one_int)
% 178.91/179.09 Clause #6357 (by forward contextual literal cutting #[6331, 600]): Eq (hBOOL fTrue) True
% 178.91/179.09 Clause #11965 (by clausification #[592]): ∀ (a : bool), Eq (Or (Eq a fTrue) (Eq a fFalse)) True
% 178.91/179.09 Clause #11966 (by clausification #[11965]): ∀ (a : bool), Or (Eq (Eq a fTrue) True) (Eq (Eq a fFalse) True)
% 178.91/179.09 Clause #11967 (by clausification #[11966]): ∀ (a : bool), Or (Eq (Eq a fFalse) True) (Eq a fTrue)
% 178.91/179.09 Clause #11968 (by clausification #[11967]): ∀ (a : bool), Or (Eq a fTrue) (Eq a fFalse)
% 178.91/179.09 Clause #11970 (by superposition #[11968, 6357]): ∀ (a : bool), Or (Eq a fFalse) (Eq (hBOOL a) True)
% 178.91/179.09 Clause #12261 (by superposition #[11970, 717]): Or (Eq (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) pls) fFalse) (Eq True False)
% 178.91/179.09 Clause #12288 (by superposition #[11970, 3160]): Or (Eq (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) zero_zero_real) fFalse) (Eq True False)
% 178.91/179.09 Clause #18138 (by clausification #[12288]): Eq (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) zero_zero_real) fFalse
% 178.91/179.09 Clause #18139 (by backward demodulation #[18138, 3160]): Eq (hBOOL fFalse) False
% 178.91/179.09 Clause #20921 (by clausification #[12261]): Eq (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) pls) fFalse
% 178.91/179.09 Clause #50465 (by clausification #[593]): Eq
% 178.91/179.09 (Ne
% 178.91/179.09 (hAPP_nat_int (power_power_int (hAPP_int_int (plus_plus_int one_one_int) (hAPP_nat_int semiri1621563631at_int n)))
% 178.91/179.09 (number_number_of_nat (bit0 (bit1 pls))))
% 178.91/179.09 zero_zero_int)
% 178.91/179.09 False
% 178.91/179.09 Clause #50466 (by clausification #[50465]): Eq
% 178.91/179.09 (hAPP_nat_int (power_power_int (hAPP_int_int (plus_plus_int one_one_int) (hAPP_nat_int semiri1621563631at_int n)))
% 178.91/179.09 (number_number_of_nat (bit0 (bit1 pls))))
% 178.91/179.09 zero_zero_int
% 178.91/179.09 Clause #50467 (by forward demodulation #[50466, 658]): Eq
% 178.91/179.09 (hAPP_nat_int (power_power_int (hAPP_int_int (plus_plus_int one_one_int) (hAPP_nat_int semiri1621563631at_int n)))
% 178.91/179.09 (number_number_of_nat (bit0 one_one_int)))
% 178.91/179.09 zero_zero_int
% 178.91/179.09 Clause #50468 (by forward demodulation #[50467, 1794]): Eq
% 178.91/179.09 (hAPP_nat_int (power_power_int (succ (hAPP_nat_int semiri1621563631at_int n)))
% 178.91/179.09 (number_number_of_nat (bit0 one_one_int)))
% 179.06/179.38 zero_zero_int
% 179.06/179.38 Clause #50469 (by forward demodulation #[50468, 599]): Eq
% 179.06/179.38 (hAPP_nat_int (power_power_int (succ (hAPP_nat_int semiri1621563631at_int n)))
% 179.06/179.38 (number_number_of_nat (bit0 one_one_int)))
% 179.06/179.38 pls
% 179.06/179.38 Clause #50483 (by superposition #[50469, 6060]): Or (Eq (succ (hAPP_nat_int semiri1621563631at_int n)) pls) (Ne pls pls)
% 179.06/179.38 Clause #50501 (by eliminate resolved literals #[50483]): Eq (succ (hAPP_nat_int semiri1621563631at_int n)) pls
% 179.06/179.38 Clause #50603 (by forward demodulation #[601, 1794]): Eq (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) (succ (hAPP_nat_int semiri1621563631at_int n)))) True
% 179.06/179.38 Clause #50604 (by forward demodulation #[50603, 50501]): Eq (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) pls)) True
% 179.06/179.38 Clause #50605 (by forward demodulation #[50604, 20921]): Eq (hBOOL fFalse) True
% 179.06/179.38 Clause #50606 (by superposition #[50605, 18139]): Eq True False
% 179.06/179.38 Clause #50691 (by clausification #[50606]): False
% 179.06/179.38 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------