%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : NUM926_2 : TPTP v8.1.2. Released v5.3.0.
% 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 : Thu Aug 31 10:58:19 EDT 2023

% Result   : Theorem 134.99s 135.17s
% Output   : Proof 135.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM926_2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14  % Command    : duper %s
% 0.16/0.35  % Computer : n019.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit   : 300
% 0.16/0.35  % WCLimit    : 300
% 0.16/0.35  % DateTime   : Fri Aug 25 16:37:13 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 134.99/135.17  SZS status Theorem for theBenchmark.p
% 134.99/135.17  SZS output start Proof for theBenchmark.p
% 134.99/135.17  Clause #0 (by assumption #[]): Eq (ord_less_eq_int one_one_int t) True
% 134.99/135.17  Clause #1 (by assumption #[]): Eq
% 134.99/135.17    (Eq t one_one_int →
% 134.99/135.17      Exists fun X =>
% 134.99/135.17        Exists fun Y =>
% 134.99/135.17          Eq
% 134.99/135.17            (plus_plus_int (power_power_int X (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.17              (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.17            (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.17    True
% 134.99/135.17  Clause #2 (by assumption #[]): Eq
% 134.99/135.17    (ord_less_int one_one_int t →
% 134.99/135.17      Exists fun X =>
% 134.99/135.17        Exists fun Y =>
% 134.99/135.17          Eq
% 134.99/135.17            (plus_plus_int (power_power_int X (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.17              (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.17            (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.17    True
% 134.99/135.17  Clause #59 (by assumption #[]): Eq (∀ (Z : nat), Eq (times_times_nat (number_number_of_nat (bit0 (bit1 pls))) Z) (plus_plus_nat Z Z)) True
% 134.99/135.17  Clause #93 (by assumption #[]): Eq
% 134.99/135.17    (∀ (Lx_3 Ly_1 Rx_3 : int),
% 134.99/135.17      Eq (times_times_int (times_times_int Lx_3 Ly_1) Rx_3) (times_times_int (times_times_int Lx_3 Rx_3) Ly_1))
% 134.99/135.17    True
% 134.99/135.17  Clause #111 (by assumption #[]): Eq
% 134.99/135.17    (∀ (A_54 B_15 C_9 : int),
% 134.99/135.17      Eq (plus_plus_int (plus_plus_int A_54 B_15) C_9) (plus_plus_int (plus_plus_int A_54 C_9) B_15))
% 134.99/135.17    True
% 134.99/135.17  Clause #131 (by assumption #[]): Eq (∀ (K : int), Eq (number_number_of_int K) K) True
% 134.99/135.17  Clause #157 (by assumption #[]): Eq
% 134.99/135.17    (∀ (A_48 M_12 B_13 : int),
% 134.99/135.17      Eq (plus_plus_int (times_times_int A_48 M_12) (times_times_int B_13 M_12))
% 134.99/135.17        (times_times_int (plus_plus_int A_48 B_13) M_12))
% 134.99/135.17    True
% 134.99/135.17  Clause #168 (by assumption #[]): Eq (∀ (A_46 : nat), Eq (times_times_nat A_46 one_one_nat) A_46) True
% 134.99/135.17  Clause #172 (by assumption #[]): Eq (∀ (A_45 : int), Eq (times_times_int one_one_int A_45) A_45) True
% 134.99/135.17  Clause #186 (by assumption #[]): Eq (∀ (K : int), Eq (plus_plus_int pls K) K) True
% 134.99/135.17  Clause #188 (by assumption #[]): Eq (∀ (K : int), Eq (bit0 K) (plus_plus_int K K)) True
% 134.99/135.17  Clause #227 (by assumption #[]): Eq (∀ (K L : int), Eq (plus_plus_int (bit1 K) (bit0 L)) (bit1 (plus_plus_int K L))) True
% 134.99/135.17  Clause #239 (by assumption #[]): Eq (Eq one_one_int (number_number_of_int (bit1 pls))) True
% 134.99/135.17  Clause #513 (by assumption #[]): Eq (∀ (X_3 Y_3 : int), ord_less_eq_int X_3 Y_3 → Ne X_3 Y_3 → ord_less_int X_3 Y_3) True
% 134.99/135.17  Clause #636 (by assumption #[]): Eq
% 134.99/135.17    (Not
% 134.99/135.17      (Exists fun X =>
% 134.99/135.17        Exists fun Y =>
% 134.99/135.17          Eq
% 134.99/135.17            (plus_plus_int (power_power_int X (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.17              (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.17            (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int)))
% 134.99/135.17    True
% 134.99/135.17  Clause #639 (by clausification #[1]): Or (Eq (Eq t one_one_int) False)
% 134.99/135.17    (Eq
% 134.99/135.17      (Exists fun X =>
% 134.99/135.17        Exists fun Y =>
% 134.99/135.17          Eq
% 134.99/135.17            (plus_plus_int (power_power_int X (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.17              (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.17            (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.17      True)
% 134.99/135.17  Clause #640 (by clausification #[639]): Or
% 134.99/135.17    (Eq
% 134.99/135.17      (Exists fun X =>
% 134.99/135.17        Exists fun Y =>
% 134.99/135.17          Eq
% 134.99/135.17            (plus_plus_int (power_power_int X (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.17              (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.17            (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.17      True)
% 134.99/135.17    (Ne t one_one_int)
% 134.99/135.17  Clause #641 (by clausification #[640]): ∀ (a : int),
% 134.99/135.17    Or (Ne t one_one_int)
% 134.99/135.17      (Eq
% 134.99/135.17        (Exists fun Y =>
% 134.99/135.17          Eq
% 134.99/135.17            (plus_plus_int (power_power_int (skS.0 0 a) (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.17              (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.17            (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.17        True)
% 134.99/135.17  Clause #642 (by clausification #[641]): ∀ (a a_1 : int),
% 134.99/135.19    Or (Ne t one_one_int)
% 134.99/135.19      (Eq
% 134.99/135.19        (Eq
% 134.99/135.19          (plus_plus_int (power_power_int (skS.0 0 a) (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.19            (power_power_int (skS.0 1 a a_1) (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.19          (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.19        True)
% 134.99/135.19  Clause #643 (by clausification #[642]): ∀ (a a_1 : int),
% 134.99/135.19    Or (Ne t one_one_int)
% 134.99/135.19      (Eq
% 134.99/135.19        (plus_plus_int (power_power_int (skS.0 0 a) (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.19          (power_power_int (skS.0 1 a a_1) (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.19        (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.19  Clause #649 (by clausification #[2]): Or (Eq (ord_less_int one_one_int t) False)
% 134.99/135.19    (Eq
% 134.99/135.19      (Exists fun X =>
% 134.99/135.19        Exists fun Y =>
% 134.99/135.19          Eq
% 134.99/135.19            (plus_plus_int (power_power_int X (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.19              (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.19            (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.19      True)
% 134.99/135.19  Clause #650 (by clausification #[649]): ∀ (a : int),
% 134.99/135.19    Or (Eq (ord_less_int one_one_int t) False)
% 134.99/135.19      (Eq
% 134.99/135.19        (Exists fun Y =>
% 134.99/135.19          Eq
% 134.99/135.19            (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.19              (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.19            (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.19        True)
% 134.99/135.19  Clause #651 (by clausification #[650]): ∀ (a a_1 : int),
% 134.99/135.19    Or (Eq (ord_less_int one_one_int t) False)
% 134.99/135.19      (Eq
% 134.99/135.19        (Eq
% 134.99/135.19          (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.19            (power_power_int (skS.0 3 a a_1) (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.19          (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.19        True)
% 134.99/135.19  Clause #652 (by clausification #[651]): ∀ (a a_1 : int),
% 134.99/135.19    Or (Eq (ord_less_int one_one_int t) False)
% 134.99/135.19      (Eq
% 134.99/135.19        (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.19          (power_power_int (skS.0 3 a a_1) (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.19        (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 134.99/135.19  Clause #681 (by clausification #[239]): Eq one_one_int (number_number_of_int (bit1 pls))
% 134.99/135.19  Clause #701 (by clausification #[131]): ∀ (a : int), Eq (Eq (number_number_of_int a) a) True
% 134.99/135.19  Clause #702 (by clausification #[701]): ∀ (a : int), Eq (number_number_of_int a) a
% 134.99/135.19  Clause #703 (by backward demodulation #[702, 643]): ∀ (a a_1 : int),
% 134.99/135.19    Or (Ne t one_one_int)
% 134.99/135.19      (Eq
% 134.99/135.19        (plus_plus_int (power_power_int (skS.0 0 a) (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.19          (power_power_int (skS.0 1 a a_1) (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.19        (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int))
% 134.99/135.19  Clause #704 (by backward demodulation #[702, 652]): ∀ (a a_1 : int),
% 134.99/135.19    Or (Eq (ord_less_int one_one_int t) False)
% 134.99/135.19      (Eq
% 134.99/135.19        (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 (bit1 pls))))
% 134.99/135.19          (power_power_int (skS.0 3 a a_1) (number_number_of_nat (bit0 (bit1 pls)))))
% 134.99/135.19        (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int))
% 134.99/135.19  Clause #711 (by superposition #[702, 681]): Eq one_one_int (bit1 pls)
% 134.99/135.19  Clause #914 (by clausification #[186]): ∀ (a : int), Eq (Eq (plus_plus_int pls a) a) True
% 134.99/135.19  Clause #915 (by clausification #[914]): ∀ (a : int), Eq (plus_plus_int pls a) a
% 134.99/135.19  Clause #1005 (by clausification #[513]): ∀ (a : int), Eq (∀ (Y_3 : int), ord_less_eq_int a Y_3 → Ne a Y_3 → ord_less_int a Y_3) True
% 134.99/135.19  Clause #1006 (by clausification #[1005]): ∀ (a a_1 : int), Eq (ord_less_eq_int a a_1 → Ne a a_1 → ord_less_int a a_1) True
% 134.99/135.19  Clause #1007 (by clausification #[1006]): ∀ (a a_1 : int), Or (Eq (ord_less_eq_int a a_1) False) (Eq (Ne a a_1 → ord_less_int a a_1) True)
% 134.99/135.19  Clause #1008 (by clausification #[1007]): ∀ (a a_1 : int), Or (Eq (ord_less_eq_int a a_1) False) (Or (Eq (Ne a a_1) False) (Eq (ord_less_int a a_1) True))
% 134.99/135.22  Clause #1009 (by clausification #[1008]): ∀ (a a_1 : int), Or (Eq (ord_less_eq_int a a_1) False) (Or (Eq (ord_less_int a a_1) True) (Eq a a_1))
% 134.99/135.22  Clause #1011 (by superposition #[1009, 0]): Or (Eq (ord_less_int one_one_int t) True) (Or (Eq one_one_int t) (Eq False True))
% 134.99/135.22  Clause #1021 (by clausification #[1011]): Or (Eq (ord_less_int one_one_int t) True) (Eq one_one_int t)
% 134.99/135.22  Clause #1045 (by clausification #[172]): ∀ (a : int), Eq (Eq (times_times_int one_one_int a) a) True
% 134.99/135.22  Clause #1046 (by clausification #[1045]): ∀ (a : int), Eq (times_times_int one_one_int a) a
% 134.99/135.22  Clause #1056 (by clausification #[168]): ∀ (a : nat), Eq (Eq (times_times_nat a one_one_nat) a) True
% 134.99/135.22  Clause #1057 (by clausification #[1056]): ∀ (a : nat), Eq (times_times_nat a one_one_nat) a
% 134.99/135.22  Clause #1306 (by clausification #[188]): ∀ (a : int), Eq (Eq (bit0 a) (plus_plus_int a a)) True
% 134.99/135.22  Clause #1307 (by clausification #[1306]): ∀ (a : int), Eq (bit0 a) (plus_plus_int a a)
% 134.99/135.22  Clause #2523 (by clausification #[59]): ∀ (a : nat), Eq (Eq (times_times_nat (number_number_of_nat (bit0 (bit1 pls))) a) (plus_plus_nat a a)) True
% 134.99/135.22  Clause #2524 (by clausification #[2523]): ∀ (a : nat), Eq (times_times_nat (number_number_of_nat (bit0 (bit1 pls))) a) (plus_plus_nat a a)
% 134.99/135.22  Clause #2525 (by forward demodulation #[2524, 711]): ∀ (a : nat), Eq (times_times_nat (number_number_of_nat (bit0 one_one_int)) a) (plus_plus_nat a a)
% 134.99/135.22  Clause #2527 (by superposition #[2525, 1057]): Eq (plus_plus_nat one_one_nat one_one_nat) (number_number_of_nat (bit0 one_one_int))
% 134.99/135.22  Clause #4417 (by clausification #[93]): ∀ (a : int),
% 134.99/135.22    Eq
% 134.99/135.22      (∀ (Ly_1 Rx_3 : int),
% 134.99/135.22        Eq (times_times_int (times_times_int a Ly_1) Rx_3) (times_times_int (times_times_int a Rx_3) Ly_1))
% 134.99/135.22      True
% 134.99/135.22  Clause #4418 (by clausification #[4417]): ∀ (a a_1 : int),
% 134.99/135.22    Eq (∀ (Rx_3 : int), Eq (times_times_int (times_times_int a a_1) Rx_3) (times_times_int (times_times_int a Rx_3) a_1))
% 134.99/135.22      True
% 134.99/135.22  Clause #4419 (by clausification #[4418]): ∀ (a a_1 a_2 : int),
% 134.99/135.22    Eq (Eq (times_times_int (times_times_int a a_1) a_2) (times_times_int (times_times_int a a_2) a_1)) True
% 134.99/135.22  Clause #4420 (by clausification #[4419]): ∀ (a a_1 a_2 : int), Eq (times_times_int (times_times_int a a_1) a_2) (times_times_int (times_times_int a a_2) a_1)
% 134.99/135.22  Clause #4432 (by superposition #[4420, 1046]): ∀ (a a_1 : int), Eq (times_times_int a a_1) (times_times_int (times_times_int one_one_int a_1) a)
% 134.99/135.22  Clause #4446 (by forward demodulation #[4432, 1046]): ∀ (a a_1 : int), Eq (times_times_int a a_1) (times_times_int a_1 a)
% 134.99/135.22  Clause #4986 (by clausification #[111]): ∀ (a : int),
% 134.99/135.22    Eq (∀ (B_15 C_9 : int), Eq (plus_plus_int (plus_plus_int a B_15) C_9) (plus_plus_int (plus_plus_int a C_9) B_15)) True
% 134.99/135.22  Clause #4987 (by clausification #[4986]): ∀ (a a_1 : int),
% 134.99/135.22    Eq (∀ (C_9 : int), Eq (plus_plus_int (plus_plus_int a a_1) C_9) (plus_plus_int (plus_plus_int a C_9) a_1)) True
% 134.99/135.22  Clause #4988 (by clausification #[4987]): ∀ (a a_1 a_2 : int), Eq (Eq (plus_plus_int (plus_plus_int a a_1) a_2) (plus_plus_int (plus_plus_int a a_2) a_1)) True
% 134.99/135.22  Clause #4989 (by clausification #[4988]): ∀ (a a_1 a_2 : int), Eq (plus_plus_int (plus_plus_int a a_1) a_2) (plus_plus_int (plus_plus_int a a_2) a_1)
% 134.99/135.22  Clause #5009 (by superposition #[4989, 915]): ∀ (a a_1 : int), Eq (plus_plus_int (plus_plus_int pls a) a_1) (plus_plus_int a_1 a)
% 134.99/135.22  Clause #5013 (by forward demodulation #[5009, 915]): ∀ (a a_1 : int), Eq (plus_plus_int a a_1) (plus_plus_int a_1 a)
% 134.99/135.22  Clause #7523 (by clausification #[157]): ∀ (a : int),
% 134.99/135.22    Eq
% 134.99/135.22      (∀ (M_12 B_13 : int),
% 134.99/135.22        Eq (plus_plus_int (times_times_int a M_12) (times_times_int B_13 M_12))
% 134.99/135.22          (times_times_int (plus_plus_int a B_13) M_12))
% 134.99/135.22      True
% 134.99/135.22  Clause #7524 (by clausification #[7523]): ∀ (a a_1 : int),
% 134.99/135.22    Eq
% 134.99/135.22      (∀ (B_13 : int),
% 134.99/135.22        Eq (plus_plus_int (times_times_int a a_1) (times_times_int B_13 a_1))
% 134.99/135.22          (times_times_int (plus_plus_int a B_13) a_1))
% 134.99/135.22      True
% 134.99/135.22  Clause #7525 (by clausification #[7524]): ∀ (a a_1 a_2 : int),
% 134.99/135.22    Eq (Eq (plus_plus_int (times_times_int a a_1) (times_times_int a_2 a_1)) (times_times_int (plus_plus_int a a_2) a_1))
% 135.08/135.24      True
% 135.08/135.24  Clause #7526 (by clausification #[7525]): ∀ (a a_1 a_2 : int),
% 135.08/135.24    Eq (plus_plus_int (times_times_int a a_1) (times_times_int a_2 a_1)) (times_times_int (plus_plus_int a a_2) a_1)
% 135.08/135.24  Clause #7527 (by superposition #[7526, 1307]): ∀ (a a_1 : int), Eq (bit0 (times_times_int a a_1)) (times_times_int (plus_plus_int a a) a_1)
% 135.08/135.24  Clause #7563 (by forward demodulation #[7527, 1307]): ∀ (a a_1 : int), Eq (bit0 (times_times_int a a_1)) (times_times_int (bit0 a) a_1)
% 135.08/135.24  Clause #7578 (by superposition #[7563, 1046]): ∀ (a : int), Eq (bit0 a) (times_times_int (bit0 one_one_int) a)
% 135.08/135.24  Clause #7581 (by superposition #[7563, 4446]): ∀ (a a_1 : int), Eq (bit0 (times_times_int a a_1)) (times_times_int (bit0 a_1) a)
% 135.08/135.24  Clause #7640 (by superposition #[7578, 7563]): ∀ (a : int), Eq (bit0 (bit0 a)) (times_times_int (bit0 (bit0 one_one_int)) a)
% 135.08/135.24  Clause #7820 (by superposition #[7640, 4446]): ∀ (a : int), Eq (times_times_int a (bit0 (bit0 one_one_int))) (bit0 (bit0 a))
% 135.08/135.24  Clause #8026 (by superposition #[7581, 7563]): ∀ (a a_1 : int), Eq (times_times_int (bit0 a) a_1) (times_times_int (bit0 a_1) a)
% 135.08/135.24  Clause #8049 (by superposition #[8026, 4446]): ∀ (a a_1 : int), Eq (times_times_int a (bit0 a_1)) (times_times_int (bit0 a) a_1)
% 135.08/135.24  Clause #8123 (by superposition #[8049, 4446]): ∀ (a a_1 : int), Eq (times_times_int a (bit0 a_1)) (times_times_int a_1 (bit0 a))
% 135.08/135.24  Clause #9837 (by clausification #[227]): ∀ (a : int), Eq (∀ (L : int), Eq (plus_plus_int (bit1 a) (bit0 L)) (bit1 (plus_plus_int a L))) True
% 135.08/135.24  Clause #9838 (by clausification #[9837]): ∀ (a a_1 : int), Eq (Eq (plus_plus_int (bit1 a) (bit0 a_1)) (bit1 (plus_plus_int a a_1))) True
% 135.08/135.24  Clause #9839 (by clausification #[9838]): ∀ (a a_1 : int), Eq (plus_plus_int (bit1 a) (bit0 a_1)) (bit1 (plus_plus_int a a_1))
% 135.08/135.24  Clause #9859 (by superposition #[9839, 711]): ∀ (a : int), Eq (plus_plus_int one_one_int (bit0 a)) (bit1 (plus_plus_int pls a))
% 135.08/135.24  Clause #9862 (by forward demodulation #[9859, 915]): ∀ (a : int), Eq (plus_plus_int one_one_int (bit0 a)) (bit1 a)
% 135.08/135.24  Clause #31479 (by clausification #[636]): Eq
% 135.08/135.24    (Exists fun X =>
% 135.08/135.24      Exists fun Y =>
% 135.08/135.24        Eq
% 135.08/135.24          (plus_plus_int (power_power_int X (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.24            (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 135.08/135.24          (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 135.08/135.24    False
% 135.08/135.24  Clause #31480 (by clausification #[31479]): ∀ (a : int),
% 135.08/135.24    Eq
% 135.08/135.24      (Exists fun Y =>
% 135.08/135.24        Eq
% 135.08/135.24          (plus_plus_int (power_power_int a (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.24            (power_power_int Y (number_number_of_nat (bit0 (bit1 pls)))))
% 135.08/135.24          (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 135.08/135.24      False
% 135.08/135.24  Clause #31481 (by clausification #[31480]): ∀ (a a_1 : int),
% 135.08/135.24    Eq
% 135.08/135.24      (Eq
% 135.08/135.24        (plus_plus_int (power_power_int a (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.24          (power_power_int a_1 (number_number_of_nat (bit0 (bit1 pls)))))
% 135.08/135.24        (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int))
% 135.08/135.24      False
% 135.08/135.24  Clause #31482 (by clausification #[31481]): ∀ (a a_1 : int),
% 135.08/135.24    Ne
% 135.08/135.24      (plus_plus_int (power_power_int a (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.24        (power_power_int a_1 (number_number_of_nat (bit0 (bit1 pls)))))
% 135.08/135.24      (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int)
% 135.08/135.24  Clause #31483 (by forward demodulation #[31482, 711]): ∀ (a a_1 : int),
% 135.08/135.24    Ne
% 135.08/135.24      (plus_plus_int (power_power_int a (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.24        (power_power_int a_1 (number_number_of_nat (bit0 one_one_int))))
% 135.08/135.24      (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int)
% 135.08/135.24  Clause #31484 (by forward demodulation #[31483, 2527]): ∀ (a a_1 : int),
% 135.08/135.24    Ne
% 135.08/135.24      (plus_plus_int (power_power_int a (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.24        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.24      (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int)
% 135.08/135.26  Clause #31485 (by forward demodulation #[31484, 711]): ∀ (a a_1 : int),
% 135.08/135.26    Ne
% 135.08/135.26      (plus_plus_int (power_power_int a (number_number_of_nat (bit0 one_one_int)))
% 135.08/135.26        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26      (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int)
% 135.08/135.26  Clause #31486 (by forward demodulation #[31485, 2527]): ∀ (a a_1 : int),
% 135.08/135.26    Ne
% 135.08/135.26      (plus_plus_int (power_power_int a (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.26        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26      (plus_plus_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m) one_one_int)
% 135.08/135.26  Clause #31487 (by forward demodulation #[31486, 5013]): ∀ (a a_1 : int),
% 135.08/135.26    Ne
% 135.08/135.26      (plus_plus_int (power_power_int a (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.26        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26      (plus_plus_int one_one_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls)))) m))
% 135.08/135.26  Clause #31488 (by forward demodulation #[31487, 4446]): ∀ (a a_1 : int),
% 135.08/135.26    Ne
% 135.08/135.26      (plus_plus_int (power_power_int a (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.26        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26      (plus_plus_int one_one_int (times_times_int m (number_number_of_int (bit0 (bit0 (bit1 pls))))))
% 135.08/135.26  Clause #31489 (by forward demodulation #[31488, 702]): ∀ (a a_1 : int),
% 135.08/135.26    Ne
% 135.08/135.26      (plus_plus_int (power_power_int a (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.26        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26      (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 (bit1 pls)))))
% 135.08/135.26  Clause #31490 (by forward demodulation #[31489, 711]): ∀ (a a_1 : int),
% 135.08/135.26    Ne
% 135.08/135.26      (plus_plus_int (power_power_int a (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.26        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26      (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 one_one_int))))
% 135.08/135.26  Clause #31491 (by forward demodulation #[31490, 7820]): ∀ (a a_1 : int),
% 135.08/135.26    Ne
% 135.08/135.26      (plus_plus_int (power_power_int a (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.26        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26      (plus_plus_int one_one_int (bit0 (bit0 m)))
% 135.08/135.26  Clause #31492 (by forward demodulation #[31491, 9862]): ∀ (a a_1 : int),
% 135.08/135.26    Ne
% 135.08/135.26      (plus_plus_int (power_power_int a (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.26        (power_power_int a_1 (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26      (bit1 (bit0 m))
% 135.08/135.26  Clause #31624 (by forward demodulation #[703, 711]): ∀ (a a_1 : int),
% 135.08/135.26    Or (Ne t one_one_int)
% 135.08/135.26      (Eq
% 135.08/135.26        (plus_plus_int (power_power_int (skS.0 0 a) (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.26          (power_power_int (skS.0 1 a a_1) (number_number_of_nat (bit0 one_one_int))))
% 135.08/135.26        (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int))
% 135.08/135.26  Clause #31625 (by forward demodulation #[31624, 2527]): ∀ (a a_1 : int),
% 135.08/135.26    Or (Ne t one_one_int)
% 135.08/135.26      (Eq
% 135.08/135.26        (plus_plus_int (power_power_int (skS.0 0 a) (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.26          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26        (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int))
% 135.08/135.26  Clause #31626 (by forward demodulation #[31625, 711]): ∀ (a a_1 : int),
% 135.08/135.26    Or (Ne t one_one_int)
% 135.08/135.26      (Eq
% 135.08/135.26        (plus_plus_int (power_power_int (skS.0 0 a) (number_number_of_nat (bit0 one_one_int)))
% 135.08/135.26          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26        (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int))
% 135.08/135.26  Clause #31627 (by forward demodulation #[31626, 2527]): ∀ (a a_1 : int),
% 135.08/135.26    Or (Ne t one_one_int)
% 135.08/135.26      (Eq
% 135.08/135.26        (plus_plus_int (power_power_int (skS.0 0 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.26          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.26        (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int))
% 135.08/135.26  Clause #31628 (by forward demodulation #[31627, 5013]): ∀ (a a_1 : int),
% 135.08/135.26    Or (Ne t one_one_int)
% 135.08/135.26      (Eq
% 135.08/135.26        (plus_plus_int (power_power_int (skS.0 0 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.28          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28        (plus_plus_int one_one_int (times_times_int (bit0 (bit0 (bit1 pls))) m)))
% 135.08/135.28  Clause #31629 (by forward demodulation #[31628, 8049]): ∀ (a a_1 : int),
% 135.08/135.28    Or (Ne t one_one_int)
% 135.08/135.28      (Eq
% 135.08/135.28        (plus_plus_int (power_power_int (skS.0 0 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.28          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28        (plus_plus_int one_one_int (times_times_int (bit0 (bit1 pls)) (bit0 m))))
% 135.08/135.28  Clause #31630 (by forward demodulation #[31629, 8123]): ∀ (a a_1 : int),
% 135.08/135.28    Or (Ne t one_one_int)
% 135.08/135.28      (Eq
% 135.08/135.28        (plus_plus_int (power_power_int (skS.0 0 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.28          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28        (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 (bit1 pls))))))
% 135.08/135.28  Clause #31631 (by forward demodulation #[31630, 711]): ∀ (a a_1 : int),
% 135.08/135.28    Or (Ne t one_one_int)
% 135.08/135.28      (Eq
% 135.08/135.28        (plus_plus_int (power_power_int (skS.0 0 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.28          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28        (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 one_one_int)))))
% 135.08/135.28  Clause #31632 (by forward demodulation #[31631, 7820]): ∀ (a a_1 : int),
% 135.08/135.28    Or (Ne t one_one_int)
% 135.08/135.28      (Eq
% 135.08/135.28        (plus_plus_int (power_power_int (skS.0 0 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.28          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28        (plus_plus_int one_one_int (bit0 (bit0 m))))
% 135.08/135.28  Clause #31633 (by forward demodulation #[31632, 9862]): ∀ (a a_1 : int),
% 135.08/135.28    Or (Ne t one_one_int)
% 135.08/135.28      (Eq
% 135.08/135.28        (plus_plus_int (power_power_int (skS.0 0 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.28          (power_power_int (skS.0 1 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28        (bit1 (bit0 m)))
% 135.08/135.28  Clause #31634 (by forward contextual literal cutting #[31633, 31492]): Ne t one_one_int
% 135.08/135.28  Clause #31635 (by backward contextual literal cutting #[31634, 1021]): Eq (ord_less_int one_one_int t) True
% 135.08/135.28  Clause #31681 (by forward demodulation #[704, 31635]): ∀ (a a_1 : int),
% 135.08/135.28    Or (Eq True False)
% 135.08/135.28      (Eq
% 135.08/135.28        (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.28          (power_power_int (skS.0 3 a a_1) (number_number_of_nat (bit0 (bit1 pls)))))
% 135.08/135.28        (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int))
% 135.08/135.28  Clause #31682 (by clausification #[31681]): ∀ (a a_1 : int),
% 135.08/135.28    Eq
% 135.08/135.28      (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.28        (power_power_int (skS.0 3 a a_1) (number_number_of_nat (bit0 (bit1 pls)))))
% 135.08/135.28      (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int)
% 135.08/135.28  Clause #31683 (by forward demodulation #[31682, 711]): ∀ (a a_1 : int),
% 135.08/135.28    Eq
% 135.08/135.28      (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.28        (power_power_int (skS.0 3 a a_1) (number_number_of_nat (bit0 one_one_int))))
% 135.08/135.28      (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int)
% 135.08/135.28  Clause #31684 (by forward demodulation #[31683, 2527]): ∀ (a a_1 : int),
% 135.08/135.28    Eq
% 135.08/135.28      (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 (bit1 pls))))
% 135.08/135.28        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28      (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int)
% 135.08/135.28  Clause #31685 (by forward demodulation #[31684, 711]): ∀ (a a_1 : int),
% 135.08/135.28    Eq
% 135.08/135.28      (plus_plus_int (power_power_int (skS.0 2 a) (number_number_of_nat (bit0 one_one_int)))
% 135.08/135.28        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28      (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int)
% 135.08/135.28  Clause #31686 (by forward demodulation #[31685, 2527]): ∀ (a a_1 : int),
% 135.08/135.28    Eq
% 135.08/135.28      (plus_plus_int (power_power_int (skS.0 2 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.08/135.28        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.08/135.28      (plus_plus_int (times_times_int (bit0 (bit0 (bit1 pls))) m) one_one_int)
% 135.29/135.45  Clause #31687 (by forward demodulation #[31686, 5013]): ∀ (a a_1 : int),
% 135.29/135.45    Eq
% 135.29/135.45      (plus_plus_int (power_power_int (skS.0 2 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.29/135.45        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.29/135.45      (plus_plus_int one_one_int (times_times_int (bit0 (bit0 (bit1 pls))) m))
% 135.29/135.45  Clause #31688 (by forward demodulation #[31687, 8049]): ∀ (a a_1 : int),
% 135.29/135.45    Eq
% 135.29/135.45      (plus_plus_int (power_power_int (skS.0 2 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.29/135.45        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.29/135.45      (plus_plus_int one_one_int (times_times_int (bit0 (bit1 pls)) (bit0 m)))
% 135.29/135.45  Clause #31689 (by forward demodulation #[31688, 8123]): ∀ (a a_1 : int),
% 135.29/135.45    Eq
% 135.29/135.45      (plus_plus_int (power_power_int (skS.0 2 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.29/135.45        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.29/135.45      (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 (bit1 pls)))))
% 135.29/135.45  Clause #31690 (by forward demodulation #[31689, 711]): ∀ (a a_1 : int),
% 135.29/135.45    Eq
% 135.29/135.45      (plus_plus_int (power_power_int (skS.0 2 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.29/135.45        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.29/135.45      (plus_plus_int one_one_int (times_times_int m (bit0 (bit0 one_one_int))))
% 135.29/135.45  Clause #31691 (by forward demodulation #[31690, 7820]): ∀ (a a_1 : int),
% 135.29/135.45    Eq
% 135.29/135.45      (plus_plus_int (power_power_int (skS.0 2 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.29/135.45        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.29/135.45      (plus_plus_int one_one_int (bit0 (bit0 m)))
% 135.29/135.45  Clause #31692 (by forward demodulation #[31691, 9862]): ∀ (a a_1 : int),
% 135.29/135.45    Eq
% 135.29/135.45      (plus_plus_int (power_power_int (skS.0 2 a) (plus_plus_nat one_one_nat one_one_nat))
% 135.29/135.45        (power_power_int (skS.0 3 a a_1) (plus_plus_nat one_one_nat one_one_nat)))
% 135.29/135.45      (bit1 (bit0 m))
% 135.29/135.45  Clause #31693 (by forward contextual literal cutting #[31692, 31492]): False
% 135.29/135.45  SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------