TSTP Solution File: NUM926+5 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 : Wed Jul 27 13:10:18 EDT 2022
% Result : Theorem 2.23s 2.39s
% Output : Refutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 12 unt; 1 nHn; 16 RR)
% Number of literals : 23 ( 16 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 9 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(25,axiom,
( t != one_one(int)
| plus_plus(int,power_power(int,dollar_c2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,dollar_c1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('NUM926+5.p',unknown),
[] ).
cnf(26,plain,
( one_one(int) != t
| plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,power_power(int,dollar_c2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,dollar_c1,number_number_of(nat,bit0(bit1(pls))))) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])])]),
[iquote('copy,25,flip.1,flip.2')] ).
cnf(27,axiom,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,dollar_c4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,dollar_c3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('NUM926+5.p',unknown),
[] ).
cnf(28,plain,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,power_power(int,dollar_c4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,dollar_c3,number_number_of(nat,bit0(bit1(pls))))) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[27])]),
[iquote('copy,27,flip.2')] ).
cnf(40,axiom,
( ord_less(int,A,B)
| ~ ord_less_e_q(int,A,B)
| A = B ),
file('NUM926+5.p',unknown),
[] ).
cnf(115,axiom,
plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
file('NUM926+5.p',unknown),
[] ).
cnf(118,plain,
plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) != plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[115])]),
[iquote('copy,115,flip.1')] ).
cnf(138,axiom,
ord_less_e_q(int,one_one(int),t),
file('NUM926+5.p',unknown),
[] ).
cnf(163,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('NUM926+5.p',unknown),
[] ).
cnf(167,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
file('NUM926+5.p',unknown),
[] ).
cnf(169,plain,
one_one(nat) = number_number_of(nat,bit1(pls)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[167])]),
[iquote('copy,167,flip.1')] ).
cnf(175,axiom,
number_number_of(int,A) = A,
file('NUM926+5.p',unknown),
[] ).
cnf(203,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[163]),169,169])]),
[iquote('back_demod,163,demod,169,169,flip.1')] ).
cnf(215,plain,
plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)) != plus_plus(int,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))),power_power(int,B,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls))))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[118]),175,203,203]),
[iquote('back_demod,118,demod,175,203,203')] ).
cnf(217,plain,
~ ord_less(int,one_one(int),t),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),175,203,203]),215]),
[iquote('back_demod,28,demod,175,203,203,unit_del,215')] ).
cnf(218,plain,
one_one(int) != t,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),175,203,203]),215]),
[iquote('back_demod,26,demod,175,203,203,unit_del,215')] ).
cnf(231,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[138,40]),217,218]),
[iquote('hyper,138,40,unit_del,217,218')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:04:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.23/2.37 ----- Otter 3.3f, August 2004 -----
% 2.23/2.37 The process was started by sandbox2 on n028.cluster.edu,
% 2.23/2.37 Wed Jul 27 10:04:19 2022
% 2.23/2.37 The command was "./otter". The process ID is 21570.
% 2.23/2.37
% 2.23/2.37 set(prolog_style_variables).
% 2.23/2.37 set(auto).
% 2.23/2.37 dependent: set(auto1).
% 2.23/2.37 dependent: set(process_input).
% 2.23/2.37 dependent: clear(print_kept).
% 2.23/2.37 dependent: clear(print_new_demod).
% 2.23/2.37 dependent: clear(print_back_demod).
% 2.23/2.37 dependent: clear(print_back_sub).
% 2.23/2.37 dependent: set(control_memory).
% 2.23/2.37 dependent: assign(max_mem, 12000).
% 2.23/2.37 dependent: assign(pick_given_ratio, 4).
% 2.23/2.37 dependent: assign(stats_level, 1).
% 2.23/2.37 dependent: assign(max_seconds, 10800).
% 2.23/2.37 clear(print_given).
% 2.23/2.37
% 2.23/2.37 formula_list(usable).
% 2.23/2.37 all A (A=A).
% 2.23/2.37 all X_a (semiring_1(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)).
% 2.23/2.37 all B_1 B_2 X_a (comm_semiring_1(X_a)->plus_plus(X_a,ti(X_a,B_1),B_2)=plus_plus(X_a,B_1,B_2)).
% 2.23/2.37 all B_1 B_2 X_a (comm_semiring_1(X_a)->plus_plus(X_a,B_1,ti(X_a,B_2))=plus_plus(X_a,B_1,B_2)).
% 2.23/2.37 all B_1 B_2 X_a (comm_semiring_1(X_a)->ti(X_a,plus_plus(X_a,B_1,B_2))=plus_plus(X_a,B_1,B_2)).
% 2.23/2.37 all B_1 B_2 X_a (monoid_mult(X_a)->times_times(X_a,ti(X_a,B_1),B_2)=times_times(X_a,B_1,B_2)).
% 2.23/2.37 all B_1 B_2 X_a (monoid_mult(X_a)->times_times(X_a,B_1,ti(X_a,B_2))=times_times(X_a,B_1,B_2)).
% 2.23/2.37 all B_1 B_2 X_a (monoid_mult(X_a)->ti(X_a,times_times(X_a,B_1,B_2))=times_times(X_a,B_1,B_2)).
% 2.23/2.37 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 2.23/2.37 all B_1 (zprime(ti(int,B_1))<->zprime(B_1)).
% 2.23/2.37 all B_1 (bit0(ti(int,B_1))=bit0(B_1)).
% 2.23/2.37 all B_1 (ti(int,bit0(B_1))=bit0(B_1)).
% 2.23/2.37 all B_1 (bit1(ti(int,B_1))=bit1(B_1)).
% 2.23/2.37 all B_1 (ti(int,bit1(B_1))=bit1(B_1)).
% 2.23/2.37 ti(int,pls)=pls.
% 2.23/2.37 all B_1 X_a (number(X_a)->number_number_of(X_a,ti(int,B_1))=number_number_of(X_a,B_1)).
% 2.23/2.37 all B_1 X_a (number(X_a)->ti(X_a,number_number_of(X_a,B_1))=number_number_of(X_a,B_1)).
% 2.23/2.37 all B_1 B_2 X_a (number(X_a)&linorder(X_a)-> (ord_less(X_a,ti(X_a,B_1),B_2)<->ord_less(X_a,B_1,B_2))).
% 2.23/2.37 all B_1 B_2 X_a (number(X_a)&linorder(X_a)-> (ord_less(X_a,B_1,ti(X_a,B_2))<->ord_less(X_a,B_1,B_2))).
% 2.23/2.37 all B_1 B_2 X_a (number(X_a)&linorder(X_a)-> (ord_less_e_q(X_a,ti(X_a,B_1),B_2)<->ord_less_e_q(X_a,B_1,B_2))).
% 2.23/2.37 all B_1 B_2 X_a (number(X_a)&linorder(X_a)-> (ord_less_e_q(X_a,B_1,ti(X_a,B_2))<->ord_less_e_q(X_a,B_1,B_2))).
% 2.23/2.37 all B_1 B_2 X_a (monoid_mult(X_a)->power_power(X_a,ti(X_a,B_1),B_2)=power_power(X_a,B_1,B_2)).
% 2.23/2.37 all B_1 B_2 X_a (monoid_mult(X_a)->power_power(X_a,B_1,ti(nat,B_2))=power_power(X_a,B_1,B_2)).
% 2.23/2.37 all B_1 B_2 X_a (monoid_mult(X_a)->ti(X_a,power_power(X_a,B_1,B_2))=power_power(X_a,B_1,B_2)).
% 2.23/2.37 all B_1 (twoSqu33214720sum2sq(ti(int,B_1))<->twoSqu33214720sum2sq(B_1)).
% 2.23/2.37 ti(int,m)=m.
% 2.23/2.37 ti(int,s)=s.
% 2.23/2.37 ti(int,t)=t.
% 2.23/2.37 ord_less_e_q(int,one_one(int),t).
% 2.23/2.37 t=one_one(int)-> (exists X Y (plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls)))))=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 2.23/2.37 ord_less(int,one_one(int),t)-> (exists X Y (plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls)))))=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 2.23/2.37 ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 2.23/2.37 zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 2.23/2.37 plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t).
% 2.23/2.37 twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)).
% 2.23/2.37 all A_1 B (power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,plus_plus(int,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A_1),B)),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))).
% 2.23/2.37 all A_1 B (power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,A_1,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,A_1,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls)))))).
% 2.23/2.37 all X_a (number_semiring(X_a)-> (all X_1 Y_1 (power_power(X_a,plus_plus(X_a,X_1,Y_1),number_number_of(nat,bit0(bit1(pls))))=plus_plus(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X_1),Y_1))))).
% 2.23/2.37 all X_b (monoid_mult(X_b)&number(X_b)-> (all W (power_power(X_b,number_number_of(X_b,W),number_number_of(nat,bit0(bit1(pls))))=times_times(X_b,number_number_of(X_b,W),number_number_of(X_b,W))))).
% 2.23/2.37 all A_1 (times_times(int,A_1,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))))=power_power(int,A_1,number_number_of(nat,bit1(bit1(pls))))).
% 2.23/2.37 all X_a (semiring_1(X_a)->power_power(X_a,one_one(X_a),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a)).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all X_1 (times_times(X_a,X_1,X_1)=power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls))))))).
% 2.23/2.37 all X_a (monoid_mult(X_a)-> (all A_1 (power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls))))=times_times(X_a,A_1,A_1)))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all X_1 N (power_power(X_a,X_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=times_times(X_a,power_power(X_a,X_1,N),power_power(X_a,X_1,N))))).
% 2.23/2.37 all X_a (number_ring(X_a)-> (all W (plus_plus(X_a,one_one(X_a),number_number_of(X_a,W))=number_number_of(X_a,plus_plus(int,bit1(pls),W))))).
% 2.23/2.37 all X_a (number_ring(X_a)-> (all V (plus_plus(X_a,number_number_of(X_a,V),one_one(X_a))=number_number_of(X_a,plus_plus(int,V,bit1(pls)))))).
% 2.23/2.37 all X_a (number_ring(X_a)->plus_plus(X_a,one_one(X_a),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls)))).
% 2.23/2.37 -(all T_1 (plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))!=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),T_1))).
% 2.23/2.37 all W ord_less_e_q(int,W,W).
% 2.23/2.37 all Z W (ord_less_e_q(int,Z,W)|ord_less_e_q(int,W,Z)).
% 2.23/2.37 all Z_1 W_1 (ord_less(int,Z_1,W_1)<->ord_less_e_q(int,Z_1,W_1)&Z_1!=W_1).
% 2.23/2.37 all X_1 Y_1 (ord_less(int,X_1,Y_1)|X_1=Y_1|ord_less(int,Y_1,X_1)).
% 2.23/2.37 all K_1 I J (ord_less_e_q(int,I,J)-> (ord_less_e_q(int,J,K_1)->ord_less_e_q(int,I,K_1))).
% 2.23/2.37 all Z W (ord_less_e_q(int,Z,W)-> (ord_less_e_q(int,W,Z)->Z=W)).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all X_1 P Q (power_power(X_a,power_power(X_a,X_1,P),Q)=power_power(X_a,X_1,times_times(nat,P,Q))))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all X_1 (power_power(X_a,X_1,one_one(nat))=ti(X_a,X_1)))).
% 2.23/2.37 all X_1 Y_1 Z (power_power(int,power_power(int,X_1,Y_1),Z)=power_power(int,X_1,times_times(nat,Y_1,Z))).
% 2.23/2.37 all X_a (number(X_a)&linorder(X_a)-> (all V_2 W_1 (ord_less_e_q(X_a,number_number_of(X_a,V_2),number_number_of(X_a,W_1))<-> -ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_2))))).
% 2.23/2.37 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 Y_2 (ord_less(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))<->ord_less(int,X_2,Y_2)))).
% 2.23/2.37 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 Y_2 (ord_less_e_q(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))<->ord_less_e_q(int,X_2,Y_2)))).
% 2.23/2.37 all Z_2 Z W_2 W (ord_less(int,W_2,W)-> (ord_less_e_q(int,Z_2,Z)->ord_less(int,plus_plus(int,W_2,Z_2),plus_plus(int,W,Z)))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all X_1 P Q (times_times(X_a,power_power(X_a,X_1,P),power_power(X_a,X_1,Q))=power_power(X_a,X_1,plus_plus(nat,P,Q))))).
% 2.23/2.37 all X_1 Y_1 Z (power_power(int,X_1,plus_plus(nat,Y_1,Z))=times_times(int,power_power(int,X_1,Y_1),power_power(int,X_1,Z))).
% 2.23/2.37 all Z (times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z)=plus_plus(nat,Z,Z)).
% 2.23/2.37 all Z (times_times(nat,Z,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,Z,Z)).
% 2.23/2.37 plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 2.23/2.37 all K1 K2 (ord_less(int,bit1(K1),bit1(K2))<->ord_less(int,K1,K2)).
% 2.23/2.37 all K L (ord_less(int,bit1(K),bit1(L))<->ord_less(int,K,L)).
% 2.23/2.37 all K1 K2 (ord_less_e_q(int,bit1(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)).
% 2.23/2.37 all K L (ord_less_e_q(int,bit1(K),bit1(L))<->ord_less_e_q(int,K,L)).
% 2.23/2.37 -ord_less(int,pls,pls).
% 2.23/2.37 all K1 K2 (ord_less(int,bit0(K1),bit0(K2))<->ord_less(int,K1,K2)).
% 2.23/2.37 all K L (ord_less(int,bit0(K),bit0(L))<->ord_less(int,K,L)).
% 2.23/2.37 ord_less_e_q(int,pls,pls).
% 2.23/2.37 all K1 K2 (ord_less_e_q(int,bit0(K1),bit0(K2))<->ord_less_e_q(int,K1,K2)).
% 2.23/2.37 all K L (ord_less_e_q(int,bit0(K),bit0(L))<->ord_less_e_q(int,K,L)).
% 2.23/2.37 all K L (ord_less(int,number_number_of(int,K),number_number_of(int,L))<->ord_less(int,K,L)).
% 2.23/2.37 all K L (ord_less_e_q(int,number_number_of(int,K),number_number_of(int,L))<->ord_less_e_q(int,K,L)).
% 2.23/2.37 all K_1 I J (ord_less(int,I,J)->ord_less(int,plus_plus(int,I,K_1),plus_plus(int,J,K_1))).
% 2.23/2.37 all K_1 I J (ord_less_e_q(int,I,J)->ord_less_e_q(int,plus_plus(int,K_1,I),plus_plus(int,K_1,J))).
% 2.23/2.37 all V_1 V ((ord_less(int,V,pls)->plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,V_1))& (-ord_less(int,V,pls)-> (ord_less(int,V_1,pls)->plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,V))& (-ord_less(int,V_1,pls)->plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,plus_plus(int,V,V_1))))).
% 2.23/2.37 number_number_of(nat,bit1(pls))=one_one(nat).
% 2.23/2.37 one_one(nat)=number_number_of(nat,bit1(pls)).
% 2.23/2.37 all K (ord_less_e_q(int,bit1(K),pls)<->ord_less(int,K,pls)).
% 2.23/2.37 all K (ord_less(int,pls,bit1(K))<->ord_less_e_q(int,pls,K)).
% 2.23/2.37 all K1 K2 (ord_less_e_q(int,bit1(K1),bit0(K2))<->ord_less(int,K1,K2)).
% 2.23/2.37 all K L (ord_less_e_q(int,bit1(K),bit0(L))<->ord_less(int,K,L)).
% 2.23/2.37 all K1 K2 (ord_less(int,bit0(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)).
% 2.23/2.37 all K L (ord_less(int,bit0(K),bit1(L))<->ord_less_e_q(int,K,L)).
% 2.23/2.37 all W Z (ord_less(int,W,Z)->ord_less_e_q(int,plus_plus(int,W,one_one(int)),Z)).
% 2.23/2.37 all W_1 Z_1 (ord_less_e_q(int,plus_plus(int,W_1,one_one(int)),Z_1)<->ord_less(int,W_1,Z_1)).
% 2.23/2.37 all W_1 Z_1 (ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))<->ord_less_e_q(int,W_1,Z_1)).
% 2.23/2.37 zprime(number_number_of(int,bit0(bit1(pls)))).
% 2.23/2.37 all Y_1 X_1 (twoSqu33214720sum2sq(X_1)-> (twoSqu33214720sum2sq(Y_1)->twoSqu33214720sum2sq(times_times(int,X_1,Y_1)))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,times_times(X_a,Lx,Rx),times_times(X_a,Ly,Ry))))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,Rx,times_times(X_a,times_times(X_a,Lx,Ly),Ry))))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,Lx,times_times(X_a,Ly,times_times(X_a,Rx,Ry)))))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (times_times(X_a,times_times(X_a,Lx,Ly),Rx)=times_times(X_a,times_times(X_a,Lx,Rx),Ly)))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (times_times(X_a,times_times(X_a,Lx,Ly),Rx)=times_times(X_a,Lx,times_times(X_a,Ly,Rx))))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (times_times(X_a,Lx,times_times(X_a,Rx,Ry))=times_times(X_a,times_times(X_a,Lx,Rx),Ry)))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (times_times(X_a,Lx,times_times(X_a,Rx,Ry))=times_times(X_a,Rx,times_times(X_a,Lx,Ry))))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all A_1 B (times_times(X_a,A_1,B)=times_times(X_a,B,A_1)))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all A_1 B C D (plus_plus(X_a,plus_plus(X_a,A_1,B),plus_plus(X_a,C,D))=plus_plus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B,D))))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (plus_plus(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,plus_plus(X_a,A_1,C),B)))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (plus_plus(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,A_1,plus_plus(X_a,B,C))))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all A_1 C D (plus_plus(X_a,A_1,plus_plus(X_a,C,D))=plus_plus(X_a,plus_plus(X_a,A_1,C),D)))).
% 2.23/2.37 all X_a (comm_semiring_1(X_a)-> (all A_1 C D (plus_plus(X_a,A_1,plus_plus(X_a,C,D))=plus_plus(X_a,C,plus_plus(X_a,A_1,D))))).
% 2.23/2.38 all X_a (comm_semiring_1(X_a)-> (all A_1 C (plus_plus(X_a,A_1,C)=plus_plus(X_a,C,A_1)))).
% 2.23/2.38 all X_a (number_ring(X_a)&ring_char_0(X_a)-> (all X_2 Y_2 (number_number_of(X_a,X_2)=number_number_of(X_a,Y_2)<->X_2=Y_2))).
% 2.23/2.38 all X_a (number(X_a)-> (all W_1 X_2 (number_number_of(X_a,W_1)=ti(X_a,X_2)<->ti(X_a,X_2)=number_number_of(X_a,W_1)))).
% 2.23/2.38 all K L (bit1(K)=bit1(L)<->K=L).
% 2.23/2.38 all K L (bit0(K)=bit0(L)<->K=L).
% 2.23/2.38 all Z1 Z2 Z3 (times_times(int,times_times(int,Z1,Z2),Z3)=times_times(int,Z1,times_times(int,Z2,Z3))).
% 2.23/2.38 all Z W (times_times(int,Z,W)=times_times(int,W,Z)).
% 2.23/2.38 all K_1 (number_number_of(int,K_1)=K_1).
% 2.23/2.38 all Z1 Z2 Z3 (plus_plus(int,plus_plus(int,Z1,Z2),Z3)=plus_plus(int,Z1,plus_plus(int,Z2,Z3))).
% 2.23/2.38 all X_1 Y_1 Z (plus_plus(int,X_1,plus_plus(int,Y_1,Z))=plus_plus(int,Y_1,plus_plus(int,X_1,Z))).
% 2.23/2.38 all Z W (plus_plus(int,Z,W)=plus_plus(int,W,Z)).
% 2.23/2.38 all K (ord_less(int,bit1(K),pls)<->ord_less(int,K,pls)).
% 2.23/2.38 all K1 K2 (ord_less(int,bit1(K1),bit0(K2))<->ord_less(int,K1,K2)).
% 2.23/2.38 all K L (ord_less(int,bit1(K),bit0(L))<->ord_less(int,K,L)).
% 2.23/2.38 all K (ord_less(int,bit0(K),pls)<->ord_less(int,K,pls)).
% 2.23/2.38 all K (ord_less(int,pls,bit0(K))<->ord_less(int,pls,K)).
% 2.23/2.38 all K (ord_less_e_q(int,pls,bit1(K))<->ord_less_e_q(int,pls,K)).
% 2.23/2.38 all K1 K2 (ord_less_e_q(int,bit0(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)).
% 2.23/2.38 all K L (ord_less_e_q(int,bit0(K),bit1(L))<->ord_less_e_q(int,K,L)).
% 2.23/2.38 linordered_idom(int).
% 2.23/2.38 comm_semiring_1(int).
% 2.23/2.38 number_semiring(int).
% 2.23/2.38 linorder(int).
% 2.23/2.38 monoid_mult(int).
% 2.23/2.38 semiring_1(int).
% 2.23/2.38 ring_char_0(int).
% 2.23/2.38 number_ring(int).
% 2.23/2.38 number(int).
% 2.23/2.38 comm_semiring_1(nat).
% 2.23/2.38 number_semiring(nat).
% 2.23/2.38 linorder(nat).
% 2.23/2.38 monoid_mult(nat).
% 2.23/2.38 semiring_1(nat).
% 2.23/2.38 number(nat).
% 2.23/2.38 all T A (ti(T,ti(T,A))=ti(T,A)).
% 2.23/2.38 -(exists X Y (plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls)))))=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 2.23/2.38 end_of_list.
% 2.23/2.38
% 2.23/2.38 -------> usable clausifies to:
% 2.23/2.38
% 2.23/2.38 list(usable).
% 2.23/2.38 0 [] A=A.
% 2.23/2.38 0 [] -semiring_1(X_a)|ti(X_a,one_one(X_a))=one_one(X_a).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,ti(X_a,B_1),B_2)=plus_plus(X_a,B_1,B_2).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,B_1,ti(X_a,B_2))=plus_plus(X_a,B_1,B_2).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|ti(X_a,plus_plus(X_a,B_1,B_2))=plus_plus(X_a,B_1,B_2).
% 2.23/2.38 0 [] -monoid_mult(X_a)|times_times(X_a,ti(X_a,B_1),B_2)=times_times(X_a,B_1,B_2).
% 2.23/2.38 0 [] -monoid_mult(X_a)|times_times(X_a,B_1,ti(X_a,B_2))=times_times(X_a,B_1,B_2).
% 2.23/2.38 0 [] -monoid_mult(X_a)|ti(X_a,times_times(X_a,B_1,B_2))=times_times(X_a,B_1,B_2).
% 2.23/2.38 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 2.23/2.38 0 [] -zprime(ti(int,B_1))|zprime(B_1).
% 2.23/2.38 0 [] zprime(ti(int,B_1))| -zprime(B_1).
% 2.23/2.38 0 [] bit0(ti(int,B_1))=bit0(B_1).
% 2.23/2.38 0 [] ti(int,bit0(B_1))=bit0(B_1).
% 2.23/2.38 0 [] bit1(ti(int,B_1))=bit1(B_1).
% 2.23/2.38 0 [] ti(int,bit1(B_1))=bit1(B_1).
% 2.23/2.38 0 [] ti(int,pls)=pls.
% 2.23/2.38 0 [] -number(X_a)|number_number_of(X_a,ti(int,B_1))=number_number_of(X_a,B_1).
% 2.23/2.38 0 [] -number(X_a)|ti(X_a,number_number_of(X_a,B_1))=number_number_of(X_a,B_1).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)| -ord_less(X_a,ti(X_a,B_1),B_2)|ord_less(X_a,B_1,B_2).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)|ord_less(X_a,ti(X_a,B_1),B_2)| -ord_less(X_a,B_1,B_2).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)| -ord_less(X_a,B_1,ti(X_a,B_2))|ord_less(X_a,B_1,B_2).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)|ord_less(X_a,B_1,ti(X_a,B_2))| -ord_less(X_a,B_1,B_2).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)| -ord_less_e_q(X_a,ti(X_a,B_1),B_2)|ord_less_e_q(X_a,B_1,B_2).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)|ord_less_e_q(X_a,ti(X_a,B_1),B_2)| -ord_less_e_q(X_a,B_1,B_2).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)| -ord_less_e_q(X_a,B_1,ti(X_a,B_2))|ord_less_e_q(X_a,B_1,B_2).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)|ord_less_e_q(X_a,B_1,ti(X_a,B_2))| -ord_less_e_q(X_a,B_1,B_2).
% 2.23/2.38 0 [] -monoid_mult(X_a)|power_power(X_a,ti(X_a,B_1),B_2)=power_power(X_a,B_1,B_2).
% 2.23/2.38 0 [] -monoid_mult(X_a)|power_power(X_a,B_1,ti(nat,B_2))=power_power(X_a,B_1,B_2).
% 2.23/2.38 0 [] -monoid_mult(X_a)|ti(X_a,power_power(X_a,B_1,B_2))=power_power(X_a,B_1,B_2).
% 2.23/2.38 0 [] -twoSqu33214720sum2sq(ti(int,B_1))|twoSqu33214720sum2sq(B_1).
% 2.23/2.38 0 [] twoSqu33214720sum2sq(ti(int,B_1))| -twoSqu33214720sum2sq(B_1).
% 2.23/2.38 0 [] ti(int,m)=m.
% 2.23/2.38 0 [] ti(int,s)=s.
% 2.23/2.38 0 [] ti(int,t)=t.
% 2.23/2.38 0 [] ord_less_e_q(int,one_one(int),t).
% 2.23/2.38 0 [] t!=one_one(int)|plus_plus(int,power_power(int,$c2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,$c1,number_number_of(nat,bit0(bit1(pls)))))=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)).
% 2.23/2.38 0 [] -ord_less(int,one_one(int),t)|plus_plus(int,power_power(int,$c4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,$c3,number_number_of(nat,bit0(bit1(pls)))))=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)).
% 2.23/2.38 0 [] ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 2.23/2.38 0 [] zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 2.23/2.38 0 [] plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t).
% 2.23/2.38 0 [] twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)).
% 2.23/2.38 0 [] power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,plus_plus(int,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A_1),B)),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))).
% 2.23/2.38 0 [] power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,A_1,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,A_1,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls))))).
% 2.23/2.38 0 [] -number_semiring(X_a)|power_power(X_a,plus_plus(X_a,X_1,Y_1),number_number_of(nat,bit0(bit1(pls))))=plus_plus(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X_1),Y_1)).
% 2.23/2.38 0 [] -monoid_mult(X_b)| -number(X_b)|power_power(X_b,number_number_of(X_b,W),number_number_of(nat,bit0(bit1(pls))))=times_times(X_b,number_number_of(X_b,W),number_number_of(X_b,W)).
% 2.23/2.38 0 [] times_times(int,A_1,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))))=power_power(int,A_1,number_number_of(nat,bit1(bit1(pls)))).
% 2.23/2.38 0 [] -semiring_1(X_a)|power_power(X_a,one_one(X_a),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,X_1,X_1)=power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))).
% 2.23/2.38 0 [] -monoid_mult(X_a)|power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls))))=times_times(X_a,A_1,A_1).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|power_power(X_a,X_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=times_times(X_a,power_power(X_a,X_1,N),power_power(X_a,X_1,N)).
% 2.23/2.38 0 [] -number_ring(X_a)|plus_plus(X_a,one_one(X_a),number_number_of(X_a,W))=number_number_of(X_a,plus_plus(int,bit1(pls),W)).
% 2.23/2.38 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V),one_one(X_a))=number_number_of(X_a,plus_plus(int,V,bit1(pls))).
% 2.23/2.38 0 [] -number_ring(X_a)|plus_plus(X_a,one_one(X_a),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls))).
% 2.23/2.38 0 [] plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),$c5).
% 2.23/2.38 0 [] ord_less_e_q(int,W,W).
% 2.23/2.38 0 [] ord_less_e_q(int,Z,W)|ord_less_e_q(int,W,Z).
% 2.23/2.38 0 [] -ord_less(int,Z_1,W_1)|ord_less_e_q(int,Z_1,W_1).
% 2.23/2.38 0 [] -ord_less(int,Z_1,W_1)|Z_1!=W_1.
% 2.23/2.38 0 [] ord_less(int,Z_1,W_1)| -ord_less_e_q(int,Z_1,W_1)|Z_1=W_1.
% 2.23/2.38 0 [] ord_less(int,X_1,Y_1)|X_1=Y_1|ord_less(int,Y_1,X_1).
% 2.23/2.38 0 [] -ord_less_e_q(int,I,J)| -ord_less_e_q(int,J,K_1)|ord_less_e_q(int,I,K_1).
% 2.23/2.38 0 [] -ord_less_e_q(int,Z,W)| -ord_less_e_q(int,W,Z)|Z=W.
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|power_power(X_a,power_power(X_a,X_1,P),Q)=power_power(X_a,X_1,times_times(nat,P,Q)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|power_power(X_a,X_1,one_one(nat))=ti(X_a,X_1).
% 2.23/2.38 0 [] power_power(int,power_power(int,X_1,Y_1),Z)=power_power(int,X_1,times_times(nat,Y_1,Z)).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)| -ord_less_e_q(X_a,number_number_of(X_a,V_2),number_number_of(X_a,W_1))| -ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_2)).
% 2.23/2.38 0 [] -number(X_a)| -linorder(X_a)|ord_less_e_q(X_a,number_number_of(X_a,V_2),number_number_of(X_a,W_1))|ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_2)).
% 2.23/2.38 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))|ord_less(int,X_2,Y_2).
% 2.23/2.38 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))| -ord_less(int,X_2,Y_2).
% 2.23/2.38 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less_e_q(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))|ord_less_e_q(int,X_2,Y_2).
% 2.23/2.38 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less_e_q(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))| -ord_less_e_q(int,X_2,Y_2).
% 2.23/2.38 0 [] -ord_less(int,W_2,W)| -ord_less_e_q(int,Z_2,Z)|ord_less(int,plus_plus(int,W_2,Z_2),plus_plus(int,W,Z)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,power_power(X_a,X_1,P),power_power(X_a,X_1,Q))=power_power(X_a,X_1,plus_plus(nat,P,Q)).
% 2.23/2.38 0 [] power_power(int,X_1,plus_plus(nat,Y_1,Z))=times_times(int,power_power(int,X_1,Y_1),power_power(int,X_1,Z)).
% 2.23/2.38 0 [] times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z)=plus_plus(nat,Z,Z).
% 2.23/2.38 0 [] times_times(nat,Z,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,Z,Z).
% 2.23/2.38 0 [] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 2.23/2.38 0 [] -ord_less(int,bit1(K1),bit1(K2))|ord_less(int,K1,K2).
% 2.23/2.38 0 [] ord_less(int,bit1(K1),bit1(K2))| -ord_less(int,K1,K2).
% 2.23/2.38 0 [] -ord_less(int,bit1(K),bit1(L))|ord_less(int,K,L).
% 2.23/2.38 0 [] ord_less(int,bit1(K),bit1(L))| -ord_less(int,K,L).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit1(K1),bit1(K2))|ord_less_e_q(int,K1,K2).
% 2.23/2.38 0 [] ord_less_e_q(int,bit1(K1),bit1(K2))| -ord_less_e_q(int,K1,K2).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit1(K),bit1(L))|ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] ord_less_e_q(int,bit1(K),bit1(L))| -ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] -ord_less(int,pls,pls).
% 2.23/2.38 0 [] -ord_less(int,bit0(K1),bit0(K2))|ord_less(int,K1,K2).
% 2.23/2.38 0 [] ord_less(int,bit0(K1),bit0(K2))| -ord_less(int,K1,K2).
% 2.23/2.38 0 [] -ord_less(int,bit0(K),bit0(L))|ord_less(int,K,L).
% 2.23/2.38 0 [] ord_less(int,bit0(K),bit0(L))| -ord_less(int,K,L).
% 2.23/2.38 0 [] ord_less_e_q(int,pls,pls).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit0(K1),bit0(K2))|ord_less_e_q(int,K1,K2).
% 2.23/2.38 0 [] ord_less_e_q(int,bit0(K1),bit0(K2))| -ord_less_e_q(int,K1,K2).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit0(K),bit0(L))|ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] ord_less_e_q(int,bit0(K),bit0(L))| -ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] -ord_less(int,number_number_of(int,K),number_number_of(int,L))|ord_less(int,K,L).
% 2.23/2.38 0 [] ord_less(int,number_number_of(int,K),number_number_of(int,L))| -ord_less(int,K,L).
% 2.23/2.38 0 [] -ord_less_e_q(int,number_number_of(int,K),number_number_of(int,L))|ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] ord_less_e_q(int,number_number_of(int,K),number_number_of(int,L))| -ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] -ord_less(int,I,J)|ord_less(int,plus_plus(int,I,K_1),plus_plus(int,J,K_1)).
% 2.23/2.38 0 [] -ord_less_e_q(int,I,J)|ord_less_e_q(int,plus_plus(int,K_1,I),plus_plus(int,K_1,J)).
% 2.23/2.38 0 [] -ord_less(int,V,pls)|plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,V_1).
% 2.23/2.38 0 [] ord_less(int,V,pls)| -ord_less(int,V_1,pls)|plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,V).
% 2.23/2.38 0 [] ord_less(int,V,pls)|ord_less(int,V_1,pls)|plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,plus_plus(int,V,V_1)).
% 2.23/2.38 0 [] number_number_of(nat,bit1(pls))=one_one(nat).
% 2.23/2.38 0 [] one_one(nat)=number_number_of(nat,bit1(pls)).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit1(K),pls)|ord_less(int,K,pls).
% 2.23/2.38 0 [] ord_less_e_q(int,bit1(K),pls)| -ord_less(int,K,pls).
% 2.23/2.38 0 [] -ord_less(int,pls,bit1(K))|ord_less_e_q(int,pls,K).
% 2.23/2.38 0 [] ord_less(int,pls,bit1(K))| -ord_less_e_q(int,pls,K).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit1(K1),bit0(K2))|ord_less(int,K1,K2).
% 2.23/2.38 0 [] ord_less_e_q(int,bit1(K1),bit0(K2))| -ord_less(int,K1,K2).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit1(K),bit0(L))|ord_less(int,K,L).
% 2.23/2.38 0 [] ord_less_e_q(int,bit1(K),bit0(L))| -ord_less(int,K,L).
% 2.23/2.38 0 [] -ord_less(int,bit0(K1),bit1(K2))|ord_less_e_q(int,K1,K2).
% 2.23/2.38 0 [] ord_less(int,bit0(K1),bit1(K2))| -ord_less_e_q(int,K1,K2).
% 2.23/2.38 0 [] -ord_less(int,bit0(K),bit1(L))|ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] ord_less(int,bit0(K),bit1(L))| -ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] -ord_less(int,W,Z)|ord_less_e_q(int,plus_plus(int,W,one_one(int)),Z).
% 2.23/2.38 0 [] -ord_less_e_q(int,plus_plus(int,W_1,one_one(int)),Z_1)|ord_less(int,W_1,Z_1).
% 2.23/2.38 0 [] ord_less_e_q(int,plus_plus(int,W_1,one_one(int)),Z_1)| -ord_less(int,W_1,Z_1).
% 2.23/2.38 0 [] -ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))|ord_less_e_q(int,W_1,Z_1).
% 2.23/2.38 0 [] ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))| -ord_less_e_q(int,W_1,Z_1).
% 2.23/2.38 0 [] zprime(number_number_of(int,bit0(bit1(pls)))).
% 2.23/2.38 0 [] -twoSqu33214720sum2sq(X_1)| -twoSqu33214720sum2sq(Y_1)|twoSqu33214720sum2sq(times_times(int,X_1,Y_1)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,times_times(X_a,Lx,Rx),times_times(X_a,Ly,Ry)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,Rx,times_times(X_a,times_times(X_a,Lx,Ly),Ry)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,Lx,times_times(X_a,Ly,times_times(X_a,Rx,Ry))).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),Rx)=times_times(X_a,times_times(X_a,Lx,Rx),Ly).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),Rx)=times_times(X_a,Lx,times_times(X_a,Ly,Rx)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,Lx,times_times(X_a,Rx,Ry))=times_times(X_a,times_times(X_a,Lx,Rx),Ry).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,Lx,times_times(X_a,Rx,Ry))=times_times(X_a,Rx,times_times(X_a,Lx,Ry)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,B)=times_times(X_a,B,A_1).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B),plus_plus(X_a,C,D))=plus_plus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B,D)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,plus_plus(X_a,A_1,C),B).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,A_1,plus_plus(X_a,B,C)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,plus_plus(X_a,C,D))=plus_plus(X_a,plus_plus(X_a,A_1,C),D).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,plus_plus(X_a,C,D))=plus_plus(X_a,C,plus_plus(X_a,A_1,D)).
% 2.23/2.38 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,C)=plus_plus(X_a,C,A_1).
% 2.23/2.38 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,X_2)!=number_number_of(X_a,Y_2)|X_2=Y_2.
% 2.23/2.38 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,X_2)=number_number_of(X_a,Y_2)|X_2!=Y_2.
% 2.23/2.38 0 [] -number(X_a)|number_number_of(X_a,W_1)!=ti(X_a,X_2)|ti(X_a,X_2)=number_number_of(X_a,W_1).
% 2.23/2.38 0 [] -number(X_a)|number_number_of(X_a,W_1)=ti(X_a,X_2)|ti(X_a,X_2)!=number_number_of(X_a,W_1).
% 2.23/2.38 0 [] bit1(K)!=bit1(L)|K=L.
% 2.23/2.38 0 [] bit1(K)=bit1(L)|K!=L.
% 2.23/2.38 0 [] bit0(K)!=bit0(L)|K=L.
% 2.23/2.38 0 [] bit0(K)=bit0(L)|K!=L.
% 2.23/2.38 0 [] times_times(int,times_times(int,Z1,Z2),Z3)=times_times(int,Z1,times_times(int,Z2,Z3)).
% 2.23/2.38 0 [] times_times(int,Z,W)=times_times(int,W,Z).
% 2.23/2.38 0 [] number_number_of(int,K_1)=K_1.
% 2.23/2.38 0 [] plus_plus(int,plus_plus(int,Z1,Z2),Z3)=plus_plus(int,Z1,plus_plus(int,Z2,Z3)).
% 2.23/2.38 0 [] plus_plus(int,X_1,plus_plus(int,Y_1,Z))=plus_plus(int,Y_1,plus_plus(int,X_1,Z)).
% 2.23/2.38 0 [] plus_plus(int,Z,W)=plus_plus(int,W,Z).
% 2.23/2.38 0 [] -ord_less(int,bit1(K),pls)|ord_less(int,K,pls).
% 2.23/2.38 0 [] ord_less(int,bit1(K),pls)| -ord_less(int,K,pls).
% 2.23/2.38 0 [] -ord_less(int,bit1(K1),bit0(K2))|ord_less(int,K1,K2).
% 2.23/2.38 0 [] ord_less(int,bit1(K1),bit0(K2))| -ord_less(int,K1,K2).
% 2.23/2.38 0 [] -ord_less(int,bit1(K),bit0(L))|ord_less(int,K,L).
% 2.23/2.38 0 [] ord_less(int,bit1(K),bit0(L))| -ord_less(int,K,L).
% 2.23/2.38 0 [] -ord_less(int,bit0(K),pls)|ord_less(int,K,pls).
% 2.23/2.38 0 [] ord_less(int,bit0(K),pls)| -ord_less(int,K,pls).
% 2.23/2.38 0 [] -ord_less(int,pls,bit0(K))|ord_less(int,pls,K).
% 2.23/2.38 0 [] ord_less(int,pls,bit0(K))| -ord_less(int,pls,K).
% 2.23/2.38 0 [] -ord_less_e_q(int,pls,bit1(K))|ord_less_e_q(int,pls,K).
% 2.23/2.38 0 [] ord_less_e_q(int,pls,bit1(K))| -ord_less_e_q(int,pls,K).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit0(K1),bit1(K2))|ord_less_e_q(int,K1,K2).
% 2.23/2.38 0 [] ord_less_e_q(int,bit0(K1),bit1(K2))| -ord_less_e_q(int,K1,K2).
% 2.23/2.38 0 [] -ord_less_e_q(int,bit0(K),bit1(L))|ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] ord_less_e_q(int,bit0(K),bit1(L))| -ord_less_e_q(int,K,L).
% 2.23/2.38 0 [] linordered_idom(int).
% 2.23/2.38 0 [] comm_semiring_1(int).
% 2.23/2.38 0 [] number_semiring(int).
% 2.23/2.38 0 [] linorder(int).
% 2.23/2.38 0 [] monoid_mult(int).
% 2.23/2.38 0 [] semiring_1(int).
% 2.23/2.38 0 [] ring_char_0(int).
% 2.23/2.38 0 [] number_ring(int).
% 2.23/2.38 0 [] number(int).
% 2.23/2.38 0 [] comm_semiring_1(nat).
% 2.23/2.38 0 [] number_semiring(nat).
% 2.23/2.38 0 [] linorder(nat).
% 2.23/2.38 0 [] monoid_mult(nat).
% 2.23/2.38 0 [] semiring_1(nat).
% 2.23/2.38 0 [] number(nat).
% 2.23/2.38 0 [] ti(T,ti(T,A))=ti(T,A).
% 2.23/2.38 0 [] plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls)))))!=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)).
% 2.23/2.38 end_of_list.
% 2.23/2.38
% 2.23/2.38 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.23/2.38
% 2.23/2.38 This ia a non-Horn set with equality. The strategy will be
% 2.23/2.38 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.23/2.38 deletion, with positive clauses in sos and nonpositive
% 2.23/2.38 clauses in usable.
% 2.23/2.38
% 2.23/2.38 dependent: set(knuth_bendix).
% 2.23/2.38 dependent: set(anl_eq).
% 2.23/2.38 dependent: set(para_from).
% 2.23/2.38 dependent: set(para_into).
% 2.23/2.38 dependent: clear(para_from_right).
% 2.23/2.38 dependent: clear(para_into_right).
% 2.23/2.38 dependent: set(para_from_vars).
% 2.23/2.38 dependent: set(eq_units_both_ways).
% 2.23/2.38 dependent: set(dynamic_demod_all).
% 2.23/2.38 dependent: set(dynamic_demod).
% 2.23/2.38 dependent: set(order_eq).
% 2.23/2.38 dependent: set(back_demod).
% 2.23/2.38 dependent: set(lrpo).
% 2.23/2.38 dependent: set(hyper_res).
% 2.23/2.38 dependent: set(unit_deletion).
% 2.23/2.38 dependent: set(factor).
% 2.23/2.38
% 2.23/2.38 ------------> process usable:
% 2.23/2.38 ** KEPT (pick-wt=9): 1 [] -semiring_1(A)|ti(A,one_one(A))=one_one(A).
% 2.23/2.38 ** KEPT (pick-wt=13): 2 [] -comm_semiring_1(A)|plus_plus(A,ti(A,B),C)=plus_plus(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=13): 3 [] -comm_semiring_1(A)|plus_plus(A,B,ti(A,C))=plus_plus(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=13): 4 [] -comm_semiring_1(A)|ti(A,plus_plus(A,B,C))=plus_plus(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=13): 5 [] -monoid_mult(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=13): 6 [] -monoid_mult(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=13): 7 [] -monoid_mult(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=6): 8 [] -zprime(ti(int,A))|zprime(A).
% 2.23/2.38 ** KEPT (pick-wt=6): 9 [] zprime(ti(int,A))| -zprime(A).
% 2.23/2.38 ** KEPT (pick-wt=11): 10 [] -number(A)|number_number_of(A,ti(int,B))=number_number_of(A,B).
% 2.23/2.38 ** KEPT (pick-wt=11): 11 [] -number(A)|ti(A,number_number_of(A,B))=number_number_of(A,B).
% 2.23/2.38 ** KEPT (pick-wt=14): 12 [] -number(A)| -linorder(A)| -ord_less(A,ti(A,B),C)|ord_less(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=14): 13 [] -number(A)| -linorder(A)|ord_less(A,ti(A,B),C)| -ord_less(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=14): 14 [] -number(A)| -linorder(A)| -ord_less(A,B,ti(A,C))|ord_less(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=14): 15 [] -number(A)| -linorder(A)|ord_less(A,B,ti(A,C))| -ord_less(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=14): 16 [] -number(A)| -linorder(A)| -ord_less_e_q(A,ti(A,B),C)|ord_less_e_q(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=14): 17 [] -number(A)| -linorder(A)|ord_less_e_q(A,ti(A,B),C)| -ord_less_e_q(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=14): 18 [] -number(A)| -linorder(A)| -ord_less_e_q(A,B,ti(A,C))|ord_less_e_q(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=14): 19 [] -number(A)| -linorder(A)|ord_less_e_q(A,B,ti(A,C))| -ord_less_e_q(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=13): 20 [] -monoid_mult(A)|power_power(A,ti(A,B),C)=power_power(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=13): 21 [] -monoid_mult(A)|power_power(A,B,ti(nat,C))=power_power(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=13): 22 [] -monoid_mult(A)|ti(A,power_power(A,B,C))=power_power(A,B,C).
% 2.23/2.38 ** KEPT (pick-wt=6): 23 [] -twoSqu33214720sum2sq(ti(int,A))|twoSqu33214720sum2sq(A).
% 2.23/2.38 ** KEPT (pick-wt=6): 24 [] twoSqu33214720sum2sq(ti(int,A))| -twoSqu33214720sum2sq(A).
% 2.23/2.38 ** KEPT (pick-wt=36): 26 [copy,25,flip.1,flip.2] one_one(int)!=t|plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))=plus_plus(int,power_power(int,$c2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,$c1,number_number_of(nat,bit0(bit1(pls))))).
% 2.23/2.38 ** KEPT (pick-wt=37): 28 [copy,27,flip.2] -ord_less(int,one_one(int),t)|plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))=plus_plus(int,power_power(int,$c4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,$c3,number_number_of(nat,bit0(bit1(pls))))).
% 2.23/2.38 ** KEPT (pick-wt=45): 29 [] -number_semiring(A)|power_power(A,plus_plus(A,B,C),number_number_of(nat,bit0(bit1(pls))))=plus_plus(A,plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls))))),times_times(A,times_times(A,number_number_of(A,bit0(bit1(pls))),B),C)).
% 2.23/2.38 ** KEPT (pick-wt=23): 30 [] -monoid_mult(A)| -number(A)|power_power(A,number_number_of(A,B),number_number_of(nat,bit0(bit1(pls))))=times_times(A,number_number_of(A,B),number_number_of(A,B)).
% 2.23/2.38 ** KEPT (pick-wt=14): 31 [] -semiring_1(A)|power_power(A,one_one(A),number_number_of(nat,bit0(bit1(pls))))=one_one(A).
% 2.23/2.38 ** KEPT (pick-wt=15): 32 [] -comm_semiring_1(A)|times_times(A,B,B)=power_power(A,B,number_number_of(nat,bit0(bit1(pls)))).
% 2.23/2.38 ** KEPT (pick-wt=15): 33 [] -monoid_mult(A)|power_power(A,B,number_number_of(nat,bit0(bit1(pls))))=times_times(A,B,B).
% 2.23/2.38 ** KEPT (pick-wt=24): 34 [] -comm_semiring_1(A)|power_power(A,B,times_times(nat,number_number_of(nat,bit0(bit1(pls))),C))=times_times(A,power_power(A,B,C),power_power(A,B,C)).
% 2.23/2.38 ** KEPT (pick-wt=17): 35 [] -number_ring(A)|plus_plus(A,one_one(A),number_number_of(A,B))=number_number_of(A,plus_plus(int,bit1(pls),B)).
% 2.23/2.38 ** KEPT (pick-wt=17): 36 [] -number_ring(A)|plus_plus(A,number_number_of(A,B),one_one(A))=number_number_of(A,plus_plus(int,B,bit1(pls))).
% 2.23/2.38 ** KEPT (pick-wt=14): 37 [] -number_ring(A)|plus_plus(A,one_one(A),one_one(A))=number_number_of(A,bit0(bit1(pls))).
% 2.23/2.38 ** KEPT (pick-wt=8): 38 [] -ord_less(int,A,B)|ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=7): 39 [] -ord_less(int,A,B)|A!=B.
% 2.23/2.38 ** KEPT (pick-wt=11): 40 [] ord_less(int,A,B)| -ord_less_e_q(int,A,B)|A=B.
% 2.23/2.38 ** KEPT (pick-wt=12): 41 [] -ord_less_e_q(int,A,B)| -ord_less_e_q(int,B,C)|ord_less_e_q(int,A,C).
% 2.23/2.38 ** KEPT (pick-wt=11): 42 [] -ord_less_e_q(int,A,B)| -ord_less_e_q(int,B,A)|A=B.
% 2.23/2.38 ** KEPT (pick-wt=17): 43 [] -comm_semiring_1(A)|power_power(A,power_power(A,B,C),D)=power_power(A,B,times_times(nat,C,D)).
% 2.23/2.38 ** KEPT (pick-wt=11): 44 [] -comm_semiring_1(A)|power_power(A,B,one_one(nat))=ti(A,B).
% 2.23/2.38 ** KEPT (pick-wt=20): 45 [] -number(A)| -linorder(A)| -ord_less_e_q(A,number_number_of(A,B),number_number_of(A,C))| -ord_less(A,number_number_of(A,C),number_number_of(A,B)).
% 2.23/2.38 ** KEPT (pick-wt=20): 46 [] -number(A)| -linorder(A)|ord_less_e_q(A,number_number_of(A,B),number_number_of(A,C))|ord_less(A,number_number_of(A,C),number_number_of(A,B)).
% 2.23/2.38 ** KEPT (pick-wt=16): 47 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,number_number_of(A,B),number_number_of(A,C))|ord_less(int,B,C).
% 2.23/2.38 ** KEPT (pick-wt=16): 48 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,number_number_of(A,B),number_number_of(A,C))| -ord_less(int,B,C).
% 2.23/2.38 ** KEPT (pick-wt=16): 49 [] -number_ring(A)| -linordered_idom(A)| -ord_less_e_q(A,number_number_of(A,B),number_number_of(A,C))|ord_less_e_q(int,B,C).
% 2.23/2.38 ** KEPT (pick-wt=16): 50 [] -number_ring(A)| -linordered_idom(A)|ord_less_e_q(A,number_number_of(A,B),number_number_of(A,C))| -ord_less_e_q(int,B,C).
% 2.23/2.38 ** KEPT (pick-wt=18): 51 [] -ord_less(int,A,B)| -ord_less_e_q(int,C,D)|ord_less(int,plus_plus(int,A,C),plus_plus(int,B,D)).
% 2.23/2.38 ** KEPT (pick-wt=20): 52 [] -comm_semiring_1(A)|times_times(A,power_power(A,B,C),power_power(A,B,D))=power_power(A,B,plus_plus(nat,C,D)).
% 2.23/2.38 ** KEPT (pick-wt=10): 53 [] -ord_less(int,bit1(A),bit1(B))|ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 54 [] ord_less(int,bit1(A),bit1(B))| -ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 53 during input processing: 0 [] -ord_less(int,bit1(A),bit1(B))|ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 54 during input processing: 0 [] ord_less(int,bit1(A),bit1(B))| -ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 55 [] -ord_less_e_q(int,bit1(A),bit1(B))|ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 56 [] ord_less_e_q(int,bit1(A),bit1(B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 Following clause subsumed by 55 during input processing: 0 [] -ord_less_e_q(int,bit1(A),bit1(B))|ord_less_e_q(int,A,B).
% 2.23/2.38 Following clause subsumed by 56 during input processing: 0 [] ord_less_e_q(int,bit1(A),bit1(B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=4): 57 [] -ord_less(int,pls,pls).
% 2.23/2.38 ** KEPT (pick-wt=10): 58 [] -ord_less(int,bit0(A),bit0(B))|ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 59 [] ord_less(int,bit0(A),bit0(B))| -ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 58 during input processing: 0 [] -ord_less(int,bit0(A),bit0(B))|ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 59 during input processing: 0 [] ord_less(int,bit0(A),bit0(B))| -ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 60 [] -ord_less_e_q(int,bit0(A),bit0(B))|ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 61 [] ord_less_e_q(int,bit0(A),bit0(B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 Following clause subsumed by 60 during input processing: 0 [] -ord_less_e_q(int,bit0(A),bit0(B))|ord_less_e_q(int,A,B).
% 2.23/2.38 Following clause subsumed by 61 during input processing: 0 [] ord_less_e_q(int,bit0(A),bit0(B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=12): 62 [] -ord_less(int,number_number_of(int,A),number_number_of(int,B))|ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=12): 63 [] ord_less(int,number_number_of(int,A),number_number_of(int,B))| -ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=12): 64 [] -ord_less_e_q(int,number_number_of(int,A),number_number_of(int,B))|ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=12): 65 [] ord_less_e_q(int,number_number_of(int,A),number_number_of(int,B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=14): 66 [] -ord_less(int,A,B)|ord_less(int,plus_plus(int,A,C),plus_plus(int,B,C)).
% 2.23/2.38 ** KEPT (pick-wt=14): 67 [] -ord_less_e_q(int,A,B)|ord_less_e_q(int,plus_plus(int,C,A),plus_plus(int,C,B)).
% 2.23/2.38 ** KEPT (pick-wt=16): 68 [] -ord_less(int,A,pls)|plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B))=number_number_of(nat,B).
% 2.23/2.38 ** KEPT (pick-wt=20): 69 [] ord_less(int,A,pls)| -ord_less(int,B,pls)|plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B))=number_number_of(nat,A).
% 2.23/2.38 ** KEPT (pick-wt=9): 70 [] -ord_less_e_q(int,bit1(A),pls)|ord_less(int,A,pls).
% 2.23/2.38 ** KEPT (pick-wt=9): 71 [] ord_less_e_q(int,bit1(A),pls)| -ord_less(int,A,pls).
% 2.23/2.38 ** KEPT (pick-wt=9): 72 [] -ord_less(int,pls,bit1(A))|ord_less_e_q(int,pls,A).
% 2.23/2.38 ** KEPT (pick-wt=9): 73 [] ord_less(int,pls,bit1(A))| -ord_less_e_q(int,pls,A).
% 2.23/2.38 ** KEPT (pick-wt=10): 74 [] -ord_less_e_q(int,bit1(A),bit0(B))|ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 75 [] ord_less_e_q(int,bit1(A),bit0(B))| -ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 74 during input processing: 0 [] -ord_less_e_q(int,bit1(A),bit0(B))|ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 75 during input processing: 0 [] ord_less_e_q(int,bit1(A),bit0(B))| -ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 76 [] -ord_less(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 77 [] ord_less(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 Following clause subsumed by 76 during input processing: 0 [] -ord_less(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B).
% 2.23/2.38 Following clause subsumed by 77 during input processing: 0 [] ord_less(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=12): 78 [] -ord_less(int,A,B)|ord_less_e_q(int,plus_plus(int,A,one_one(int)),B).
% 2.23/2.38 ** KEPT (pick-wt=12): 79 [] -ord_less_e_q(int,plus_plus(int,A,one_one(int)),B)|ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 78 during input processing: 0 [] ord_less_e_q(int,plus_plus(int,A,one_one(int)),B)| -ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=12): 80 [] -ord_less(int,A,plus_plus(int,B,one_one(int)))|ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=12): 81 [] ord_less(int,A,plus_plus(int,B,one_one(int)))| -ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=9): 82 [] -twoSqu33214720sum2sq(A)| -twoSqu33214720sum2sq(B)|twoSqu33214720sum2sq(times_times(int,A,B)).
% 2.23/2.38 ** KEPT (pick-wt=23): 83 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),times_times(A,D,E))=times_times(A,times_times(A,B,D),times_times(A,C,E)).
% 2.23/2.38 ** KEPT (pick-wt=23): 84 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),times_times(A,D,E))=times_times(A,D,times_times(A,times_times(A,B,C),E)).
% 2.23/2.38 ** KEPT (pick-wt=23): 85 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),times_times(A,D,E))=times_times(A,B,times_times(A,C,times_times(A,D,E))).
% 2.23/2.38 ** KEPT (pick-wt=17): 86 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,times_times(A,B,D),C).
% 2.23/2.38 ** KEPT (pick-wt=17): 87 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,B,times_times(A,C,D)).
% 2.23/2.38 Following clause subsumed by 87 during input processing: 0 [flip.2] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,B,times_times(A,C,D)).
% 2.23/2.38 ** KEPT (pick-wt=17): 88 [] -comm_semiring_1(A)|times_times(A,B,times_times(A,C,D))=times_times(A,C,times_times(A,B,D)).
% 2.23/2.38 ** KEPT (pick-wt=11): 89 [] -comm_semiring_1(A)|times_times(A,B,C)=times_times(A,C,B).
% 2.23/2.38 ** KEPT (pick-wt=23): 90 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),plus_plus(A,D,E))=plus_plus(A,plus_plus(A,B,D),plus_plus(A,C,E)).
% 2.23/2.38 ** KEPT (pick-wt=17): 91 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,plus_plus(A,B,D),C).
% 2.23/2.38 ** KEPT (pick-wt=17): 92 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)).
% 2.23/2.38 Following clause subsumed by 92 during input processing: 0 [flip.2] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)).
% 2.23/2.38 ** KEPT (pick-wt=17): 93 [] -comm_semiring_1(A)|plus_plus(A,B,plus_plus(A,C,D))=plus_plus(A,C,plus_plus(A,B,D)).
% 2.23/2.38 ** KEPT (pick-wt=11): 94 [] -comm_semiring_1(A)|plus_plus(A,B,C)=plus_plus(A,C,B).
% 2.23/2.38 ** KEPT (pick-wt=14): 95 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)!=number_number_of(A,C)|B=C.
% 2.23/2.38 ** KEPT (pick-wt=14): 96 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)=number_number_of(A,C)|B!=C.
% 2.23/2.38 ** KEPT (pick-wt=16): 97 [] -number(A)|number_number_of(A,B)!=ti(A,C)|ti(A,C)=number_number_of(A,B).
% 2.23/2.38 ** KEPT (pick-wt=16): 98 [] -number(A)|number_number_of(A,B)=ti(A,C)|ti(A,C)!=number_number_of(A,B).
% 2.23/2.38 ** KEPT (pick-wt=8): 99 [] bit1(A)!=bit1(B)|A=B.
% 2.23/2.38 ** KEPT (pick-wt=8): 100 [] bit1(A)=bit1(B)|A!=B.
% 2.23/2.38 ** KEPT (pick-wt=8): 101 [] bit0(A)!=bit0(B)|A=B.
% 2.23/2.38 ** KEPT (pick-wt=8): 102 [] bit0(A)=bit0(B)|A!=B.
% 2.23/2.38 ** KEPT (pick-wt=9): 103 [] -ord_less(int,bit1(A),pls)|ord_less(int,A,pls).
% 2.23/2.38 ** KEPT (pick-wt=9): 104 [] ord_less(int,bit1(A),pls)| -ord_less(int,A,pls).
% 2.23/2.38 ** KEPT (pick-wt=10): 105 [] -ord_less(int,bit1(A),bit0(B))|ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 106 [] ord_less(int,bit1(A),bit0(B))| -ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 105 during input processing: 0 [] -ord_less(int,bit1(A),bit0(B))|ord_less(int,A,B).
% 2.23/2.38 Following clause subsumed by 106 during input processing: 0 [] ord_less(int,bit1(A),bit0(B))| -ord_less(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=9): 107 [] -ord_less(int,bit0(A),pls)|ord_less(int,A,pls).
% 2.23/2.38 ** KEPT (pick-wt=9): 108 [] ord_less(int,bit0(A),pls)| -ord_less(int,A,pls).
% 2.23/2.38 ** KEPT (pick-wt=9): 109 [] -ord_less(int,pls,bit0(A))|ord_less(int,pls,A).
% 2.23/2.38 ** KEPT (pick-wt=9): 110 [] ord_less(int,pls,bit0(A))| -ord_less(int,pls,A).
% 2.23/2.38 ** KEPT (pick-wt=9): 111 [] -ord_less_e_q(int,pls,bit1(A))|ord_less_e_q(int,pls,A).
% 2.23/2.38 ** KEPT (pick-wt=9): 112 [] ord_less_e_q(int,pls,bit1(A))| -ord_less_e_q(int,pls,A).
% 2.23/2.38 ** KEPT (pick-wt=10): 113 [] -ord_less_e_q(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=10): 114 [] ord_less_e_q(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 Following clause subsumed by 113 during input processing: 0 [] -ord_less_e_q(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B).
% 2.23/2.38 Following clause subsumed by 114 during input processing: 0 [] ord_less_e_q(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B).
% 2.23/2.38 ** KEPT (pick-wt=32): 115 [] plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))!=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)).
% 2.23/2.38 33 back subsumes 30.
% 2.23/2.38 87 back subsumes 85.
% 2.23/2.38 88 back subsumes 84.
% 2.23/2.38 ** KEPT (pick-wt=32): 118 [copy,115,flip.1] plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))!=plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))).
% 2.23/2.38 Following clause subsumed by 115 during input processing: 0 [copy,118,flip.1] plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))!=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)).
% 2.23/2.38
% 2.23/2.38 ------------> process sos:
% 2.23/2.38 ** KEPT (pick-wt=3): 119 [] A=A.
% 2.23/2.38 ** KEPT (pick-wt=7): 120 [] ti(A,undefined(A))=undefined(A).
% 2.23/2.38 ---> New Demodulator: 121 [new_demod,120] ti(A,undefined(A))=undefined(A).
% 2.23/2.38 ** KEPT (pick-wt=7): 122 [] bit0(ti(int,A))=bit0(A).
% 2.23/2.38 ---> New Demodulator: 123 [new_demod,122] bit0(ti(int,A))=bit0(A).
% 2.23/2.38 ** KEPT (pick-wt=7): 124 [] ti(int,bit0(A))=bit0(A).
% 2.23/2.38 ---> New Demodulator: 125 [new_demod,124] ti(int,bit0(A))=bit0(A).
% 2.23/2.38 ** KEPT (pick-wt=7): 126 [] bit1(ti(int,A))=bit1(A).
% 2.23/2.38 ---> New Demodulator: 127 [new_demod,126] bit1(ti(int,A))=bit1(A).
% 2.23/2.38 ** KEPT (pick-wt=7): 128 [] ti(int,bit1(A))=bit1(A).
% 2.23/2.38 ---> New Demodulator: 129 [new_demod,128] ti(int,bit1(A))=bit1(A).
% 2.23/2.38 ** KEPT (pick-wt=5): 130 [] ti(int,pls)=pls.
% 2.23/2.38 ---> New Demodulator: 131 [new_demod,130] ti(int,pls)=pls.
% 2.23/2.38 ** KEPT (pick-wt=5): 132 [] ti(int,m)=m.
% 2.23/2.38 ---> New Demodulator: 133 [new_demod,132] ti(int,m)=m.
% 2.23/2.38 ** KEPT (pick-wt=5): 134 [] ti(int,s)=s.
% 2.23/2.38 ---> New Demodulator: 135 [new_demod,134] ti(int,s)=s.
% 2.23/2.38 ** KEPT (pick-wt=5): 136 [] ti(int,t)=t.
% 2.23/2.38 ---> New Demodulator: 137 [new_demod,136] ti(int,t)=t.
% 2.23/2.38 ** KEPT (pick-wt=5): 138 [] ord_less_e_q(int,one_one(int),t).
% 2.23/2.38 ** KEPT (pick-wt=16): 139 [] ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 2.23/2.38 ** KEPT (pick-wt=14): 140 [] zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 2.23/2.38 ** KEPT (pick-wt=29): 142 [copy,141,flip.1] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 2.23/2.38 ---> New Demodulator: 143 [new_demod,142] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 2.23/2.38 ** KEPT (pick-wt=13): 145 [copy,144,demod,143] twoSqu33214720sum2sq(plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))).
% 2.23/2.38 ** KEPT (pick-wt=43): 146 [] power_power(int,plus_plus(int,A,B),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A),B)),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))).
% 2.23/2.38 ** KEPT (pick-wt=70): 147 [] power_power(int,plus_plus(int,A,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,A,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,A,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls))))).
% 2.23/2.38 ** KEPT (pick-wt=20): 148 [] times_times(int,A,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))))=power_power(int,A,number_number_of(nat,bit1(bit1(pls)))).
% 2.23/2.38 ** KEPT (pick-wt=29): 150 [copy,149,flip.1] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),$c5)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 2.23/2.38 ---> New Demodulator: 151 [new_demod,150] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),$c5)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 2.23/2.39 ** KEPT (pick-wt=4): 152 [] ord_less_e_q(int,A,A).
% 2.23/2.39 ** KEPT (pick-wt=8): 153 [] ord_less_e_q(int,A,B)|ord_less_e_q(int,B,A).
% 2.23/2.39 ** KEPT (pick-wt=11): 154 [] ord_less(int,A,B)|A=B|ord_less(int,B,A).
% 2.23/2.39 ** KEPT (pick-wt=15): 155 [] power_power(int,power_power(int,A,B),C)=power_power(int,A,times_times(nat,B,C)).
% 2.23/2.39 ** KEPT (pick-wt=18): 157 [copy,156,flip.1] times_times(int,power_power(int,A,B),power_power(int,A,C))=power_power(int,A,plus_plus(nat,B,C)).
% 2.23/2.39 ---> New Demodulator: 158 [new_demod,157] times_times(int,power_power(int,A,B),power_power(int,A,C))=power_power(int,A,plus_plus(nat,B,C)).
% 2.23/2.39 ** KEPT (pick-wt=13): 159 [] times_times(nat,number_number_of(nat,bit0(bit1(pls))),A)=plus_plus(nat,A,A).
% 2.23/2.39 ---> New Demodulator: 160 [new_demod,159] times_times(nat,number_number_of(nat,bit0(bit1(pls))),A)=plus_plus(nat,A,A).
% 2.23/2.39 ** KEPT (pick-wt=13): 161 [] times_times(nat,A,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,A,A).
% 2.23/2.39 ---> New Demodulator: 162 [new_demod,161] times_times(nat,A,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,A,A).
% 2.23/2.39 ** KEPT (pick-wt=12): 163 [] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 2.23/2.39 ---> New Demodulator: 164 [new_demod,163] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 2.23/2.39 Following clause subsumed by 152 during input processing: 0 [] ord_less_e_q(int,pls,pls).
% 2.23/2.39 ** KEPT (pick-wt=23): 166 [copy,165,flip.3] ord_less(int,A,pls)|ord_less(int,B,pls)|number_number_of(nat,plus_plus(int,A,B))=plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B)).
% 2.23/2.39 ** KEPT (pick-wt=7): 168 [copy,167,flip.1] one_one(nat)=number_number_of(nat,bit1(pls)).
% 2.23/2.39 ---> New Demodulator: 169 [new_demod,168] one_one(nat)=number_number_of(nat,bit1(pls)).
% 2.23/2.39 Following clause subsumed by 119 during input processing: 0 [demod,169] number_number_of(nat,bit1(pls))=number_number_of(nat,bit1(pls)).
% 2.23/2.39 ** KEPT (pick-wt=6): 170 [] zprime(number_number_of(int,bit0(bit1(pls)))).
% 2.23/2.39 ** KEPT (pick-wt=15): 171 [] times_times(int,times_times(int,A,B),C)=times_times(int,A,times_times(int,B,C)).
% 2.23/2.39 ---> New Demodulator: 172 [new_demod,171] times_times(int,times_times(int,A,B),C)=times_times(int,A,times_times(int,B,C)).
% 2.23/2.39 ** KEPT (pick-wt=9): 173 [] times_times(int,A,B)=times_times(int,B,A).
% 2.23/2.39 ** KEPT (pick-wt=5): 174 [] number_number_of(int,A)=A.
% 2.23/2.39 ---> New Demodulator: 175 [new_demod,174] number_number_of(int,A)=A.
% 2.23/2.39 ** KEPT (pick-wt=15): 176 [] plus_plus(int,plus_plus(int,A,B),C)=plus_plus(int,A,plus_plus(int,B,C)).
% 2.23/2.39 ---> New Demodulator: 177 [new_demod,176] plus_plus(int,plus_plus(int,A,B),C)=plus_plus(int,A,plus_plus(int,B,C)).
% 2.23/2.39 ** KEPT (pick-wt=15): 178 [] plus_plus(int,A,plus_plus(int,B,C))=plus_plus(int,B,plus_plus(int,A,C)).
% 2.23/2.39 ** KEPT (pick-wt=9): 179 [] plus_plus(int,A,B)=plus_plus(int,B,A).
% 2.23/2.39 ** KEPT (pick-wt=2): 180 [] linordered_idom(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 181 [] comm_semiring_1(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 182 [] number_semiring(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 183 [] linorder(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 184 [] monoid_mult(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 185 [] semiring_1(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 186 [] ring_char_0(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 187 [] number_ring(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 188 [] number(int).
% 2.23/2.39 ** KEPT (pick-wt=2): 189 [] comm_semiring_1(nat).
% 2.23/2.39 ** KEPT (pick-wt=2): 190 [] number_semiring(nat).
% 2.23/2.39 ** KEPT (pick-wt=2): 191 [] linorder(nat).
% 2.23/2.39 ** KEPT (pick-wt=2): 192 [] monoid_mult(nat).
% 2.23/2.39 ** KEPT (pick-wt=2): 193 [] semiring_1(nat).
% 2.23/2.39 ** KEPT (pick-wt=2): 194 [] number(nat).
% 2.23/2.39 ** KEPT (pick-wt=9): 195 [] ti(A,ti(A,B))=ti(A,B).
% 2.23/2.39 ---> New Demodulator: 196 [new_demod,195] ti(A,ti(A,B))=ti(A,B).
% 2.23/2.39 Following clause subsumed by 119 during input processing: 0 [copy,119,flip.1] A=A.
% 2.23/2.39 119 back subsumes 116.
% 2.23/2.39 >>>> Starting back demodulation with 121.
% 2.23/2.39 >>>> Starting back demodulation with 123.
% 2.23/2.39 >>>> Starting back demodulation with 125.
% 2.23/2.39 >>>> Starting back demodulation with 127.
% 2.23/2.39 >>>> Starting back demodulation with 129.
% 2.23/2.39 >>>> Starting back demodulation with 131.
% 2.23/2.39 >>>> Starting back demodulation with 133.
% 2.23/2.39 >>>> Starting back demodulation with 135.
% 2.23/2.39 >>>> Starting back demodulation with 137.
% 2.23/2.39 >>>> Starting back demodulation with 143.
% 2.23/2.39 ** KEPT (pick-wt=41): 197 [copy,146,flip.1,demod,175,172,177] plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),plus_plus(int,times_times(int,bit0(bit1(pls)),times_times(int,A,B)),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))))=power_power(int,plus_plus(int,A,B),number_number_of(nat,bit0(bit1(pls)))).
% 2.23/2.39 ** KEPT (pick-wt=66): 198 [copy,147,flip.1,demod,175,172,175,172,177,177,177] plus_plus(int,power_power(int,A,number_number_of(nat,bit1(bit1(pls)))),plus_plus(int,times_times(int,bit1(bit1(pls)),times_times(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),B)),plus_plus(int,times_times(int,bit1(bit1(pls)),times_times(int,A,power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls)))))))=power_power(int,plus_plus(int,A,B),number_number_of(nat,bit1(bit1(pls)))).
% 2.23/2.39 ** KEPT (pick-wt=20): 199 [copy,148,flip.1] power_power(int,A,number_number_of(nat,bit1(bit1(pls))))=times_times(int,A,power_power(int,A,number_number_of(nat,bit0(bit1(pls))))).
% 2.23/2.39 >>>> Starting back demodulation with 151.
% 2.23/2.39 ** KEPT (pick-wt=15): 200 [copy,155,flip.1] power_power(int,A,times_times(nat,B,C))=power_power(int,power_power(int,A,B),C).
% 2.23/2.39 >>>> Starting back demodulation with 158.
% 2.23/2.39 >>>> Starting back demodulation with 160.
% 2.23/2.39 >> back demodulating 34 with 160.
% 2.23/2.39 >>>> Starting back demodulation with 162.
% 2.23/2.39 >>>> Starting back demodulation with 164.
% 2.23/2.39 >>>> Starting back demodulation with 169.
% 2.23/2.39 >> back demodulating 163 with 169.
% 2.23/2.39 >> back demodulating 44 with 169.
% 2.23/2.39 >>>> Starting back demodulation with 172.
% 2.23/2.39 >> back demodulating 147 with 172.
% 2.23/2.39 >> back demodulating 146 with 172.
% 2.23/2.39 Following clause subsumed by 173 during input processing: 0 [copy,173,flip.1] times_times(int,A,B)=times_times(int,B,A).
% 2.23/2.39 >>>> Starting back demodulation with 175.
% 2.23/2.39 >> back demodulating 170 with 175.
% 2.23/2.39 >> back demodulating 150 with 175.
% 2.23/2.39 >> back demodulating 142 with 175.
% 2.23/2.39 >> back demodulating 140 with 175.
% 2.23/2.39 >> back demodulating 139 with 175.
% 2.23/2.39 >> back demodulating 118 with 175.
% 2.23/2.39 >> back demodulating 115 with 175.
% 2.23/2.39 >> back demodulating 65 with 175.
% 2.23/2.39 >> back demodulating 64 with 175.
% 2.23/2.39 >> back demodulating 63 with 175.
% 2.23/2.39 >> back demodulating 62 with 175.
% 2.23/2.39 >> back demodulating 28 with 175.
% 2.23/2.39 >> back demodulating 26 with 175.
% 2.23/2.39 >>>> Starting back demodulation with 177.
% 2.23/2.39 Following clause subsumed by 178 during input processing: 0 [copy,178,flip.1] plus_plus(int,A,plus_plus(int,B,C))=plus_plus(int,B,plus_plus(int,A,C)).
% 2.23/2.39 Following clause subsumed by 179 during input processing: 0 [copy,179,flip.1] plus_plus(int,A,B)=plus_plus(int,B,A).
% 2.23/2.39 >>>> Starting back demodulation with 196.
% 2.23/2.39 Following clause subsumed by 119 during input processing: 0 [copy,197,flip.1,demod,203,203,203,207] power_power(int,plus_plus(int,A,B),plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls))))=power_power(int,plus_plus(int,A,B),plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))).
% 2.23/2.39 Following clause subsumed by 205 during input processing: 0 [copy,198,flip.1,demod,203,203] power_power(int,plus_plus(int,A,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,power_power(int,A,number_number_of(nat,bit1(bit1(pls)))),plus_plus(int,times_times(int,bit1(bit1(pls)),times_times(int,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))),B)),plus_plus(int,times_times(int,bit1(bit1(pls)),times_times(int,A,power_power(int,B,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls))))))).
% 2.23/2.39 ** KEPT (pick-wt=25): 219 [copy,199,flip.1,demod,203] times_times(int,A,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))))=power_power(int,A,number_number_of(nat,bit1(bit1(pls)))).
% 2.23/2.39 Following clause subsumed by 155 during input processing: 0 [copy,200,flip.1] power_power(int,power_power(int,A,B),C)=power_power(int,A,times_times(nat,B,C)).
% 2.23/2.39 >>>> Starting back demodulation with 203.
% 2.23/2.39 >> back demodulating 199 with 203.
% 2.23/2.39 >> back demodulating 198 with 203.
% 2.23/2.39 >> back demodulating 197 with 203.
% 2.23/2.39 >> back demodulating 161 with 203.
% 2.23/2.39 >> back demodulating 159 with 203.
% 2.23/2.39 >> back demodulating 148 with 203.
% 2.23/2.39 >> back demodulating 145 with 203.
% 2.23/2.39 >> back demodulating 33 with 203.
% 2.23/2.39 >> back demodulating 32 with 203.
% 2.23/2.39 >> back demodulating 31 with 203.
% 2.23/2.39 >> back demodulating 29 with 203.
% 2.23/2.39 Following clause subsumed by 221 during input processing: 0 [copy,205,flip.1] plus_plus(int,power_power(int,A,number_number_of(nat,bit1(bit1(pls)))),plus_plus(int,times_times(int,bit1(bit1(pls)),times_times(int,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))),B)),plus_plus(int,times_times(int,bit1(bit1(pls)),times_times(int,A,power_power(int,B,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls)))))))=power_power(int,plus_plus(int,A,B),number_number_of(nat,bit1(bit1(pls)))).
% 2.23/2.39 >>>> Starting back demodulation with 207.
% 2.23/2.39 >>>> Starting back demodulation with 210.
% 2.23/2.39 >>>> Starting back demodulation with 212.
% 2.23/2.39 Following clause subsumed by 216 during input processing: 0 [copy,215,flip.1] plus_plus(int,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))),power_power(int,B,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))))!=plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)).
% 2.23/2.39 Following clause subsumed by 215 during input processing: 0 [copy,216,flip.1] plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))!=plus_plus(int,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))),power_power(int,B,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls))))).
% 2.23/2.39 Following clause subsumed by 220 during input processing: 0 [copy,219,flip.1] power_power(int,A,number_number_of(nat,bit1(bit1(pls))))=times_times(int,A,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls))))).
% 2.23/2.39 Following clause subsumed by 219 during input processing: 0 [copy,220,flip.1] times_times(int,A,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))))=power_power(int,A,number_number_of(nat,bit1(bit1(pls)))).
% 2.23/2.39 Following clause subsumed by 205 during input processing: 0 [copy,221,flip.1] power_power(int,plus_plus(int,A,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,power_power(int,A,number_number_of(nat,bit1(bit1(pls)))),plus_plus(int,times_times(int,bit1(bit1(pls)),times_times(int,power_power(int,A,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))),B)),plus_plus(int,times_times(int,bit1(bit1(pls)),times_times(int,A,power_power(int,B,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls))))))).
% 2.23/2.39 >>>> Starting back demodulation with 223.
% 2.23/2.39 >>>> Starting back demodulation with 225.
% 2.23/2.39
% 2.23/2.39 ======= end of input processing =======
% 2.23/2.39
% 2.23/2.39 =========== start of search ===========
% 2.23/2.39
% 2.23/2.39
% 2.23/2.39 Resetting weight limit to 2.
% 2.23/2.39
% 2.23/2.39
% 2.23/2.39 Resetting weight limit to 2.
% 2.23/2.39
% 2.23/2.39 sos_size=64
% 2.23/2.39
% 2.23/2.39 -------- PROOF --------
% 2.23/2.39
% 2.23/2.39 -----> EMPTY CLAUSE at 0.02 sec ----> 231 [hyper,138,40,unit_del,217,218] $F.
% 2.23/2.39
% 2.23/2.39 Length of proof is 8. Level of proof is 4.
% 2.23/2.39
% 2.23/2.39 ---------------- PROOF ----------------
% 2.23/2.39 % SZS status Theorem
% 2.23/2.39 % SZS output start Refutation
% See solution above
% 2.23/2.39 ------------ end of proof -------------
% 2.23/2.39
% 2.23/2.39
% 2.23/2.39 Search stopped by max_proofs option.
% 2.23/2.39
% 2.23/2.39
% 2.23/2.39 Search stopped by max_proofs option.
% 2.23/2.39
% 2.23/2.39 ============ end of search ============
% 2.23/2.39
% 2.23/2.39 -------------- statistics -------------
% 2.23/2.39 clauses given 29
% 2.23/2.39 clauses generated 610
% 2.23/2.39 clauses kept 196
% 2.23/2.39 clauses forward subsumed 40
% 2.23/2.39 clauses back subsumed 4
% 2.23/2.39 Kbytes malloced 4882
% 2.23/2.39
% 2.23/2.39 ----------- times (seconds) -----------
% 2.23/2.39 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 2.23/2.39 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.23/2.39 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.23/2.39
% 2.23/2.39 That finishes the proof of the theorem.
% 2.23/2.39
% 2.23/2.39 Process 21570 finished Wed Jul 27 10:04:21 2022
% 2.23/2.39 Otter interrupted
% 2.23/2.39 PROOF FOUND
%------------------------------------------------------------------------------