TSTP Solution File: NUM926+5 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n015.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 10:25:52 EDT 2023
% Result : Theorem 0.19s 0.69s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 16:51:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 % File :CSE---1.6
% 0.19/0.66 % Problem :theBenchmark
% 0.19/0.66 % Transform :cnf
% 0.19/0.66 % Format :tptp:raw
% 0.19/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.66
% 0.19/0.66 % Result :Theorem 0.030000s
% 0.19/0.66 % Output :CNFRefutation 0.030000s
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 %------------------------------------------------------------------------------
% 0.19/0.66 % File : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 0.19/0.66 % Domain : Number Theory
% 0.19/0.66 % Problem : Sum of two squares line 258, 100 axioms selected
% 0.19/0.66 % Version : Especial.
% 0.19/0.66 % English :
% 0.19/0.66
% 0.19/0.66 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.19/0.66 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.19/0.66 % Source : [Bla11]
% 0.19/0.66 % Names : s2s_100_fofpt_l258 [Bla11]
% 0.19/0.66
% 0.19/0.66 % Status : Theorem
% 0.19/0.66 % Rating : 0.11 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.23 v7.3.0, 0.21 v7.2.0, 0.17 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.21 v6.2.0, 0.24 v6.1.0, 0.20 v6.0.0, 0.22 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0
% 0.19/0.66 % Syntax : Number of formulae : 142 ( 52 unt; 0 def)
% 0.19/0.66 % Number of atoms : 261 ( 84 equ)
% 0.19/0.66 % Maximal formula atoms : 7 ( 1 avg)
% 0.19/0.66 % Number of connectives : 126 ( 7 ~; 3 |; 12 &)
% 0.19/0.66 % ( 40 <=>; 64 =>; 0 <=; 0 <~>)
% 0.19/0.66 % Maximal formula depth : 8 ( 4 avg)
% 0.19/0.66 % Maximal term depth : 10 ( 2 avg)
% 0.19/0.66 % Number of predicates : 14 ( 13 usr; 0 prp; 1-3 aty)
% 0.19/0.66 % Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% 0.19/0.66 % Number of variables : 266 ( 260 !; 6 ?)
% 0.19/0.66 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.66
% 0.19/0.66 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.19/0.66 % 2011-08-09 14:14:19
% 0.19/0.66 % : Encoded with polymorphic tags.
% 0.19/0.66 %------------------------------------------------------------------------------
% 0.19/0.66 %----Explicit typings (27)
% 0.19/0.66 fof(tsy_c_Groups_Oone__class_Oone_res,axiom,
% 0.19/0.66 ! [X_a] :
% 0.19/0.66 ( semiring_1(X_a)
% 0.19/0.66 => ti(X_a,one_one(X_a)) = one_one(X_a) ) ).
% 0.19/0.66
% 0.19/0.67 fof(tsy_c_Groups_Oplus__class_Oplus_arg1,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( comm_semiring_1(X_a)
% 0.19/0.67 => plus_plus(X_a,ti(X_a,B_1),B_2) = plus_plus(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Groups_Oplus__class_Oplus_arg2,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( comm_semiring_1(X_a)
% 0.19/0.67 => plus_plus(X_a,B_1,ti(X_a,B_2)) = plus_plus(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Groups_Oplus__class_Oplus_res,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( comm_semiring_1(X_a)
% 0.19/0.67 => ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Groups_Otimes__class_Otimes_arg1,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( monoid_mult(X_a)
% 0.19/0.67 => times_times(X_a,ti(X_a,B_1),B_2) = times_times(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Groups_Otimes__class_Otimes_arg2,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( monoid_mult(X_a)
% 0.19/0.67 => times_times(X_a,B_1,ti(X_a,B_2)) = times_times(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Groups_Otimes__class_Otimes_res,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( monoid_mult(X_a)
% 0.19/0.67 => ti(X_a,times_times(X_a,B_1,B_2)) = times_times(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_HOL_Oundefined_res,axiom,
% 0.19/0.67 ! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_IntPrimes_Ozprime_arg1,axiom,
% 0.19/0.67 ! [B_1] :
% 0.19/0.67 ( zprime(ti(int,B_1))
% 0.19/0.67 <=> zprime(B_1) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Int_OBit0_arg1,hypothesis,
% 0.19/0.67 ! [B_1] : bit0(ti(int,B_1)) = bit0(B_1) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Int_OBit0_res,hypothesis,
% 0.19/0.67 ! [B_1] : ti(int,bit0(B_1)) = bit0(B_1) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Int_OBit1_arg1,hypothesis,
% 0.19/0.67 ! [B_1] : bit1(ti(int,B_1)) = bit1(B_1) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Int_OBit1_res,hypothesis,
% 0.19/0.67 ! [B_1] : ti(int,bit1(B_1)) = bit1(B_1) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Int_OPls_res,hypothesis,
% 0.19/0.67 ti(int,pls) = pls ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Int_Onumber__class_Onumber__of_arg1,axiom,
% 0.19/0.67 ! [B_1,X_a] :
% 0.19/0.67 ( number(X_a)
% 0.19/0.67 => number_number_of(X_a,ti(int,B_1)) = number_number_of(X_a,B_1) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Int_Onumber__class_Onumber__of_res,axiom,
% 0.19/0.67 ! [B_1,X_a] :
% 0.19/0.67 ( number(X_a)
% 0.19/0.67 => ti(X_a,number_number_of(X_a,B_1)) = number_number_of(X_a,B_1) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Orderings_Oord__class_Oless_arg1,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( ( number(X_a)
% 0.19/0.67 & linorder(X_a) )
% 0.19/0.67 => ( ord_less(X_a,ti(X_a,B_1),B_2)
% 0.19/0.67 <=> ord_less(X_a,B_1,B_2) ) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Orderings_Oord__class_Oless_arg2,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( ( number(X_a)
% 0.19/0.67 & linorder(X_a) )
% 0.19/0.67 => ( ord_less(X_a,B_1,ti(X_a,B_2))
% 0.19/0.67 <=> ord_less(X_a,B_1,B_2) ) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Orderings_Oord__class_Oless__eq_arg1,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( ( number(X_a)
% 0.19/0.67 & linorder(X_a) )
% 0.19/0.67 => ( ord_less_eq(X_a,ti(X_a,B_1),B_2)
% 0.19/0.67 <=> ord_less_eq(X_a,B_1,B_2) ) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Orderings_Oord__class_Oless__eq_arg2,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( ( number(X_a)
% 0.19/0.67 & linorder(X_a) )
% 0.19/0.67 => ( ord_less_eq(X_a,B_1,ti(X_a,B_2))
% 0.19/0.67 <=> ord_less_eq(X_a,B_1,B_2) ) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Power_Opower__class_Opower_arg1,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( monoid_mult(X_a)
% 0.19/0.67 => power_power(X_a,ti(X_a,B_1),B_2) = power_power(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Power_Opower__class_Opower_arg2,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( monoid_mult(X_a)
% 0.19/0.67 => power_power(X_a,B_1,ti(nat,B_2)) = power_power(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_Power_Opower__class_Opower_res,axiom,
% 0.19/0.67 ! [B_1,B_2,X_a] :
% 0.19/0.67 ( monoid_mult(X_a)
% 0.19/0.67 => ti(X_a,power_power(X_a,B_1,B_2)) = power_power(X_a,B_1,B_2) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1,axiom,
% 0.19/0.67 ! [B_1] :
% 0.19/0.67 ( twoSqu33214720sum2sq(ti(int,B_1))
% 0.19/0.67 <=> twoSqu33214720sum2sq(B_1) ) ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_v_m_res,hypothesis,
% 0.19/0.67 ti(int,m) = m ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_v_s_____res,axiom,
% 0.19/0.67 ti(int,s) = s ).
% 0.19/0.67
% 0.19/0.67 fof(tsy_v_t_____res,axiom,
% 0.19/0.67 ti(int,t) = t ).
% 0.19/0.67
% 0.19/0.67 %----Relevant facts (98)
% 0.19/0.67 fof(fact_0_tpos,axiom,
% 0.19/0.67 ord_less_eq(int,one_one(int),t) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
% 0.19/0.67 ( t = one_one(int)
% 0.19/0.67 => ? [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)) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
% 0.19/0.67 ( ord_less(int,one_one(int),t)
% 0.19/0.67 => ? [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)) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_3_t__l__p,axiom,
% 0.19/0.67 ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_4_p,axiom,
% 0.19/0.67 zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_5_t,axiom,
% 0.19/0.67 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) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_6_qf1pt,axiom,
% 0.19/0.67 twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_7_zadd__power2,axiom,
% 0.19/0.67 ! [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))))) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_8_zadd__power3,axiom,
% 0.19/0.67 ! [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))))) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_9_power2__sum,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( number_semiring(X_a)
% 0.19/0.67 => ! [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)) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_10_power2__eq__square__number__of,axiom,
% 0.19/0.67 ! [X_b] :
% 0.19/0.67 ( ( monoid_mult(X_b)
% 0.19/0.67 & number(X_b) )
% 0.19/0.67 => ! [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)) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_11_cube__square,axiom,
% 0.19/0.67 ! [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)))) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_12_one__power2,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( semiring_1(X_a)
% 0.19/0.67 => power_power(X_a,one_one(X_a),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( comm_semiring_1(X_a)
% 0.19/0.67 => ! [X_1] : times_times(X_a,X_1,X_1) = power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_14_power2__eq__square,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( monoid_mult(X_a)
% 0.19/0.67 => ! [A_1] : power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls)))) = times_times(X_a,A_1,A_1) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( comm_semiring_1(X_a)
% 0.19/0.67 => ! [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)) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_16_add__special_I2_J,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( number_ring(X_a)
% 0.19/0.67 => ! [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)) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_17_add__special_I3_J,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( number_ring(X_a)
% 0.19/0.67 => ! [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))) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_18_one__add__one__is__two,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( number_ring(X_a)
% 0.19/0.67 => plus_plus(X_a,one_one(X_a),one_one(X_a)) = number_number_of(X_a,bit0(bit1(pls))) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_19__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,
% 0.19/0.67 ~ ! [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) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_20_zle__refl,axiom,
% 0.19/0.67 ! [W] : ord_less_eq(int,W,W) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_21_zle__linear,axiom,
% 0.19/0.67 ! [Z,W] :
% 0.19/0.67 ( ord_less_eq(int,Z,W)
% 0.19/0.67 | ord_less_eq(int,W,Z) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_22_zless__le,axiom,
% 0.19/0.67 ! [Z_1,W_1] :
% 0.19/0.67 ( ord_less(int,Z_1,W_1)
% 0.19/0.67 <=> ( ord_less_eq(int,Z_1,W_1)
% 0.19/0.67 & Z_1 != W_1 ) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_23_zless__linear,axiom,
% 0.19/0.67 ! [X_1,Y_1] :
% 0.19/0.67 ( ord_less(int,X_1,Y_1)
% 0.19/0.67 | X_1 = Y_1
% 0.19/0.67 | ord_less(int,Y_1,X_1) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_24_zle__trans,axiom,
% 0.19/0.67 ! [K_1,I,J] :
% 0.19/0.67 ( ord_less_eq(int,I,J)
% 0.19/0.67 => ( ord_less_eq(int,J,K_1)
% 0.19/0.67 => ord_less_eq(int,I,K_1) ) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_25_zle__antisym,axiom,
% 0.19/0.67 ! [Z,W] :
% 0.19/0.67 ( ord_less_eq(int,Z,W)
% 0.19/0.67 => ( ord_less_eq(int,W,Z)
% 0.19/0.67 => Z = W ) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 0.19/0.67 ! [X_a] :
% 0.19/0.67 ( comm_semiring_1(X_a)
% 0.19/0.67 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [X_1] : power_power(X_a,X_1,one_one(nat)) = ti(X_a,X_1) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_28_zpower__zpower,axiom,
% 0.19/0.68 ! [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)) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_29_le__number__of__eq__not__less,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( ( number(X_a)
% 0.19/0.68 & linorder(X_a) )
% 0.19/0.68 => ! [V_2,W_1] :
% 0.19/0.68 ( ord_less_eq(X_a,number_number_of(X_a,V_2),number_number_of(X_a,W_1))
% 0.19/0.68 <=> ~ ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_2)) ) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_30_less__number__of,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( ( number_ring(X_a)
% 0.19/0.68 & linordered_idom(X_a) )
% 0.19/0.68 => ! [X_2,Y_2] :
% 0.19/0.68 ( ord_less(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))
% 0.19/0.68 <=> ord_less(int,X_2,Y_2) ) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_31_le__number__of,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( ( number_ring(X_a)
% 0.19/0.68 & linordered_idom(X_a) )
% 0.19/0.68 => ! [X_2,Y_2] :
% 0.19/0.68 ( ord_less_eq(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))
% 0.19/0.68 <=> ord_less_eq(int,X_2,Y_2) ) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_32_zadd__zless__mono,axiom,
% 0.19/0.68 ! [Z_2,Z,W_2,W] :
% 0.19/0.68 ( ord_less(int,W_2,W)
% 0.19/0.68 => ( ord_less_eq(int,Z_2,Z)
% 0.19/0.68 => ord_less(int,plus_plus(int,W_2,Z_2),plus_plus(int,W,Z)) ) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_34_zpower__zadd__distrib,axiom,
% 0.19/0.68 ! [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)) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_35_nat__mult__2,axiom,
% 0.19/0.68 ! [Z] : times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z) = plus_plus(nat,Z,Z) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_36_nat__mult__2__right,axiom,
% 0.19/0.68 ! [Z] : times_times(nat,Z,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,Z,Z) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_37_nat__1__add__1,axiom,
% 0.19/0.68 plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_38_less__int__code_I16_J,axiom,
% 0.19/0.68 ! [K1,K2] :
% 0.19/0.68 ( ord_less(int,bit1(K1),bit1(K2))
% 0.19/0.68 <=> ord_less(int,K1,K2) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_39_rel__simps_I17_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less(int,bit1(K),bit1(L))
% 0.19/0.68 <=> ord_less(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_40_less__eq__int__code_I16_J,axiom,
% 0.19/0.68 ! [K1,K2] :
% 0.19/0.68 ( ord_less_eq(int,bit1(K1),bit1(K2))
% 0.19/0.68 <=> ord_less_eq(int,K1,K2) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_41_rel__simps_I34_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less_eq(int,bit1(K),bit1(L))
% 0.19/0.68 <=> ord_less_eq(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_42_rel__simps_I2_J,axiom,
% 0.19/0.68 ~ ord_less(int,pls,pls) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_43_less__int__code_I13_J,axiom,
% 0.19/0.68 ! [K1,K2] :
% 0.19/0.68 ( ord_less(int,bit0(K1),bit0(K2))
% 0.19/0.68 <=> ord_less(int,K1,K2) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_44_rel__simps_I14_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less(int,bit0(K),bit0(L))
% 0.19/0.68 <=> ord_less(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_45_rel__simps_I19_J,axiom,
% 0.19/0.68 ord_less_eq(int,pls,pls) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_46_less__eq__int__code_I13_J,axiom,
% 0.19/0.68 ! [K1,K2] :
% 0.19/0.68 ( ord_less_eq(int,bit0(K1),bit0(K2))
% 0.19/0.68 <=> ord_less_eq(int,K1,K2) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_47_rel__simps_I31_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less_eq(int,bit0(K),bit0(L))
% 0.19/0.68 <=> ord_less_eq(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_48_less__number__of__int__code,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less(int,number_number_of(int,K),number_number_of(int,L))
% 0.19/0.68 <=> ord_less(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_49_less__eq__number__of__int__code,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less_eq(int,number_number_of(int,K),number_number_of(int,L))
% 0.19/0.68 <=> ord_less_eq(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_50_zadd__strict__right__mono,axiom,
% 0.19/0.68 ! [K_1,I,J] :
% 0.19/0.68 ( ord_less(int,I,J)
% 0.19/0.68 => ord_less(int,plus_plus(int,I,K_1),plus_plus(int,J,K_1)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_51_zadd__left__mono,axiom,
% 0.19/0.68 ! [K_1,I,J] :
% 0.19/0.68 ( ord_less_eq(int,I,J)
% 0.19/0.68 => ord_less_eq(int,plus_plus(int,K_1,I),plus_plus(int,K_1,J)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_52_add__nat__number__of,axiom,
% 0.19/0.68 ! [V_1,V] :
% 0.19/0.68 ( ( ord_less(int,V,pls)
% 0.19/0.68 => plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1)) = number_number_of(nat,V_1) )
% 0.19/0.68 & ( ~ ord_less(int,V,pls)
% 0.19/0.68 => ( ( ord_less(int,V_1,pls)
% 0.19/0.68 => plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1)) = number_number_of(nat,V) )
% 0.19/0.68 & ( ~ ord_less(int,V_1,pls)
% 0.19/0.68 => plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1)) = number_number_of(nat,plus_plus(int,V,V_1)) ) ) ) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_53_nat__numeral__1__eq__1,axiom,
% 0.19/0.68 number_number_of(nat,bit1(pls)) = one_one(nat) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_54_Numeral1__eq1__nat,axiom,
% 0.19/0.68 one_one(nat) = number_number_of(nat,bit1(pls)) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_55_rel__simps_I29_J,axiom,
% 0.19/0.68 ! [K] :
% 0.19/0.68 ( ord_less_eq(int,bit1(K),pls)
% 0.19/0.68 <=> ord_less(int,K,pls) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_56_rel__simps_I5_J,axiom,
% 0.19/0.68 ! [K] :
% 0.19/0.68 ( ord_less(int,pls,bit1(K))
% 0.19/0.68 <=> ord_less_eq(int,pls,K) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_57_less__eq__int__code_I15_J,axiom,
% 0.19/0.68 ! [K1,K2] :
% 0.19/0.68 ( ord_less_eq(int,bit1(K1),bit0(K2))
% 0.19/0.68 <=> ord_less(int,K1,K2) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_58_rel__simps_I33_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less_eq(int,bit1(K),bit0(L))
% 0.19/0.68 <=> ord_less(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_59_less__int__code_I14_J,axiom,
% 0.19/0.68 ! [K1,K2] :
% 0.19/0.68 ( ord_less(int,bit0(K1),bit1(K2))
% 0.19/0.68 <=> ord_less_eq(int,K1,K2) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_60_rel__simps_I15_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less(int,bit0(K),bit1(L))
% 0.19/0.68 <=> ord_less_eq(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_61_zless__imp__add1__zle,axiom,
% 0.19/0.68 ! [W,Z] :
% 0.19/0.68 ( ord_less(int,W,Z)
% 0.19/0.68 => ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_62_add1__zle__eq,axiom,
% 0.19/0.68 ! [W_1,Z_1] :
% 0.19/0.68 ( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
% 0.19/0.68 <=> ord_less(int,W_1,Z_1) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_63_zle__add1__eq__le,axiom,
% 0.19/0.68 ! [W_1,Z_1] :
% 0.19/0.68 ( ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))
% 0.19/0.68 <=> ord_less_eq(int,W_1,Z_1) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_64_zprime__2,axiom,
% 0.19/0.68 zprime(number_number_of(int,bit0(bit1(pls)))) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_65_is__mult__sum2sq,axiom,
% 0.19/0.68 ! [Y_1,X_1] :
% 0.19/0.68 ( twoSqu33214720sum2sq(X_1)
% 0.19/0.68 => ( twoSqu33214720sum2sq(Y_1)
% 0.19/0.68 => twoSqu33214720sum2sq(times_times(int,X_1,Y_1)) ) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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))) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [A_1,B] : times_times(X_a,A_1,B) = times_times(X_a,B,A_1) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [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)) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( comm_semiring_1(X_a)
% 0.19/0.68 => ! [A_1,C] : plus_plus(X_a,A_1,C) = plus_plus(X_a,C,A_1) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_80_eq__number__of,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( ( number_ring(X_a)
% 0.19/0.68 & ring_char_0(X_a) )
% 0.19/0.68 => ! [X_2,Y_2] :
% 0.19/0.68 ( number_number_of(X_a,X_2) = number_number_of(X_a,Y_2)
% 0.19/0.68 <=> X_2 = Y_2 ) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_81_number__of__reorient,axiom,
% 0.19/0.68 ! [X_a] :
% 0.19/0.68 ( number(X_a)
% 0.19/0.68 => ! [W_1,X_2] :
% 0.19/0.68 ( number_number_of(X_a,W_1) = ti(X_a,X_2)
% 0.19/0.68 <=> ti(X_a,X_2) = number_number_of(X_a,W_1) ) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_82_rel__simps_I51_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( bit1(K) = bit1(L)
% 0.19/0.68 <=> K = L ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_83_rel__simps_I48_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( bit0(K) = bit0(L)
% 0.19/0.68 <=> K = L ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_84_zmult__assoc,axiom,
% 0.19/0.68 ! [Z1,Z2,Z3] : times_times(int,times_times(int,Z1,Z2),Z3) = times_times(int,Z1,times_times(int,Z2,Z3)) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_85_zmult__commute,axiom,
% 0.19/0.68 ! [Z,W] : times_times(int,Z,W) = times_times(int,W,Z) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_86_number__of__is__id,axiom,
% 0.19/0.68 ! [K_1] : number_number_of(int,K_1) = K_1 ).
% 0.19/0.68
% 0.19/0.68 fof(fact_87_zadd__assoc,axiom,
% 0.19/0.68 ! [Z1,Z2,Z3] : plus_plus(int,plus_plus(int,Z1,Z2),Z3) = plus_plus(int,Z1,plus_plus(int,Z2,Z3)) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_88_zadd__left__commute,axiom,
% 0.19/0.68 ! [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)) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_89_zadd__commute,axiom,
% 0.19/0.68 ! [Z,W] : plus_plus(int,Z,W) = plus_plus(int,W,Z) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_90_rel__simps_I12_J,axiom,
% 0.19/0.68 ! [K] :
% 0.19/0.68 ( ord_less(int,bit1(K),pls)
% 0.19/0.68 <=> ord_less(int,K,pls) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_91_less__int__code_I15_J,axiom,
% 0.19/0.68 ! [K1,K2] :
% 0.19/0.68 ( ord_less(int,bit1(K1),bit0(K2))
% 0.19/0.68 <=> ord_less(int,K1,K2) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_92_rel__simps_I16_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less(int,bit1(K),bit0(L))
% 0.19/0.68 <=> ord_less(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_93_rel__simps_I10_J,axiom,
% 0.19/0.68 ! [K] :
% 0.19/0.68 ( ord_less(int,bit0(K),pls)
% 0.19/0.68 <=> ord_less(int,K,pls) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_94_rel__simps_I4_J,axiom,
% 0.19/0.68 ! [K] :
% 0.19/0.68 ( ord_less(int,pls,bit0(K))
% 0.19/0.68 <=> ord_less(int,pls,K) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_95_rel__simps_I22_J,axiom,
% 0.19/0.68 ! [K] :
% 0.19/0.68 ( ord_less_eq(int,pls,bit1(K))
% 0.19/0.68 <=> ord_less_eq(int,pls,K) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_96_less__eq__int__code_I14_J,axiom,
% 0.19/0.68 ! [K1,K2] :
% 0.19/0.68 ( ord_less_eq(int,bit0(K1),bit1(K2))
% 0.19/0.68 <=> ord_less_eq(int,K1,K2) ) ).
% 0.19/0.68
% 0.19/0.68 fof(fact_97_rel__simps_I32_J,axiom,
% 0.19/0.68 ! [K,L] :
% 0.19/0.68 ( ord_less_eq(int,bit0(K),bit1(L))
% 0.19/0.68 <=> ord_less_eq(int,K,L) ) ).
% 0.19/0.68
% 0.19/0.68 %----Arities (15)
% 0.19/0.68 fof(arity_Int_Oint___Rings_Olinordered__idom,axiom,
% 0.19/0.68 linordered_idom(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Int_Oint___Rings_Ocomm__semiring__1,axiom,
% 0.19/0.68 comm_semiring_1(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Int_Oint___Int_Onumber__semiring,axiom,
% 0.19/0.68 number_semiring(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Int_Oint___Orderings_Olinorder,axiom,
% 0.19/0.68 linorder(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Int_Oint___Groups_Omonoid__mult,axiom,
% 0.19/0.68 monoid_mult(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Int_Oint___Rings_Osemiring__1,axiom,
% 0.19/0.68 semiring_1(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Int_Oint___Int_Oring__char__0,axiom,
% 0.19/0.68 ring_char_0(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Int_Oint___Int_Onumber__ring,axiom,
% 0.19/0.68 number_ring(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Int_Oint___Int_Onumber,axiom,
% 0.19/0.68 number(int) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.19/0.68 comm_semiring_1(nat) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Nat_Onat___Int_Onumber__semiring,axiom,
% 0.19/0.68 number_semiring(nat) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Nat_Onat___Orderings_Olinorder,axiom,
% 0.19/0.68 linorder(nat) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.19/0.68 monoid_mult(nat) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Nat_Onat___Rings_Osemiring__1,axiom,
% 0.19/0.68 semiring_1(nat) ).
% 0.19/0.68
% 0.19/0.68 fof(arity_Nat_Onat___Int_Onumber,axiom,
% 0.19/0.68 number(nat) ).
% 0.19/0.68
% 0.19/0.68 %----Helper facts (1)
% 0.19/0.68 fof(help_ti_idem,axiom,
% 0.19/0.68 ! [T,A] : ti(T,ti(T,A)) = ti(T,A) ).
% 0.19/0.68
% 0.19/0.68 %----Conjectures (1)
% 0.19/0.68 fof(conj_0,conjecture,
% 0.19/0.69 ? [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)) ).
% 0.19/0.69
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 % Proof found
% 0.19/0.69 % SZS status Theorem for theBenchmark
% 0.19/0.69 % SZS output start Proof
% 0.19/0.69 %ClaNum:217(EqnAxiom:37)
% 0.19/0.69 %VarNum:720(SingletonVarNum:281)
% 0.19/0.69 %MaxLitNum:4
% 0.19/0.69 %MaxfuncDepth:6
% 0.19/0.69 %SharedTerms:74
% 0.19/0.69 %goalClause: 89
% 0.19/0.69 %singleGoalClaCount:1
% 0.19/0.69 [38]P1(a1)
% 0.19/0.69 [39]P1(a9)
% 0.19/0.69 [40]P2(a1)
% 0.19/0.69 [41]P2(a9)
% 0.19/0.69 [42]P3(a1)
% 0.19/0.69 [43]P3(a9)
% 0.19/0.69 [44]P6(a1)
% 0.19/0.69 [45]P6(a9)
% 0.19/0.69 [46]P4(a1)
% 0.19/0.69 [47]P4(a9)
% 0.19/0.69 [48]P7(a1)
% 0.19/0.69 [49]P7(a9)
% 0.19/0.69 [50]P8(a1)
% 0.19/0.69 [51]P5(a1)
% 0.19/0.69 [52]P9(a1)
% 0.19/0.69 [88]~P11(a1,a11,a11)
% 0.19/0.69 [53]E(f14(a1,a11),a11)
% 0.19/0.69 [54]E(f14(a1,a10),a10)
% 0.19/0.69 [55]E(f14(a1,a15),a15)
% 0.19/0.69 [56]E(f14(a1,a18),a18)
% 0.19/0.69 [69]P10(a1,f13(a1),a18)
% 0.19/0.69 [59]E(f12(a9,f2(a11)),f13(a9))
% 0.19/0.69 [81]P12(f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)))
% 0.19/0.69 [82]P11(a1,a18,f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)))
% 0.19/0.69 [66]P12(f12(a1,f3(f2(a11))))
% 0.19/0.69 [70]E(f16(a9,f13(a9),f13(a9)),f12(a9,f3(f2(a11))))
% 0.19/0.69 [83]E(f20(a1,f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)),a18),f16(a1,f17(a1,a15,f12(a9,f3(f2(a11)))),f13(a1)))
% 0.19/0.69 [84]E(f20(a1,f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)),a4),f16(a1,f17(a1,a15,f12(a9,f3(f2(a11)))),f13(a1)))
% 0.19/0.69 [85]P13(f20(a1,f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)),a18))
% 0.19/0.69 [67]P10(a1,x671,x671)
% 0.19/0.69 [57]E(f12(a1,x571),x571)
% 0.19/0.69 [60]E(f14(a1,f3(x601)),f3(x601))
% 0.19/0.69 [61]E(f14(a1,f2(x611)),f2(x611))
% 0.19/0.69 [62]E(f14(x621,f19(x621)),f19(x621))
% 0.19/0.69 [63]E(f3(f14(a1,x631)),f3(x631))
% 0.19/0.69 [64]E(f2(f14(a1,x641)),f2(x641))
% 0.19/0.69 [73]E(f20(a9,x731,f12(a9,f3(f2(a11)))),f16(a9,x731,x731))
% 0.19/0.69 [74]E(f20(a9,f12(a9,f3(f2(a11))),x741),f16(a9,x741,x741))
% 0.19/0.69 [79]E(f20(a1,x791,f17(a1,x791,f12(a9,f3(f2(a11))))),f17(a1,x791,f12(a9,f2(f2(a11)))))
% 0.19/0.69 [71]E(f16(a1,x711,x712),f16(a1,x712,x711))
% 0.19/0.69 [72]E(f20(a1,x721,x722),f20(a1,x722,x721))
% 0.19/0.69 [68]E(f14(x681,f14(x681,x682)),f14(x681,x682))
% 0.19/0.69 [86]E(f16(a1,f16(a1,f17(a1,x861,f12(a9,f3(f2(a11)))),f20(a1,f20(a1,f12(a1,f3(f2(a11))),x861),x862)),f17(a1,x862,f12(a9,f3(f2(a11))))),f17(a1,f16(a1,x861,x862),f12(a9,f3(f2(a11)))))
% 0.19/0.69 [87]E(f16(a1,f16(a1,f16(a1,f17(a1,x871,f12(a9,f2(f2(a11)))),f20(a1,f20(a1,f12(a1,f2(f2(a11))),f17(a1,x871,f12(a9,f3(f2(a11))))),x872)),f20(a1,f20(a1,f12(a1,f2(f2(a11))),x871),f17(a1,x872,f12(a9,f3(f2(a11)))))),f17(a1,x872,f12(a9,f2(f2(a11))))),f17(a1,f16(a1,x871,x872),f12(a9,f2(f2(a11)))))
% 0.19/0.69 [89]~E(f16(a1,f17(a1,x891,f12(a9,f3(f2(a11)))),f17(a1,x892,f12(a9,f3(f2(a11))))),f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)))
% 0.19/0.69 [75]E(f16(a1,x751,f16(a1,x752,x753)),f16(a1,x752,f16(a1,x751,x753)))
% 0.19/0.69 [76]E(f16(a1,f16(a1,x761,x762),x763),f16(a1,x761,f16(a1,x762,x763)))
% 0.19/0.69 [77]E(f20(a1,f20(a1,x771,x772),x773),f20(a1,x771,f20(a1,x772,x773)))
% 0.19/0.69 [78]E(f17(a1,f17(a1,x781,x782),x783),f17(a1,x781,f20(a9,x782,x783)))
% 0.19/0.69 [80]E(f20(a1,f17(a1,x801,x802),f17(a1,x801,x803)),f17(a1,x801,f16(a9,x802,x803)))
% 0.19/0.69 [215]~E(f13(a1),a18)+E(f16(a1,f17(a1,a5,f12(a9,f3(f2(a11)))),f17(a1,a6,f12(a9,f3(f2(a11))))),f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)))
% 0.19/0.69 [216]~P11(a1,f13(a1),a18)+E(f16(a1,f17(a1,a7,f12(a9,f3(f2(a11)))),f17(a1,a8,f12(a9,f3(f2(a11))))),f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)))
% 0.19/0.69 [93]~P12(x931)+P12(f14(a1,x931))
% 0.19/0.69 [94]~P13(x941)+P13(f14(a1,x941))
% 0.19/0.69 [95]P12(x951)+~P12(f14(a1,x951))
% 0.19/0.69 [96]P13(x961)+~P13(f14(a1,x961))
% 0.19/0.69 [111]~P11(a1,a11,x1111)+P11(a1,a11,f3(x1111))
% 0.19/0.69 [112]~P10(a1,a11,x1121)+P11(a1,a11,f2(x1121))
% 0.19/0.69 [113]~P10(a1,a11,x1131)+P10(a1,a11,f2(x1131))
% 0.19/0.69 [114]~P11(a1,x1141,a11)+P11(a1,f3(x1141),a11)
% 0.19/0.69 [115]~P11(a1,x1151,a11)+P11(a1,f2(x1151),a11)
% 0.19/0.69 [116]~P11(a1,x1161,a11)+P10(a1,f2(x1161),a11)
% 0.19/0.69 [123]P11(a1,x1231,a11)+~P11(a1,f3(x1231),a11)
% 0.19/0.69 [124]P11(a1,x1241,a11)+~P11(a1,f2(x1241),a11)
% 0.19/0.69 [125]P11(a1,x1251,a11)+~P10(a1,f2(x1251),a11)
% 0.19/0.69 [126]P11(a1,a11,x1261)+~P11(a1,a11,f3(x1261))
% 0.19/0.69 [127]P10(a1,a11,x1271)+~P11(a1,a11,f2(x1271))
% 0.19/0.69 [128]P10(a1,a11,x1281)+~P10(a1,a11,f2(x1281))
% 0.19/0.69 [92]~P1(x921)+E(f14(x921,f13(x921)),f13(x921))
% 0.19/0.69 [102]~P8(x1021)+E(f16(x1021,f13(x1021),f13(x1021)),f12(x1021,f3(f2(a11))))
% 0.19/0.69 [107]~P1(x1071)+E(f17(x1071,f13(x1071),f12(a9,f3(f2(a11)))),f13(x1071))
% 0.19/0.69 [101]~E(x1011,x1012)+~P11(a1,x1011,x1012)
% 0.19/0.69 [103]P10(a1,x1032,x1031)+P10(a1,x1031,x1032)
% 0.19/0.69 [109]~P11(a1,x1091,x1092)+P10(a1,x1091,x1092)
% 0.19/0.69 [90]E(x901,x902)+~E(f3(x901),f3(x902))
% 0.19/0.69 [91]E(x911,x912)+~E(f2(x911),f2(x912))
% 0.19/0.69 [130]~P11(a1,x1301,x1302)+P11(a1,f3(x1301),f3(x1302))
% 0.19/0.69 [132]~P10(a1,x1321,x1322)+P11(a1,f3(x1321),f2(x1322))
% 0.19/0.69 [134]~P11(a1,x1341,x1342)+P11(a1,f2(x1341),f3(x1342))
% 0.19/0.69 [136]~P11(a1,x1361,x1362)+P11(a1,f2(x1361),f2(x1362))
% 0.19/0.69 [138]~P10(a1,x1381,x1382)+P10(a1,f3(x1381),f3(x1382))
% 0.19/0.69 [140]~P10(a1,x1401,x1402)+P10(a1,f3(x1401),f2(x1402))
% 0.19/0.69 [142]~P11(a1,x1421,x1422)+P10(a1,f2(x1421),f3(x1422))
% 0.19/0.69 [144]~P10(a1,x1441,x1442)+P10(a1,f2(x1441),f2(x1442))
% 0.19/0.69 [146]P11(a1,x1461,x1462)+~P11(a1,f3(x1461),f3(x1462))
% 0.19/0.69 [148]P11(a1,x1481,x1482)+~P11(a1,f2(x1481),f3(x1482))
% 0.19/0.69 [150]P11(a1,x1501,x1502)+~P11(a1,f2(x1501),f2(x1502))
% 0.19/0.69 [152]P11(a1,x1521,x1522)+~P10(a1,f2(x1521),f3(x1522))
% 0.19/0.69 [154]P10(a1,x1541,x1542)+~P11(a1,f3(x1541),f2(x1542))
% 0.19/0.69 [156]P10(a1,x1561,x1562)+~P10(a1,f3(x1561),f3(x1562))
% 0.19/0.69 [158]P10(a1,x1581,x1582)+~P10(a1,f3(x1581),f2(x1582))
% 0.19/0.69 [160]P10(a1,x1601,x1602)+~P10(a1,f2(x1601),f2(x1602))
% 0.19/0.69 [171]~P11(a1,x1711,x1712)+P11(a1,f12(a1,x1711),f12(a1,x1712))
% 0.19/0.69 [172]~P10(a1,x1721,x1722)+P10(a1,f12(a1,x1721),f12(a1,x1722))
% 0.19/0.69 [180]P11(a1,x1801,x1802)+~P11(a1,f12(a1,x1801),f12(a1,x1802))
% 0.19/0.69 [181]P10(a1,x1811,x1812)+~P10(a1,f12(a1,x1811),f12(a1,x1812))
% 0.19/0.69 [97]~P6(x971)+E(f12(x971,f14(a1,x972)),f12(x971,x972))
% 0.19/0.69 [99]~P6(x991)+E(f14(x991,f12(x991,x992)),f12(x991,x992))
% 0.19/0.69 [100]~P2(x1001)+E(f17(x1001,x1002,f13(a9)),f14(x1001,x1002))
% 0.19/0.69 [173]~P11(a1,x1731,a11)+E(f16(a9,f12(a9,x1731),f12(a9,x1732)),f12(a9,x1732))
% 0.19/0.69 [189]~P10(a1,x1891,x1892)+P11(a1,x1891,f16(a1,x1892,f13(a1)))
% 0.19/0.69 [191]~P11(a1,x1911,x1912)+P10(a1,f16(a1,x1911,f13(a1)),x1912)
% 0.19/0.69 [193]P10(a1,x1931,x1932)+~P11(a1,x1931,f16(a1,x1932,f13(a1)))
% 0.19/0.69 [194]P11(a1,x1941,x1942)+~P10(a1,f16(a1,x1941,f13(a1)),x1942)
% 0.19/0.69 [182]~P8(x1821)+E(f16(x1821,f13(x1821),f12(x1821,x1822)),f12(x1821,f16(a1,f2(a11),x1822)))
% 0.19/0.69 [183]~P8(x1831)+E(f16(x1831,f12(x1831,x1832),f13(x1831)),f12(x1831,f16(a1,x1832,f2(a11))))
% 0.19/0.69 [161]~P2(x1611)+E(f20(x1611,x1612,x1612),f17(x1611,x1612,f12(a9,f3(f2(a11)))))
% 0.19/0.69 [162]~P3(x1621)+E(f17(x1621,x1622,f12(a9,f3(f2(a11)))),f20(x1621,x1622,x1622))
% 0.19/0.69 [105]~P2(x1051)+E(f16(x1051,x1052,x1053),f16(x1051,x1053,x1052))
% 0.19/0.69 [106]~P2(x1061)+E(f20(x1061,x1062,x1063),f20(x1061,x1063,x1062))
% 0.19/0.69 [205]~P11(a1,x2051,x2053)+P11(a1,f16(a1,x2051,x2052),f16(a1,x2053,x2052))
% 0.19/0.69 [206]~P10(a1,x2062,x2063)+P10(a1,f16(a1,x2061,x2062),f16(a1,x2061,x2063))
% 0.19/0.69 [110]~P3(x1101)+E(f17(x1101,x1102,f14(a9,x1103)),f17(x1101,x1102,x1103))
% 0.19/0.69 [118]~P2(x1181)+E(f16(x1181,x1182,f14(x1181,x1183)),f16(x1181,x1182,x1183))
% 0.19/0.69 [119]~P3(x1191)+E(f20(x1191,x1192,f14(x1191,x1193)),f20(x1191,x1192,x1193))
% 0.19/0.69 [120]~P2(x1201)+E(f16(x1201,f14(x1201,x1202),x1203),f16(x1201,x1202,x1203))
% 0.19/0.69 [121]~P3(x1211)+E(f20(x1211,f14(x1211,x1212),x1213),f20(x1211,x1212,x1213))
% 0.19/0.69 [122]~P3(x1221)+E(f17(x1221,f14(x1221,x1222),x1223),f17(x1221,x1222,x1223))
% 0.19/0.69 [168]~P2(x1681)+E(f14(x1681,f16(x1681,x1682,x1683)),f16(x1681,x1682,x1683))
% 0.19/0.69 [169]~P3(x1691)+E(f14(x1691,f20(x1691,x1692,x1693)),f20(x1691,x1692,x1693))
% 0.19/0.69 [170]~P3(x1701)+E(f14(x1701,f17(x1701,x1702,x1703)),f17(x1701,x1702,x1703))
% 0.19/0.69 [210]~P2(x2101)+E(f17(x2101,x2102,f20(a9,f12(a9,f3(f2(a11))),x2103)),f20(x2101,f17(x2101,x2102,x2103),f17(x2101,x2102,x2103)))
% 0.19/0.69 [217]~P7(x2171)+E(f16(x2171,f16(x2171,f17(x2171,x2172,f12(a9,f3(f2(a11)))),f17(x2171,x2173,f12(a9,f3(f2(a11))))),f20(x2171,f20(x2171,f12(x2171,f3(f2(a11))),x2172),x2173)),f17(x2171,f16(x2171,x2172,x2173),f12(a9,f3(f2(a11)))))
% 0.19/0.69 [196]~P2(x1961)+E(f17(x1961,f17(x1961,x1962,x1963),x1964),f17(x1961,x1962,f20(a9,x1963,x1964)))
% 0.19/0.69 [197]~P2(x1971)+E(f16(x1971,x1972,f16(x1971,x1973,x1974)),f16(x1971,x1973,f16(x1971,x1972,x1974)))
% 0.19/0.69 [198]~P2(x1981)+E(f20(x1981,x1982,f20(x1981,x1983,x1984)),f20(x1981,x1983,f20(x1981,x1982,x1984)))
% 0.19/0.69 [201]~P2(x2011)+E(f16(x2011,f16(x2011,x2012,x2013),x2014),f16(x2011,x2012,f16(x2011,x2013,x2014)))
% 0.19/0.69 [202]~P2(x2021)+E(f20(x2021,f20(x2021,x2022,x2023),x2024),f20(x2021,x2022,f20(x2021,x2023,x2024)))
% 0.19/0.69 [203]~P2(x2031)+E(f16(x2031,f16(x2031,x2032,x2033),x2034),f16(x2031,f16(x2031,x2032,x2034),x2033))
% 0.19/0.69 [204]~P2(x2041)+E(f20(x2041,f20(x2041,x2042,x2043),x2044),f20(x2041,f20(x2041,x2042,x2044),x2043))
% 0.19/0.69 [209]~P2(x2091)+E(f20(x2091,f17(x2091,x2092,x2093),f17(x2091,x2092,x2094)),f17(x2091,x2092,f16(a9,x2093,x2094)))
% 0.19/0.69 [211]~P2(x2111)+E(f16(x2111,f16(x2111,x2112,x2113),f16(x2111,x2114,x2115)),f16(x2111,f16(x2111,x2112,x2114),f16(x2111,x2113,x2115)))
% 0.19/0.69 [212]~P2(x2121)+E(f20(x2121,f20(x2121,x2122,x2123),f20(x2121,x2124,x2125)),f20(x2121,f20(x2121,x2122,x2124),f20(x2121,x2123,x2125)))
% 0.19/0.69 [104]E(x1041,x1042)+P11(a1,x1042,x1041)+P11(a1,x1041,x1042)
% 0.19/0.69 [117]E(x1171,x1172)+P11(a1,x1171,x1172)+~P10(a1,x1171,x1172)
% 0.19/0.69 [163]E(x1631,x1632)+~P10(a1,x1632,x1631)+~P10(a1,x1631,x1632)
% 0.19/0.69 [108]~P13(x1082)+~P13(x1081)+P13(f20(a1,x1081,x1082))
% 0.19/0.69 [188]P11(a1,x1881,a11)+~P11(a1,x1882,a11)+E(f16(a9,f12(a9,x1881),f12(a9,x1882)),f12(a9,x1881))
% 0.19/0.69 [195]P11(a1,x1951,a11)+P11(a1,x1952,a11)+E(f16(a9,f12(a9,x1951),f12(a9,x1952)),f12(a9,f16(a1,x1951,x1952)))
% 0.19/0.69 [184]~P10(a1,x1841,x1843)+P10(a1,x1841,x1842)+~P10(a1,x1843,x1842)
% 0.19/0.69 [208]~P11(a1,x2081,x2083)+~P10(a1,x2082,x2084)+P11(a1,f16(a1,x2081,x2082),f16(a1,x2083,x2084))
% 0.19/0.69 [98]~P8(x983)+~P9(x983)+E(x981,x982)+~E(f12(x983,x981),f12(x983,x982))
% 0.19/0.69 [164]~P6(x1641)+~P4(x1641)+~P11(x1641,x1642,x1643)+P11(x1641,x1642,f14(x1641,x1643))
% 0.19/0.69 [165]~P6(x1651)+~P4(x1651)+~P10(x1651,x1652,x1653)+P10(x1651,x1652,f14(x1651,x1653))
% 0.19/0.69 [166]~P6(x1661)+~P4(x1661)+~P11(x1661,x1662,x1663)+P11(x1661,f14(x1661,x1662),x1663)
% 0.19/0.69 [167]~P6(x1671)+~P4(x1671)+~P10(x1671,x1672,x1673)+P10(x1671,f14(x1671,x1672),x1673)
% 0.19/0.69 [174]~P6(x1741)+~P4(x1741)+P11(x1741,x1742,x1743)+~P11(x1741,x1742,f14(x1741,x1743))
% 0.19/0.69 [175]~P6(x1751)+~P4(x1751)+P10(x1751,x1752,x1753)+~P10(x1751,x1752,f14(x1751,x1753))
% 0.19/0.69 [176]~P6(x1761)+~P4(x1761)+P11(x1761,x1762,x1763)+~P11(x1761,f14(x1761,x1762),x1763)
% 0.19/0.69 [177]~P6(x1771)+~P4(x1771)+P10(x1771,x1772,x1773)+~P10(x1771,f14(x1771,x1772),x1773)
% 0.19/0.69 [178]~P8(x1781)+~P5(x1781)+~P11(a1,x1782,x1783)+P11(x1781,f12(x1781,x1782),f12(x1781,x1783))
% 0.19/0.69 [179]~P8(x1791)+~P5(x1791)+~P10(a1,x1792,x1793)+P10(x1791,f12(x1791,x1792),f12(x1791,x1793))
% 0.19/0.69 [185]~P6(x1851)+~P4(x1851)+P11(x1851,f12(x1851,x1852),f12(x1851,x1853))+P10(x1851,f12(x1851,x1853),f12(x1851,x1852))
% 0.19/0.69 [186]~P5(x1863)+~P8(x1863)+~P11(x1863,f12(x1863,x1861),f12(x1863,x1862))+P11(a1,x1861,x1862)
% 0.19/0.69 [187]~P5(x1873)+~P8(x1873)+~P10(x1873,f12(x1873,x1871),f12(x1873,x1872))+P10(a1,x1871,x1872)
% 0.19/0.69 [207]~P4(x2071)+~P6(x2071)+~P11(x2071,f12(x2071,x2072),f12(x2071,x2073))+~P10(x2071,f12(x2071,x2073),f12(x2071,x2072))
% 0.19/0.69 %EqnAxiom
% 0.19/0.69 [1]E(x11,x11)
% 0.19/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.69 [4]~E(x41,x42)+E(f14(x41,x43),f14(x42,x43))
% 0.19/0.69 [5]~E(x51,x52)+E(f14(x53,x51),f14(x53,x52))
% 0.19/0.69 [6]~E(x61,x62)+E(f17(x61,x63,x64),f17(x62,x63,x64))
% 0.19/0.69 [7]~E(x71,x72)+E(f17(x73,x71,x74),f17(x73,x72,x74))
% 0.19/0.69 [8]~E(x81,x82)+E(f17(x83,x84,x81),f17(x83,x84,x82))
% 0.19/0.69 [9]~E(x91,x92)+E(f12(x91,x93),f12(x92,x93))
% 0.19/0.69 [10]~E(x101,x102)+E(f12(x103,x101),f12(x103,x102))
% 0.19/0.69 [11]~E(x111,x112)+E(f3(x111),f3(x112))
% 0.19/0.69 [12]~E(x121,x122)+E(f20(x121,x123,x124),f20(x122,x123,x124))
% 0.19/0.69 [13]~E(x131,x132)+E(f20(x133,x131,x134),f20(x133,x132,x134))
% 0.19/0.69 [14]~E(x141,x142)+E(f20(x143,x144,x141),f20(x143,x144,x142))
% 0.19/0.69 [15]~E(x151,x152)+E(f2(x151),f2(x152))
% 0.19/0.69 [16]~E(x161,x162)+E(f16(x161,x163,x164),f16(x162,x163,x164))
% 0.19/0.69 [17]~E(x171,x172)+E(f16(x173,x171,x174),f16(x173,x172,x174))
% 0.19/0.69 [18]~E(x181,x182)+E(f16(x183,x184,x181),f16(x183,x184,x182))
% 0.19/0.69 [19]~E(x191,x192)+E(f13(x191),f13(x192))
% 0.19/0.69 [20]~E(x201,x202)+E(f19(x201),f19(x202))
% 0.19/0.69 [21]~P1(x211)+P1(x212)+~E(x211,x212)
% 0.19/0.69 [22]~P7(x221)+P7(x222)+~E(x221,x222)
% 0.19/0.69 [23]~P2(x231)+P2(x232)+~E(x231,x232)
% 0.19/0.69 [24]P10(x242,x243,x244)+~E(x241,x242)+~P10(x241,x243,x244)
% 0.19/0.69 [25]P10(x253,x252,x254)+~E(x251,x252)+~P10(x253,x251,x254)
% 0.19/0.69 [26]P10(x263,x264,x262)+~E(x261,x262)+~P10(x263,x264,x261)
% 0.19/0.69 [27]~P3(x271)+P3(x272)+~E(x271,x272)
% 0.19/0.69 [28]P11(x282,x283,x284)+~E(x281,x282)+~P11(x281,x283,x284)
% 0.19/0.69 [29]P11(x293,x292,x294)+~E(x291,x292)+~P11(x293,x291,x294)
% 0.19/0.69 [30]P11(x303,x304,x302)+~E(x301,x302)+~P11(x303,x304,x301)
% 0.19/0.69 [31]~P6(x311)+P6(x312)+~E(x311,x312)
% 0.19/0.69 [32]~P5(x321)+P5(x322)+~E(x321,x322)
% 0.19/0.69 [33]~P4(x331)+P4(x332)+~E(x331,x332)
% 0.19/0.69 [34]~P8(x341)+P8(x342)+~E(x341,x342)
% 0.19/0.69 [35]~P9(x351)+P9(x352)+~E(x351,x352)
% 0.19/0.69 [36]~P13(x361)+P13(x362)+~E(x361,x362)
% 0.19/0.69 [37]~P12(x371)+P12(x372)+~E(x371,x372)
% 0.19/0.69
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 cnf(222,plain,
% 0.19/0.69 (~E(f16(a1,f17(a1,x2221,f12(a9,f3(f2(a11)))),f17(a1,x2222,f12(a9,f3(f2(a11))))),f16(a1,f20(a1,f12(a1,f3(f3(f2(a11)))),a10),f13(a1)))),
% 0.19/0.69 inference(rename_variables,[],[89])).
% 0.19/0.69 cnf(226,plain,
% 0.19/0.69 (P10(a1,x2261,x2261)),
% 0.19/0.69 inference(rename_variables,[],[67])).
% 0.19/0.69 cnf(233,plain,
% 0.19/0.69 (E(f12(a1,x2331),x2331)),
% 0.19/0.69 inference(rename_variables,[],[57])).
% 0.19/0.69 cnf(239,plain,
% 0.19/0.69 (P10(a1,x2391,x2391)),
% 0.19/0.69 inference(rename_variables,[],[67])).
% 0.19/0.69 cnf(244,plain,
% 0.19/0.69 ($false),
% 0.19/0.69 inference(scs_inference,[],[89,222,67,226,239,69,53,66,82,85,83,57,233,71,64,2,101,216,215,194,193,91,37,36,30,29,26,25,3,117]),
% 0.19/0.69 ['proof']).
% 0.19/0.69 % SZS output end Proof
% 0.19/0.69 % Total time :0.030000s
%------------------------------------------------------------------------------