TSTP Solution File: SWV676-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV676-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 Sep 29 15:24:02 EDT 2022
% Result : Unsatisfiable 95.47s 61.73s
% Output : Proof 95.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 174
% Syntax : Number of formulae : 422 ( 126 unt; 22 typ; 0 def)
% Number of atoms : 1725 ( 764 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 2184 ( 927 ~;1100 |; 0 &)
% ( 157 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 68 ( 68 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 17 >; 13 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 986 ( 906 !; 0 ?; 986 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(v_y_type,type,
v_y: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(1,plain,
( class_Ring__and__Field_Ofield(t_a)
<=> class_Ring__and__Field_Ofield(t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(3,plain,
class_Ring__and__Field_Ofield(t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
tff(8,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Power_Opower) ).
tff(20,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Power_Opower(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Power_Opower(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Power_Opower(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Power_Opower(t_a) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
class_Power_Opower(t_a),
inference(unit_resolution,[status(thm)],[25,3,22]) ).
tff(27,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
tff(31,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ),
inference(unit_resolution,[status(thm)],[36,33]) ).
tff(38,plain,
c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(unit_resolution,[status(thm)],[37,26]) ).
tff(39,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Omult__zero) ).
tff(45,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Omult__zero(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Omult__zero(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Omult__zero(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Omult__zero(t_a) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
class_Ring__and__Field_Omult__zero(t_a),
inference(unit_resolution,[status(thm)],[50,3,47]) ).
tff(52,plain,
^ [T: $i] :
refl(
( ( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
<=> ( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ozero__neq__one) ).
tff(58,plain,
! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [T: $i] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
class_Ring__and__Field_Ozero__neq__one(t_a),
inference(unit_resolution,[status(thm)],[64,3,61]) ).
tff(66,plain,
^ [T: $i] :
refl(
( ( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
<=> ( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ono__zero__divisors) ).
tff(72,plain,
! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [T: $i] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
class_Ring__and__Field_Ono__zero__divisors(t_a),
inference(unit_resolution,[status(thm)],[78,3,75]) ).
tff(80,plain,
( ( v_a != c_HOL_Ozero__class_Ozero(t_a) )
<=> ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( $false
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( class_Ring__and__Field_Ofield(t_a)
<=> $true ),
inference(iff_true,[status(thm)],[2]) ).
tff(84,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
<=> $false ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( $false
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(transitivity,[status(thm)],[86,81]) ).
tff(88,axiom,
( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nz_0) ).
tff(89,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(modus_ponens,[status(thm)],[89,80]) ).
tff(91,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(
( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ) )),
rewrite(
( ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ) )),
rewrite(
( ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(
( ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(
( ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
tff(97,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
c_Power_Opower__class_Opower(v_a,v_x,t_a) != c_HOL_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[103,100,90,79,65,26,51]) ).
tff(105,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Odivision__ring) ).
tff(109,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Odivision__ring(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Odivision__ring(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Odivision__ring(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Odivision__ring(t_a) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
class_Ring__and__Field_Odivision__ring(t_a),
inference(unit_resolution,[status(thm)],[114,3,111]) ).
tff(116,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ) )),
( ( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(
( ( ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ) )),
( ( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
tff(122,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) )
<=> ( ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a),
inference(unit_resolution,[status(thm)],[131,125,90,115,104]) ).
tff(133,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
tff(138,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[139,135]) ).
tff(141,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) ) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),
inference(unit_resolution,[status(thm)],[143,140,3]) ).
tff(145,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Oinverse__class_Oinverse(v_a,t_a),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),
inference(transitivity,[status(thm)],[146,133,40]) ).
tff(148,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) ) ),
inference(unit_resolution,[status(thm)],[150,33]) ).
tff(152,plain,
c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),
inference(unit_resolution,[status(thm)],[151,26]) ).
tff(153,plain,
c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[153,147]) ).
tff(155,plain,
^ [V_n: $i] :
refl(
( ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) )
<=> ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) )
<=> ! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) )
<=> ! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,axiom,
! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
tff(159,plain,
! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
( ~ ! [V_n: $i] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) )
| ( c_Suc(v_y) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
c_Suc(v_y) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),
inference(unit_resolution,[status(thm)],[162,161]) ).
tff(164,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat) = c_Suc(v_y),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),t_a) = c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
^ [T: $i] :
refl(
( ( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],]) ).
tff(167,plain,
( ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
( ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
<=> ( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],]) ).
tff(170,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1) ).
tff(172,plain,
! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[172,168]) ).
tff(174,plain,
! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[174,167]) ).
tff(176,plain,
( ( ~ ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
( ~ ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(178,plain,
( ~ ! [T: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
class_Ring__and__Field_Ocomm__semiring__1(t_a),
inference(unit_resolution,[status(thm)],[178,3,175]) ).
tff(180,plain,
^ [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(181,plain,
( ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) )
<=> ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,plain,
( ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) )
<=> ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,axiom,
! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
tff(184,plain,
! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ),
inference(skolemize,[status(sab)],[184]) ).
tff(186,plain,
! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ),
inference(modus_ponens,[status(thm)],[185,181]) ).
tff(187,plain,
( ( ~ ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),t_a) ) )
<=> ( ~ ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(188,plain,
( ~ ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(189,plain,
( ~ ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),t_a) ) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),t_a),
inference(unit_resolution,[status(thm)],[189,186,179]) ).
tff(191,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
refl(
( ( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(192,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) ),
inference(quant_intro,[status(thm)],[191]) ).
tff(193,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(195,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,axiom,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
tff(197,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[197,193]) ).
tff(199,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
inference(skolemize,[status(sab)],[198]) ).
tff(200,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[199,192]) ).
tff(201,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ( ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) ) ),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) ) ),
inference(transitivity,[status(thm)],[203,201]) ).
tff(205,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) ) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
c_Power_Opower__class_Opower(v_a,v_y,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),
inference(unit_resolution,[status(thm)],[206,200,90,3]) ).
tff(208,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a) = c_Power_Opower__class_Opower(v_a,v_y,t_a),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),
inference(transitivity,[status(thm)],[209,190,165,152]) ).
tff(211,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
^ [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(213,plain,
( ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
<=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[212]) ).
tff(214,plain,
( ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
<=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(215,axiom,
! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
tff(216,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ),
inference(skolemize,[status(sab)],[216]) ).
tff(218,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[217,213]) ).
tff(219,plain,
( ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),t_a) ) )
<=> ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(220,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[221,218,179]) ).
tff(223,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(225,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(227,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
tff(228,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ),
inference(skolemize,[status(sab)],[228]) ).
tff(230,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ),
inference(modus_ponens,[status(thm)],[229,225]) ).
tff(231,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) ) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(232,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),
inference(unit_resolution,[status(thm)],[233,230,179]) ).
tff(235,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
^ [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(237,plain,
( ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
<=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) ),
inference(quant_intro,[status(thm)],[236]) ).
tff(238,plain,
( ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
<=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(239,axiom,
! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
tff(240,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
inference(skolemize,[status(sab)],[240]) ).
tff(242,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
inference(modus_ponens,[status(thm)],[241,237]) ).
tff(243,plain,
( ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) ) )
<=> ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(244,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(245,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[244,243]) ).
tff(246,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),
inference(unit_resolution,[status(thm)],[245,242,179]) ).
tff(247,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(248,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(249,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[249,230,179]) ).
tff(251,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),
inference(transitivity,[status(thm)],[250,246,235]) ).
tff(252,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),t_a) ) )
<=> ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(254,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(255,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[255,218,179]) ).
tff(257,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),
inference(symmetry,[status(thm)],[209]) ).
tff(258,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),
inference(symmetry,[status(thm)],[190]) ).
tff(259,plain,
c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_y,tc_nat),t_a),
inference(symmetry,[status(thm)],[165]) ).
tff(260,plain,
c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),
inference(transitivity,[status(thm)],[153,259,258,257]) ).
tff(261,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Oone__class_Oone(tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(263,plain,
( ( ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(264,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ) ),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ) ),
inference(transitivity,[status(thm)],[264,262]) ).
tff(266,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[266,265]) ).
tff(268,plain,
( ( c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ),
inference(unit_resolution,[status(thm)],[267,200,3]) ).
tff(269,plain,
v_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(unit_resolution,[status(thm)],[268,104]) ).
tff(270,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = v_a,
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),
inference(monotonicity,[status(thm)],[270,208]) ).
tff(272,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_y,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
^ [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(274,plain,
( ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) )
<=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[273]) ).
tff(275,plain,
( ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) )
<=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(276,axiom,
! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
tff(277,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[276,275]) ).
tff(278,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[277]) ).
tff(279,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[278,274]) ).
tff(280,plain,
( ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) ) )
<=> ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(281,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(282,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[282,279,179]) ).
tff(284,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),
inference(symmetry,[status(thm)],[283]) ).
tff(285,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[208]) ).
tff(286,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(288,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(289,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[288,287]) ).
tff(290,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[289,10,3]) ).
tff(291,plain,
( c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
<=> c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(292,axiom,
c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(293,plain,
c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat),
inference(modus_ponens,[status(thm)],[292,291]) ).
tff(294,plain,
^ [V_n: $i,V_m: $i] :
refl(
( ( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) )
<=> ( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(295,plain,
( ! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) )
<=> ! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ),
inference(quant_intro,[status(thm)],[294]) ).
tff(296,plain,
( ! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) )
<=> ! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(297,axiom,
! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
tff(298,plain,
! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
inference(modus_ponens,[status(thm)],[297,296]) ).
tff(299,plain,
! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
inference(skolemize,[status(sab)],[298]) ).
tff(300,plain,
! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
inference(modus_ponens,[status(thm)],[299,295]) ).
tff(301,plain,
( ( ~ ! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) )
| c_lessequals(v_y,v_x,tc_nat)
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat) )
<=> ( ~ ! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) )
| c_lessequals(v_y,v_x,tc_nat)
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(302,plain,
( ~ ! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) )
| c_lessequals(v_y,v_x,tc_nat)
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(303,plain,
( ~ ! [V_n: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) )
| c_lessequals(v_y,v_x,tc_nat)
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat) ),
inference(modus_ponens,[status(thm)],[302,301]) ).
tff(304,plain,
c_lessequals(v_y,v_x,tc_nat),
inference(unit_resolution,[status(thm)],[303,300,293]) ).
tff(305,plain,
( ( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) )
<=> ( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(306,axiom,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(307,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[306,305]) ).
tff(308,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[307,305]) ).
tff(309,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[308,305]) ).
tff(310,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[309,305]) ).
tff(311,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[310,305]) ).
tff(312,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[311,305]) ).
tff(313,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[312,305]) ).
tff(314,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[313,305]) ).
tff(315,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
| ~ c_lessequals(v_y,v_x,tc_nat) ),
inference(modus_ponens,[status(thm)],[314,305]) ).
tff(316,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_y,t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(unit_resolution,[status(thm)],[315,304]) ).
tff(317,plain,
^ [V_n: $i,V_m: $i] :
refl(
( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(318,plain,
( ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) ),
inference(quant_intro,[status(thm)],[317]) ).
tff(319,plain,
( ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(320,axiom,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
tff(321,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[320,319]) ).
tff(322,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(skolemize,[status(sab)],[321]) ).
tff(323,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[322,318]) ).
tff(324,plain,
( ~ ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat) = c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(325,plain,
c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat) = c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),
inference(unit_resolution,[status(thm)],[324,323]) ).
tff(326,plain,
c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),
inference(monotonicity,[status(thm)],[326]) ).
tff(328,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,v_y,tc_nat),t_a),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(transitivity,[status(thm)],[328,316,290,286]) ).
tff(330,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a),
inference(monotonicity,[status(thm)],[270,145]) ).
tff(331,plain,
c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(333,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[332]) ).
tff(334,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(335,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(336,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[335]) ).
tff(337,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
tff(338,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[337,336]) ).
tff(339,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[338,334]) ).
tff(340,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[339]) ).
tff(341,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[340,333]) ).
tff(342,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) = c_HOL_Oone__class_Oone(t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) = c_HOL_Oone__class_Oone(t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(343,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(344,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(modus_ponens,[status(thm)],[343,342]) ).
tff(345,plain,
( ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(unit_resolution,[status(thm)],[344,341,90]) ).
tff(346,plain,
c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a) = c_HOL_Oone__class_Oone(t_a),
inference(unit_resolution,[status(thm)],[345,115]) ).
tff(347,plain,
c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(v_a,c_HOL_Oinverse__class_Oinverse(v_a,t_a),t_a),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),
inference(transitivity,[status(thm)],[347,331]) ).
tff(349,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_a,c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_y,t_a),v_a,t_a),v_a,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[348,329]) ).
tff(350,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(
( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(351,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[350]) ).
tff(352,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(353,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(354,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[353]) ).
tff(355,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
tff(356,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[355,354]) ).
tff(357,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[356,352]) ).
tff(358,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ),
inference(skolemize,[status(sab)],[357]) ).
tff(359,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[358,351]) ).
tff(360,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(361,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(362,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) ) ),
inference(modus_ponens,[status(thm)],[361,360]) ).
tff(363,plain,
( ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) ) ),
inference(unit_resolution,[status(thm)],[362,90,359]) ).
tff(364,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),
inference(unit_resolution,[status(thm)],[363,115]) ).
tff(365,plain,
^ [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
refl(
( ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(366,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[365]) ).
tff(367,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(368,plain,
^ [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_n,V_m,tc_nat) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(
( ( ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(369,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[368]) ).
tff(370,axiom,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff_0) ).
tff(371,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[370,369]) ).
tff(372,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[371,367]) ).
tff(373,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[372]) ).
tff(374,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[373,366]) ).
tff(375,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(376,plain,
( ( ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(377,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) ) ),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) ) ),
inference(transitivity,[status(thm)],[377,375]) ).
tff(379,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(380,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(c_Suc(v_y),c_Suc(v_x),tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[379,378]) ).
tff(381,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),
inference(unit_resolution,[status(thm)],[380,90,374,3,293]) ).
tff(382,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a),
inference(monotonicity,[status(thm)],[382]) ).
tff(384,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),
inference(transitivity,[status(thm)],[383,364]) ).
tff(385,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a),
inference(monotonicity,[status(thm)],[384]) ).
tff(386,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a),t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(387,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(388,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[387,386]) ).
tff(389,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[388,10,3]) ).
tff(390,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[381]) ).
tff(391,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(392,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(393,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[392,391]) ).
tff(394,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a),
inference(unit_resolution,[status(thm)],[393,140,3]) ).
tff(395,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a),t_a),
inference(symmetry,[status(thm)],[364]) ).
tff(396,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),
inference(transitivity,[status(thm)],[395,394,390,389,385,349,284,272,261,256,252,223,211,154,15]) ).
tff(397,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a) )
<=> ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(398,axiom,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(399,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(c_Suc(v_x),c_Suc(v_y),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_Suc(v_y),t_a),c_Power_Opower__class_Opower(v_a,c_Suc(v_x),t_a),t_a),
inference(modus_ponens,[status(thm)],[398,397]) ).
tff(400,plain,
$false,
inference(unit_resolution,[status(thm)],[399,396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV676-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.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 : Sun Sep 4 07:19:12 EDT 2022
% 0.21/0.34 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 95.47/61.73 % SZS status Unsatisfiable
% 95.47/61.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------