%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV680-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:35:55 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.63s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 59
% Syntax : Number of formulae : 137 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 711 ( 193 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1020 ( 482 ~; 476 |; 0 &)
% ( 62 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 36 ( 36 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 307 ( 280 !; 0 ?; 307 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_i_type,type,
v_i: $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(v_k_type,type,
v_k: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(v_j_type,type,
v_j: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
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_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(1,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,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(5,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( class_Ring__and__Field_Ofield(t_a)
<=> class_Ring__and__Field_Ofield(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(10,plain,
class_Ring__and__Field_Ofield(t_a),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ono__zero__divisors(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ono__zero__divisors(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ono__zero__divisors(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ono__zero__divisors(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ono__zero__divisors(t_a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
class_Ring__and__Field_Ono__zero__divisors(t_a),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,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(16,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)],[15]) ).
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(rewrite,[status(thm)],[]) ).
tff(18,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(19,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,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(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) ),
inference(quant_inst,[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(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
class_Power_Opower(t_a),
inference(unit_resolution,[status(thm)],[24,10,21]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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(30,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Omult__zero(T) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,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(34,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(35,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)],[34,33]) ).
tff(36,plain,
class_Ring__and__Field_Omult__zero(t_a),
inference(unit_resolution,[status(thm)],[35,10,32]) ).
tff(37,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,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(41,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ozero__neq__one(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ozero__neq__one(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ozero__neq__one(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ozero__neq__one(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ozero__neq__one(t_a) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
class_Ring__and__Field_Ozero__neq__one(t_a),
inference(unit_resolution,[status(thm)],[46,10,43]) ).
tff(48,plain,
( ( v_a != c_HOL_Ozero__class_Ozero(t_a) )
<=> ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
v_a != c_HOL_Ozero__class_Ozero(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(50,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,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_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(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_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ) )),
rewrite(( ( ~ 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_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_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(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_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(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_Power_Opower(T_a) ) )),
rewrite(( ( ~ 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_Power_Opower(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_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_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_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_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)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(( ( ~ 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)
| ( 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_Omult__zero(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(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_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_Ozero__neq__one(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_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_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_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(( ( ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_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_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_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(55,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_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,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(57,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(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)
| ( c_Power_Opower__class_Opower(v_a,v_k,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_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(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)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a) )
<=> ( ( v_a = c_HOL_Ozero__class_Ozero(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)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(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)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(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)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ozero__neq__one(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_Power_Opower(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(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)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ 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)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(unit_resolution,[status(thm)],[66,60,50]) ).
tff(68,plain,
c_Power_Opower__class_Opower(v_a,v_k,t_a) != c_HOL_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[67,47,36,25,14]) ).
tff(69,plain,
^ [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
^ [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) )
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
tff(75,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_b = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( ( c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a) ) ),
inference(unit_resolution,[status(thm)],[81,78,10]) ).
tff(83,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a),
inference(unit_resolution,[status(thm)],[82,68]) ).
tff(84,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
^ [T: $i] :
refl(( ( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
^ [T: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) )
<=> ( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult) ).
tff(91,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_OrderedGroup_Omonoid__mult(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_OrderedGroup_Omonoid__mult(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_OrderedGroup_Omonoid__mult(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_OrderedGroup_Omonoid__mult(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(unit_resolution,[status(thm)],[97,10,94]) ).
tff(99,plain,
^ [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
refl(( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,axiom,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
tff(103,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a) ) ),
inference(unit_resolution,[status(thm)],[108,105]) ).
tff(110,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),
inference(unit_resolution,[status(thm)],[109,98]) ).
tff(111,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a) ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),
inference(unit_resolution,[status(thm)],[113,105,98]) ).
tff(115,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
tff(117,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
tff(122,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat) = c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat) = c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat) = c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat) = c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat) = c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),
inference(unit_resolution,[status(thm)],[127,124,117]) ).
tff(129,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_j,v_i,tc_nat),t_a),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),
inference(transitivity,[status(thm)],[130,114]) ).
tff(132,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a),
inference(monotonicity,[status(thm)],[131,110]) ).
tff(133,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
inference(transitivity,[status(thm)],[132,84]) ).
tff(134,plain,
( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) )
<=> ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,axiom,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(136,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
$false,
inference(unit_resolution,[status(thm)],[136,133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV680-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 10:38:54 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.48/0.63 % SZS status Unsatisfiable
% 0.48/0.63 % SZS output start Proof
% See solution above
% 0.48/0.69 % E exiting
%------------------------------------------------------------------------------