%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV673-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:35:54 AM UTC 2025
% Result : Unsatisfiable 9.84s 9.99s
% Output : Proof 9.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 70
% Syntax : Number of formulae : 178 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 790 ( 424 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1023 ( 432 ~; 520 |; 0 &)
% ( 71 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 432 ( 394 !; 0 ?; 432 :)
% 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(v_n_type,type,
v_n: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(v_m_type,type,
v_m: $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(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(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) ) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
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) ) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,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)],[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,
( ( ~ ! [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_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,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_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,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,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,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,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,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,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),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(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,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(20,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ocomm__semiring__1(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ocomm__semiring__1(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ocomm__semiring__1(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Ocomm__semiring__1(t_a) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
class_Ring__and__Field_Ocomm__semiring__1(t_a),
inference(unit_resolution,[status(thm)],[25,10,22]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30,29]) ).
tff(32,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)],[31]) ).
tff(33,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)],[32,28]) ).
tff(34,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(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_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) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,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(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,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(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[36,33,26]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,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)],[41,40]) ).
tff(43,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)],[42]) ).
tff(44,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)],[43,39]) ).
tff(45,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(46,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(47,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)],[46,45]) ).
tff(48,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)],[47,10,44]) ).
tff(49,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)],[48]) ).
tff(50,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
<=> ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(55,plain,
( ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
<=> ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) != c_HOL_Ozero__class_Ozero(t_a) )
<=> ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,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(65,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(66,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)],[65,64]) ).
tff(67,plain,
class_Ring__and__Field_Odivision__ring(t_a),
inference(unit_resolution,[status(thm)],[66,10,63]) ).
tff(68,plain,
( ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,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(70,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[70,10]) ).
tff(72,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_Oinverse__class_Oinverse(V_a,T_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(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,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_Oinverse__class_Oinverse(V_a,T_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_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,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_Oinverse__class_Oinverse(V_a,T_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_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,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_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(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_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,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_inverse__zero__imp__zero_0) ).
tff(78,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_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,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_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,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_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,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_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,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_Oinverse__class_Oinverse(V_a,T_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(v_a,t_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_Oinverse__class_Oinverse(V_a,T_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(v_a,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,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_Oinverse__class_Oinverse(V_a,T_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(v_a,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,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_Oinverse__class_Oinverse(V_a,T_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(v_a,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(unit_resolution,[status(thm)],[84,81,71]) ).
tff(86,plain,
c_HOL_Oinverse__class_Oinverse(v_a,t_a) != c_HOL_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[85,67]) ).
tff(87,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) != c_HOL_Ozero__class_Ozero(t_a),
inference(modus_ponens,[status(thm)],[86,56]) ).
tff(88,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(89,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)],[88]) ).
tff(90,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(91,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(92,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)],[91]) ).
tff(93,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(94,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)],[93,92]) ).
tff(95,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)],[94,90]) ).
tff(96,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)],[95]) ).
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_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)],[96,89]) ).
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_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) ) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,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) ) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ( ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_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(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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_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) ) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_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(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,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) ) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a) ) ) ),
inference(monotonicity,[status(thm)],[99]) ).
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_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) ) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_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(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,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) ) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a) ) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
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_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) ) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_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(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,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_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) ) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a),
inference(unit_resolution,[status(thm)],[103,97,67,87]) ).
tff(105,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_m,t_a),t_a),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_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] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_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_field__inverse_0) ).
tff(112,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_a,t_a) = c_HOL_Oone__class_Oone(t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_a,t_a) = c_HOL_Oone__class_Oone(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_a,t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_a,t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_a,t_a) = c_HOL_Oone__class_Oone(t_a),
inference(unit_resolution,[status(thm)],[118,115,10,71]) ).
tff(120,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_a,t_a),
inference(monotonicity,[status(thm)],[49]) ).
tff(121,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) = c_HOL_Oone__class_Oone(t_a),
inference(transitivity,[status(thm)],[120,119]) ).
tff(122,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
<=> ( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) )
<=> ( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
tff(128,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ( ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a) )
<=> ( ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) ) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) ) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b )
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),v_a,t_a) != c_HOL_Oone__class_Oone(t_a) ) ),
inference(unit_resolution,[status(thm)],[137,131,67]) ).
tff(139,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a) = v_a,
inference(unit_resolution,[status(thm)],[138,121]) ).
tff(140,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a) = c_Power_Opower__class_Opower(v_a,v_m,t_a),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
c_Power_Opower__class_Opower(v_a,v_m,t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),t_a),v_m,t_a),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
c_Power_Opower__class_Opower(v_a,v_m,t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),
inference(transitivity,[status(thm)],[141,105,53]) ).
tff(143,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,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) ) )
| ( 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(144,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,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_inst,[status(thm)],[]) ).
tff(145,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,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)],[144,143]) ).
tff(146,plain,
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(unit_resolution,[status(thm)],[145,71,97,67]) ).
tff(147,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[146,142]) ).
tff(148,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,v_m,t_a),t_a),
inference(symmetry,[status(thm)],[147]) ).
tff(149,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(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,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(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,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(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,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(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[151,10,7]) ).
tff(153,plain,
( c_lessequals(v_m,v_n,tc_nat)
<=> c_lessequals(v_m,v_n,tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,axiom,
c_lessequals(v_m,v_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(155,plain,
c_lessequals(v_m,v_n,tc_nat),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
^ [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
refl(( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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(157,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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)],[156]) ).
tff(158,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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(159,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) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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(160,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] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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)],[159]) ).
tff(161,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(162,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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)],[161,160]) ).
tff(163,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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)],[162,158]) ).
tff(164,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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)],[163]) ).
tff(165,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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)],[164,157]) ).
tff(166,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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_lessequals(v_m,v_n,tc_nat)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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_lessequals(v_m,v_n,tc_nat)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,plain,
( ( ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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_lessequals(v_m,v_n,tc_nat)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) ) ),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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_lessequals(v_m,v_n,tc_nat)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) ) ),
inference(transitivity,[status(thm)],[168,166]) ).
tff(170,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ( 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_lessequals(v_m,v_n,tc_nat)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
( ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Ozero__class_Ozero(t_a) )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a) ) ),
inference(unit_resolution,[status(thm)],[171,10,165,155]) ).
tff(173,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_n,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_m,t_a),t_a),
inference(unit_resolution,[status(thm)],[172,86]) ).
tff(174,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,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(transitivity,[status(thm)],[173,152,148,37,15]) ).
tff(175,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,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_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,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(176,axiom,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(177,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,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)],[176,175]) ).
tff(178,plain,
$false,
inference(unit_resolution,[status(thm)],[177,174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV673-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 10:42:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 9.84/9.99 % SZS status Unsatisfiable
% 9.84/9.99 % SZS output start Proof
% See solution above
% 9.84/10.06 % E exiting
%------------------------------------------------------------------------------