%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV674-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.43s 0.62s
% Output : Proof 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 47
% Syntax : Number of formulae : 114 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 356 ( 137 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 412 ( 180 ~; 194 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 195 ( 177 !; 0 ?; 195 :)
% 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_x_type,type,
v_x: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(1,plain,
( class_Ring__and__Field_Ofield(t_a)
<=> class_Ring__and__Field_Ofield(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(3,plain,
class_Ring__and__Field_Ofield(t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
tff(8,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,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_Odivision__ring(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ) )),
inference(bind,[status(th)],[]) ).
tff(17,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)],[16]) ).
tff(18,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(19,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(20,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,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(24,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(25,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)],[24,23]) ).
tff(26,plain,
class_Ring__and__Field_Odivision__ring(t_a),
inference(unit_resolution,[status(thm)],[25,3,22]) ).
tff(27,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(28,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(29,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[29,3]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34]) ).
tff(36,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(37,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)],[36,35]) ).
tff(38,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)],[37,33]) ).
tff(39,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)],[38]) ).
tff(40,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)],[39,32]) ).
tff(41,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(unit_resolution,[status(thm)],[43,40,30]) ).
tff(45,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(unit_resolution,[status(thm)],[44,26]) ).
tff(46,plain,
^ [V_m: $i] :
refl(( ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m )
<=> ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m )
<=> ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m )
<=> ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
tff(50,plain,
! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m )
| ( c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = v_x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = v_x,
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) = c_Power_Opower__class_Opower(v_a,v_x,t_a),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(transitivity,[status(thm)],[57,45]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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(63,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,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(67,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(68,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)],[67,66]) ).
tff(69,plain,
class_Power_Opower(t_a),
inference(unit_resolution,[status(thm)],[68,3,65]) ).
tff(70,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
tff(74,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(unit_resolution,[status(thm)],[79,76]) ).
tff(81,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a),
inference(unit_resolution,[status(thm)],[80,69]) ).
tff(82,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a),
inference(monotonicity,[status(thm)],[81,58]) ).
tff(83,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[82]) ).
tff(84,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(85,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)],[84]) ).
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(rewrite,[status(thm)],[]) ).
tff(87,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(88,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)],[87]) ).
tff(89,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(90,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,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(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) ),
inference(quant_inst,[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(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(unit_resolution,[status(thm)],[96,3,93]) ).
tff(98,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
tff(102,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(unit_resolution,[status(thm)],[107,104,97]) ).
tff(109,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(transitivity,[status(thm)],[109,83,15]) ).
tff(111,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
<=> ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,axiom,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(113,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
$false,
inference(unit_resolution,[status(thm)],[113,110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWV674-1 : TPTP v9.0.0. Released v4.1.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.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 10:39:31 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.43/0.62 % SZS status Unsatisfiable
% 0.43/0.62 % SZS output start Proof
% See solution above
% 0.51/0.68 % E exiting
%------------------------------------------------------------------------------