TSTP Solution File: ANA028-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA028-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Tue Sep 6 16:23:32 EDT 2022
% Result : Unsatisfiable 0.19s 0.61s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 106
% Syntax : Number of formulae : 257 ( 84 unt; 13 typ; 0 def)
% Number of atoms : 850 ( 254 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1109 ( 519 ~; 510 |; 0 &)
% ( 80 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 653 ( 614 !; 0 ?; 653 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_b_type,type,
t_b: $i ).
tff(c_plus_type,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(c_minus_type,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_k_type,type,
v_k: $i > $i ).
tff(v_g_type,type,
v_g: $i > $i ).
tff(c_0_type,type,
c_0: $i ).
tff(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(1,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(3,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
<=> ( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
tff(10,plain,
! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [T_a: $i,V_y: $i] :
refl(
( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
tff(22,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_k(v_x),t_b) = v_k(v_x) ) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_k(v_x),t_b) = v_k(v_x) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_k(v_x),t_b) = v_k(v_x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_k(v_x),t_b) = v_k(v_x) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_plus(c_0,v_k(v_x),t_b) = v_k(v_x),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
<=> ( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
tff(35,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(unit_resolution,[status(thm)],[41,38,3]) ).
tff(43,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
tff(47,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),v_f(v_x),t_b) = c_0 ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),v_f(v_x),t_b) = c_0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),v_f(v_x),t_b) = c_0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_a,T_a) = c_0 ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),v_f(v_x),t_b) = c_0 ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
c_minus(v_f(v_x),v_f(v_x),t_b) = c_0,
inference(unit_resolution,[status(thm)],[52,49,42]) ).
tff(54,plain,
c_0 = c_minus(v_f(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
c_plus(c_0,v_k(v_x),t_b) = c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_k(v_x),t_b),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_k(v_x),t_b) = c_plus(c_0,v_k(v_x),t_b),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
tff(61,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_k(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_k(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_k(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_k(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_k(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[66,63,42]) ).
tff(68,plain,
c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) = c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_k(v_x),t_b),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
tff(73,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[78,75,42]) ).
tff(80,plain,
c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = v_k(v_x),
inference(transitivity,[status(thm)],[79,68,56,28]) ).
tff(81,plain,
( c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b)
<=> c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( c_lessequals(v_g(v_x),v_k(v_x),t_b)
<=> c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b) ),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
^ [V_U: $i] :
refl(
( c_lessequals(v_g(V_U),v_k(V_U),t_b)
<=> c_lessequals(v_g(V_U),v_k(V_U),t_b) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(86,axiom,
! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(87,plain,
! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [V_U: $i] : c_lessequals(v_g(V_U),v_k(V_U),t_b)
| c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[91,82]) ).
tff(93,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),
inference(unit_resolution,[status(thm)],[95,63,42]) ).
tff(97,plain,
c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) = c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
v_k(v_x) = c_plus(c_0,v_k(v_x),t_b),
inference(symmetry,[status(thm)],[28]) ).
tff(99,plain,
v_k(v_x) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[98,55,67]) ).
tff(100,plain,
c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),t_b),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__5_0) ).
tff(106,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[111,108,42]) ).
tff(113,plain,
c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_f(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[116,63,42]) ).
tff(118,plain,
c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b),
inference(monotonicity,[status(thm)],[97]) ).
tff(119,plain,
c_minus(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) = c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),
inference(unit_resolution,[status(thm)],[122,75,42]) ).
tff(124,plain,
c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b) = c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) = c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[96,124]) ).
tff(126,plain,
c_minus(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
c_minus(c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b) = c_minus(c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b) = c_minus(c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b) = c_minus(c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b) = c_minus(c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
c_minus(v_f(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b) = c_minus(c_plus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[130,108,42]) ).
tff(132,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),
inference(unit_resolution,[status(thm)],[134,108,42]) ).
tff(136,plain,
c_minus(v_f(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b) = c_minus(v_f(v_x),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),t_b),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
c_minus(v_f(v_x),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),t_b) = c_minus(v_f(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_f(v_x),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
c_minus(v_f(v_x),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[140,108,42]) ).
tff(142,plain,
c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(v_f(v_x),c_minus(c_plus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[142,137,131,127,119]) ).
tff(144,plain,
c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) = c_plus(c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
c_plus(c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) = c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),c_plus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
c_plus(c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[148,63,42]) ).
tff(150,plain,
c_minus(c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) = c_plus(c_minus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b),
inference(unit_resolution,[status(thm)],[153,63,42]) ).
tff(155,plain,
c_minus(c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b) = c_minus(c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
c_minus(c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b) = c_minus(c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b),
inference(unit_resolution,[status(thm)],[159,75,42]) ).
tff(161,plain,
c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) = c_minus(c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b),v_f(v_x),t_b),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(c_plus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[164,63,42]) ).
tff(166,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_g(v_x),t_b) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[168,63,42]) ).
tff(170,plain,
c_plus(c_0,v_g(v_x),t_b) = c_plus(c_minus(v_f(v_x),v_f(v_x),t_b),v_g(v_x),t_b),
inference(monotonicity,[status(thm)],[54]) ).
tff(171,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_g(v_x),t_b) = v_g(v_x) ) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_g(v_x),t_b) = v_g(v_x) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_g(v_x),t_b) = v_g(v_x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_g(v_x),t_b) = v_g(v_x) ) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
c_plus(c_0,v_g(v_x),t_b) = v_g(v_x),
inference(unit_resolution,[status(thm)],[173,24,17]) ).
tff(175,plain,
v_g(v_x) = c_plus(c_0,v_g(v_x),t_b),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
v_g(v_x) = c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[175,170,169]) ).
tff(177,plain,
c_plus(v_g(v_x),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_plus(c_minus(c_plus(v_f(v_x),v_g(v_x),t_b),v_f(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_g(v_x),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_g(v_x),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_g(v_x),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_g(v_x),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
c_plus(v_g(v_x),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b),
inference(unit_resolution,[status(thm)],[180,75,42]) ).
tff(182,plain,
c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) = c_plus(v_g(v_x),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b) ) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_minus(c_plus(v_g(v_x),v_f(v_x),t_b),v_k(v_x),t_b),
inference(unit_resolution,[status(thm)],[185,108,42]) ).
tff(187,plain,
c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b) = c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),
inference(transitivity,[status(thm)],[186,182,177,165,161,156,150,145,117,113,101,97]) ).
tff(188,plain,
( c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
<=> c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b)
<=> c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b) ),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b)
<=> ~ c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b) ),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(192,plain,
( ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[191]) ).
tff(193,plain,
( ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(195,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
tff(197,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[197,193]) ).
tff(199,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[198]) ).
tff(200,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[199,192]) ).
tff(201,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(203,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unit_resolution,[status(thm)],[203,200,3]) ).
tff(205,plain,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
<=> ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(206,axiom,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(207,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(209,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(quant_intro,[status(thm)],[208]) ).
tff(210,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(211,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(212,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(quant_intro,[status(thm)],[211]) ).
tff(213,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
tff(214,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
inference(modus_ponens,[status(thm)],[213,212]) ).
tff(215,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
inference(modus_ponens,[status(thm)],[214,210]) ).
tff(216,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
inference(skolemize,[status(sab)],[215]) ).
tff(217,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
inference(modus_ponens,[status(thm)],[216,209]) ).
tff(218,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(219,plain,
( ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(220,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(transitivity,[status(thm)],[220,218]) ).
tff(222,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(unit_resolution,[status(thm)],[223,217,207]) ).
tff(225,plain,
~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[224,204]) ).
tff(226,plain,
~ c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b),
inference(modus_ponens,[status(thm)],[225,190]) ).
tff(227,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
<=> ( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(228,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(quant_intro,[status(thm)],[227]) ).
tff(229,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(230,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a) )
<=> ( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(231,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(quant_intro,[status(thm)],[230]) ).
tff(232,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
tff(233,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[233,229]) ).
tff(235,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(skolemize,[status(sab)],[234]) ).
tff(236,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[235,228]) ).
tff(237,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(238,plain,
( ( c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(239,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[239,237]) ).
tff(241,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(242,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[241,240]) ).
tff(243,plain,
( c_lessequals(c_minus(v_g(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_g(v_x),c_plus(v_f(v_x),c_minus(v_k(v_x),v_f(v_x),t_b),t_b),t_b) ),
inference(unit_resolution,[status(thm)],[242,236,204]) ).
tff(244,plain,
$false,
inference(unit_resolution,[status(thm)],[243,226,92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ANA028-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 19:25:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.61 % SZS status Unsatisfiable
% 0.19/0.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------