TSTP Solution File: ANA030-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 16:23:33 EDT 2022
% Result : Unsatisfiable 0.17s 0.51s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 105
% Syntax : Number of formulae : 231 ( 57 unt; 19 typ; 0 def)
% Number of atoms : 792 ( 146 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1048 ( 489 ~; 473 |; 0 &)
% ( 86 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 16 >; 12 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 523 ( 477 !; 0 ?; 523 :)
% 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(v_g_type,type,
v_g: $i > $i ).
tff(v_x_type,type,
v_x: $i > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(v_h_type,type,
v_h: $i > $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(c_minus_type,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(c_uminus_type,type,
c_uminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_Orderings_Omax_type,type,
c_Orderings_Omax: ( $i * $i * $i ) > $i ).
tff(c_0_type,type,
c_0: $i ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,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)],[4]) ).
tff(6,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
tff(7,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(13,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,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(15,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(16,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)],[15,14]) ).
tff(17,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
tff(22,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
tff(33,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) = c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) = c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) = c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) = c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
c_uminus(c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) = c_minus(v_g(v_x(v_c)),c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[38,35,17]) ).
tff(40,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__1_0) ).
tff(44,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b) = c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b) = c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b) = c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b) = c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b) = c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b),
inference(unit_resolution,[status(thm)],[49,46,17]) ).
tff(51,plain,
c_uminus(c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) = c_uminus(c_minus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),v_g(v_x(v_c)),t_b),t_b),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
tff(56,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) = c_plus(c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) = c_plus(c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) = c_plus(c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) = c_plus(c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
c_uminus(c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) = c_plus(c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[61,58,17]) ).
tff(63,plain,
c_plus(c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b) = c_uminus(c_plus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
^ [T_a: $i,V_y: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
tff(68,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b) = v_g(v_x(v_c)) ) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b) = v_g(v_x(v_c)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b) = v_g(v_x(v_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b) = v_g(v_x(v_c)) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b) = v_g(v_x(v_c)),
inference(unit_resolution,[status(thm)],[73,70,17]) ).
tff(75,plain,
v_g(v_x(v_c)) = c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b) ) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) = c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),
inference(unit_resolution,[status(thm)],[78,70,17]) ).
tff(80,plain,
c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b) = c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b) = c_plus(c_uminus(c_uminus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),c_uminus(c_uminus(v_g(v_x(v_c)),t_b),t_b),t_b),
inference(monotonicity,[status(thm)],[80,75]) ).
tff(82,plain,
c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b) = c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),
inference(transitivity,[status(thm)],[81,63,51,39,28]) ).
tff(83,plain,
( c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b)
<=> c_lessequals(v_f(v_x(v_c)),c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( c_lessequals(v_f(v_x(v_c)),c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b)
<=> c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) ),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ c_lessequals(v_f(v_x(v_c)),c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b)
<=> ~ c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
^ [V_U: $i] :
refl(
( ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b)
<=> ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(90,plain,
! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
( ~ ! [V_U: $i] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b)
| ~ c_lessequals(v_f(v_x(v_c)),c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
~ c_lessequals(v_f(v_x(v_c)),c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[93,92]) ).
tff(95,plain,
~ c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b),
inference(modus_ponens,[status(thm)],[94,85]) ).
tff(96,plain,
^ [T: $i] :
refl(
( ( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
<=> ( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
<=> ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
tff(102,plain,
! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ~ ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
class_Orderings_Olinorder(t_b),
inference(unit_resolution,[status(thm)],[108,13,105]) ).
tff(110,plain,
^ [T_b: $i,V_x: $i,V_y: $i] :
refl(
( ( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) )
<=> ( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) )
<=> ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) )
<=> ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,axiom,
! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Ole__maxI2_0) ).
tff(114,plain,
! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,plain,
! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ~ ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
( ~ ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b),
inference(unit_resolution,[status(thm)],[119,116,109]) ).
tff(121,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(127,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[129,122]) ).
tff(131,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[133,13,130]) ).
tff(135,plain,
^ [T_a: $i,V_y: $i] :
refl(
( ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
^ [T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| ( c_HOL_Oabs(V_y,T_a) = V_y ) )
<=> ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(139,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| ( c_HOL_Oabs(V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,axiom,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| ( c_HOL_Oabs(V_y,T_a) = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
tff(141,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[143,136]) ).
tff(145,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) ) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ( ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) )
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) )
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) ) ) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) )
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) ) ) ),
inference(transitivity,[status(thm)],[147,145]) ).
tff(149,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) )
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b)
| ( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) ) ),
inference(unit_resolution,[status(thm)],[150,144,134]) ).
tff(152,plain,
c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),
inference(unit_resolution,[status(thm)],[151,120]) ).
tff(153,plain,
c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b) = c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
<=> c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
<=> c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
^ [V_U: $i] :
refl(
( c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
<=> c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) )),
inference(bind,[status(th)],]) ).
tff(157,plain,
( ! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
<=> ! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
<=> ! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(159,axiom,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(160,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(skolemize,[status(sab)],[160]) ).
tff(162,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[161,157]) ).
tff(163,plain,
( ~ ! [V_U: $i] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[163,162]) ).
tff(165,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[164,155]) ).
tff(166,plain,
^ [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
refl(
( ( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
<=> ( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) )),
inference(bind,[status(th)],]) ).
tff(167,plain,
( ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
<=> ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
( ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
<=> ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
^ [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| c_lessequals(V_x,V_z,T_b) )
<=> ( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) )),
inference(bind,[status(th)],]) ).
tff(170,plain,
( ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| c_lessequals(V_x,V_z,T_b) )
<=> ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,axiom,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| c_lessequals(V_x,V_z,T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
tff(172,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(modus_ponens,[status(thm)],[172,168]) ).
tff(174,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(modus_ponens,[status(thm)],[174,167]) ).
tff(176,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
( ( c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) )
<=> ( ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
( c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b) ),
inference(unit_resolution,[status(thm)],[181,175,109]) ).
tff(183,plain,
c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[182,165]) ).
tff(184,plain,
^ [T: $i] :
refl(
( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ) )),
inference(bind,[status(th)],]) ).
tff(185,plain,
( ! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ) ),
inference(quant_intro,[status(thm)],[184]) ).
tff(186,plain,
( ! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,axiom,
! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
tff(188,plain,
! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(skolemize,[status(sab)],[188]) ).
tff(190,plain,
! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[189,185]) ).
tff(191,plain,
( ( ~ ! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(192,plain,
( ~ ! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
( ~ ! [T: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unit_resolution,[status(thm)],[193,190,134]) ).
tff(195,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( 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)
| ~ 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(196,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(quant_intro,[status(thm)],[195]) ).
tff(197,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,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_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) )
<=> ( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(199,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_0) ).
tff(201,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[201,197]) ).
tff(203,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(skolemize,[status(sab)],[202]) ).
tff(204,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[203,196]) ).
tff(205,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(206,plain,
( ( c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),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_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(207,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),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(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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),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(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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[207,205]) ).
tff(209,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_minus(v_f(v_x(v_c)),v_g(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
c_lessequals(v_f(v_x(v_c)),c_plus(c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),v_g(v_x(v_c)),t_b),t_b),
inference(unit_resolution,[status(thm)],[210,204,194,183]) ).
tff(212,plain,
$false,
inference(unit_resolution,[status(thm)],[211,95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n027.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Aug 29 19:42:30 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.51 % SZS status Unsatisfiable
% 0.17/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------