TSTP Solution File: ANA009-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 16:23:23 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 42
% Syntax : Number of formulae : 85 ( 23 unt; 11 typ; 0 def)
% Number of atoms : 240 ( 20 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 293 ( 135 ~; 128 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 138 ( 123 !; 0 ?; 138 :)
% 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_uminus_type,type,
c_uminus: ( $i * $i ) > $i ).
tff(v_lb_type,type,
v_lb: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(c_0_type,type,
c_0: $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(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $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/sandbox2/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_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(5,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)],[4]) ).
tff(6,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(7,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(8,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)],[7]) ).
tff(9,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(10,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T: $i] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
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)],[16,13,3]) ).
tff(18,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
tff(22,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_0 ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_0 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_0 ) ),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,plain,
c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_0,
inference(unit_resolution,[status(thm)],[28,17]) ).
tff(30,plain,
( c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
<=> c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
<=> c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
<=> ~ c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
<=> ~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(35,plain,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
~ c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[35,32]) ).
tff(37,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) )
<=> ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
tff(43,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(unit_resolution,[status(thm)],[49,46,3]) ).
tff(51,plain,
^ [V_U: $i] :
refl(
( c_lessequals(v_lb(V_U),v_f(V_U),t_b)
<=> c_lessequals(v_lb(V_U),v_f(V_U),t_b) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(55,plain,
! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b)
| c_lessequals(v_lb(v_x),v_f(v_x),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
c_lessequals(v_lb(v_x),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) )
<=> ( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a) )
<=> ( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
tff(66,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) )
| c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
| ~ c_lessequals(v_lb(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) )
| c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
| ~ c_lessequals(v_lb(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) )
| c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
| ~ c_lessequals(v_lb(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) )
| c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b)
| ~ c_lessequals(v_lb(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
c_lessequals(c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[72,69,59,50]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 18:08:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------