TSTP Solution File: ANA009-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA009-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 16:23:22 EDT 2022
% Result : Unsatisfiable 1.09s 1.07s
% Output : Proof 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 46
% Syntax : Number of formulae : 89 ( 23 unt; 14 typ; 0 def)
% Number of atoms : 250 ( 24 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 314 ( 146 ~; 136 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 9 >; 6 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 142 ( 127 !; 0 ?; 142 :)
% 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_Nat_Osize_type,type,
c_Nat_Osize: ( $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(c_Product__Type_OUnity_type,type,
c_Product__Type_OUnity: $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_0_type,type,
c_0: $i ).
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_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(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_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_4) ).
tff(8,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
| class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
| class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__group__add(t_b) )
<=> ( class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__group__add(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
| class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__group__add(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
| class_OrderedGroup_Oab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__group__add(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(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)],[16,10,3]) ).
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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ) )),
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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) )
<=> ! [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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( ~ 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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
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 ) )
<=> ! [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(23,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/Axioms/MSC001-1.ax',cls_OrderedGroup_Oright__minus_0) ).
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)],[23,22]) ).
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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ),
inference(modus_ponens,[status(thm)],[24,21]) ).
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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ),
inference(skolemize,[status(sab)],[25]) ).
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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) )
<=> ( ~ ! [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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
c_plus(v_lb(v_x),c_uminus(v_lb(v_x),t_b),t_b) = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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)],[32]) ).
tff(34,plain,
( ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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)],[33]) ).
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)
<=> ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(36,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(37,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(38,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)],[37,36]) ).
tff(39,plain,
~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,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)],[39,34]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,plain,
! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_U: $i] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,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(49,plain,
c_lessequals(v_lb(v_x),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| 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) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_37) ).
tff(54,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(unit_resolution,[status(thm)],[59,56,3]) ).
tff(61,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ 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) )
<=> ( ~ 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) ) )),
inference(bind,[status(th)],]) ).
tff(62,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] :
( ~ 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) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,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] :
( ~ 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) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,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) )
<=> ( ~ 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) ) )),
inference(bind,[status(th)],]) ).
tff(65,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] :
( ~ 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) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,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/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
tff(67,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) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,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) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,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) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,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) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,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) )
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(v_lb(v_x),v_f(v_x),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) )
<=> ( ~ ! [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) )
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(v_lb(v_x),v_f(v_x),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(rewrite,[status(thm)],]) ).
tff(72,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) )
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(v_lb(v_x),v_f(v_x),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(quant_inst,[status(thm)],]) ).
tff(73,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) )
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(v_lb(v_x),v_f(v_x),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(modus_ponens,[status(thm)],[72,71]) ).
tff(74,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)],[73,70,60,49]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA009-1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Aug 29 18:42:17 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 1.09/1.07 % SZS status Unsatisfiable
% 1.09/1.07 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------