TSTP Solution File: ANA029-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA029-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 16:23:32 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 78
% Syntax : Number of formulae : 160 ( 32 unt; 16 typ; 0 def)
% Number of atoms : 747 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1069 ( 495 ~; 504 |; 0 &)
% ( 70 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 376 ( 338 !; 0 ?; 376 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_b_type,type,
t_b: $i ).
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(c_minus_type,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(v_g_type,type,
v_g: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(v_k_type,type,
v_k: $i > $i ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $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_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(c_Orderings_Omax_type,type,
c_Orderings_Omax: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_less_type,type,
c_less: ( $i * $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,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)],[4]) ).
tff(6,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
tff(7,plain,
! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T: $i] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( class_Orderings_Olinorder(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/sandbox/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_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(15,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(16,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)],[15,14]) ).
tff(17,plain,
class_Orderings_Olinorder(t_b),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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(22,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)],[21]) ).
tff(23,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(24,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,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(29,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(30,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)],[29,28]) ).
tff(31,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[30,13,27]) ).
tff(32,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
tff(36,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(unit_resolution,[status(thm)],[41,38]) ).
tff(43,plain,
c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[42,31]) ).
tff(44,plain,
^ [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
refl(
( ( 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_y,V_z,T_b)
| ~ 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
<=> ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
<=> ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
^ [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b) )
<=> ( ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) )),
( ( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_y,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) )
<=> ( ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) )),
rewrite(
( ( ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) )),
( ( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_y,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) )
<=> ( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_y,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) )
<=> ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_y,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
tff(50,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
<=> ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(56,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) )
<=> ( c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),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(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),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(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(unit_resolution,[status(thm)],[62,56,53]) ).
tff(64,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[63,43,17]) ).
tff(65,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
tff(71,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unit_resolution,[status(thm)],[77,13,74]) ).
tff(79,plain,
^ [T: $i] :
refl(
( ( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
^ [T: $i] :
rewrite(
( ( ~ class_OrderedGroup_Opordered__ab__group__add(T)
| class_Orderings_Oorder(T) )
<=> ( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [T: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T)
| class_Orderings_Oorder(T) )
<=> ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,axiom,
! [T: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
tff(85,plain,
! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
( ( ~ ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) )
| class_Orderings_Oorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) )
| class_Orderings_Oorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) )
| class_Orderings_Oorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) )
| class_Orderings_Oorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
class_Orderings_Oorder(t_b),
inference(unit_resolution,[status(thm)],[91,88,78]) ).
tff(93,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) )
<=> ( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
tff(99,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
<=> ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(104,axiom,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(105,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Olinorder(t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Olinorder(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(unit_resolution,[status(thm)],[108,105,102]) ).
tff(110,plain,
c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),
inference(unit_resolution,[status(thm)],[109,17]) ).
tff(111,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
tff(117,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b) )
<=> ( c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) ) ),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
tff(125,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),
inference(unit_resolution,[status(thm)],[126,120,92,110]) ).
tff(128,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(
( ( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
<=> ( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_z,T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_z,T_a) )
<=> ( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
<=> ( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
tff(134,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[136,129]) ).
tff(138,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ( c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b) )
<=> ( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[140,138]) ).
tff(142,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
$false,
inference(unit_resolution,[status(thm)],[143,137,43,127,92,64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA029-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 19:33:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------