%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA025-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Sat Jun 21 04:59:12 AM UTC 2025
% Result : Unsatisfiable 1.19s 1.36s
% Output : Proof 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 86
% Syntax : Number of formulae : 211 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 1084 ( 21 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1573 ( 731 ~; 737 |; 0 &)
% ( 105 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 31 ( 31 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 554 ( 504 !; 0 ?; 554 :)
% 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(c_plus_type,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(c_uminus_type,type,
c_uminus: ( $i * $i ) > $i ).
tff(v_k_type,type,
v_k: $i > $i ).
tff(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $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_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(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $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_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) ).
tff(22,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_k(v_x),v_g(v_x),t_b) = c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_k(v_x),v_g(v_x),t_b) = c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_k(v_x),v_g(v_x),t_b) = c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_k(v_x),v_g(v_x),t_b) = c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_minus(v_k(v_x),v_g(v_x),t_b) = c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b) ) ),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,plain,
c_minus(v_k(v_x),v_g(v_x),t_b) = c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[28,17]) ).
tff(30,plain,
c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b) = c_minus(v_k(v_x),v_g(v_x),t_b),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),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_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( c_lessequals(c_minus(v_k(v_x),v_g(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_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ c_lessequals(c_minus(v_k(v_x),v_g(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_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_33) ).
tff(38,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Olinorder(t_b) )
<=> ( class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Olinorder(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Olinorder(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Olinorder(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) )
| class_Orderings_Olinorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
class_Orderings_Olinorder(t_b),
inference(unit_resolution,[status(thm)],[46,40,3]) ).
tff(48,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(52,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[57,54,3]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).
tff(63,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)],[62,61]) ).
tff(64,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)],[63]) ).
tff(65,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)],[64,60]) ).
tff(66,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(67,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(68,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)],[67,66]) ).
tff(69,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)],[68,65,58]) ).
tff(70,plain,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_k(v_x),v_g(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(71,axiom,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(72,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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)],[71,70]) ).
tff(73,plain,
^ [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
refl(( ( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
<=> ( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
<=> ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
<=> ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) )),
rewrite(( ( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
<=> ( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) )),
( ( ~ class_Orderings_Olinorder(T_b)
| ~ 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_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(77,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(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
tff(79,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),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(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),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(84,plain,
( ( ~ 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_minus(v_k(v_x),v_g(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_Orderings_Omax(c_minus(v_k(v_x),v_g(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_k(v_x),v_g(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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),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(85,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
| ~ 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_minus(v_k(v_x),v_g(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_Orderings_Omax(c_minus(v_k(v_x),v_g(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) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
| ~ 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_minus(v_k(v_x),v_g(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_Orderings_Omax(c_minus(v_k(v_x),v_g(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) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,plain,
( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
| ~ 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_minus(v_k(v_x),v_g(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_Orderings_Omax(c_minus(v_k(v_x),v_g(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(quant_inst,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [T_b: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) )
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),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)],[87,86]) ).
tff(89,plain,
( ~ class_Orderings_Olinorder(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)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(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)],[88,82,72]) ).
tff(90,plain,
~ c_lessequals(c_minus(v_k(v_x),v_g(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)],[89,69,47]) ).
tff(91,plain,
~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),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)],[90,33]) ).
tff(92,plain,
( c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b)
<=> c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(93,plain,
( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
<=> c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) ),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_54) ).
tff(98,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(transitivity,[status(thm)],[103,101]) ).
tff(105,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) )
| class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unit_resolution,[status(thm)],[106,100,3]) ).
tff(108,plain,
( ~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
<=> ~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(110,plain,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(112,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] :
( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,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] :
( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,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) )
<=> ( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(115,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] :
( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,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/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
tff(117,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) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,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) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,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) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,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) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,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) )
| ~ class_Orderings_Olinorder(t_b)
| c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) )
<=> ( ~ ! [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) )
| ~ class_Orderings_Olinorder(t_b)
| c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,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) )
| ~ class_Orderings_Olinorder(t_b)
| c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,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) )
| ~ class_Orderings_Olinorder(t_b)
| c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
( ~ class_Orderings_Olinorder(t_b)
| c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(unit_resolution,[status(thm)],[123,120,110]) ).
tff(125,plain,
c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(unit_resolution,[status(thm)],[124,47]) ).
tff(126,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
<=> ( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a)
| c_less(V_a,V_b,T_a) )
<=> ( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a)
| c_less(V_a,V_b,T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a)
| c_less(V_a,V_b,T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
tff(132,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) ),
inference(modus_ponens,[status(thm)],[134,127]) ).
tff(136,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ( c_less(v_k(v_x),v_g(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ) ),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ) ),
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),c_0,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_less(v_k(v_x),v_g(v_x),t_b)
| ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(unit_resolution,[status(thm)],[141,135]) ).
tff(143,plain,
c_less(v_k(v_x),v_g(v_x),t_b),
inference(unit_resolution,[status(thm)],[142,125,107]) ).
tff(144,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
tff(148,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Oorder(t_b) )
<=> ( class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Oorder(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Oorder(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(transitivity,[status(thm)],[153,151]) ).
tff(155,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Oorder(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
class_Orderings_Oorder(t_b),
inference(unit_resolution,[status(thm)],[156,150,3]) ).
tff(158,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ 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)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(159,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[158]) ).
tff(160,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,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_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(162,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_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,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/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
tff(164,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[164,160]) ).
tff(166,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[165]) ).
tff(167,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[166,159]) ).
tff(168,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ( ~ c_less(v_k(v_x),v_g(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) )
<=> ( ~ class_Orderings_Oorder(t_b)
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) ) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) ) ),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(v_k(v_x),v_g(v_x),t_b) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
c_lessequals(v_k(v_x),v_g(v_x),t_b),
inference(unit_resolution,[status(thm)],[173,167,157,143]) ).
tff(175,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(176,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(179,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ) ),
inference(quant_intro,[status(thm)],[178]) ).
tff(180,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
tff(181,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[181,177]) ).
tff(183,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(skolemize,[status(sab)],[182]) ).
tff(184,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(modus_ponens,[status(thm)],[183,176]) ).
tff(185,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ( ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ) ),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ) ),
inference(transitivity,[status(thm)],[187,185]) ).
tff(189,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(unit_resolution,[status(thm)],[190,184]) ).
tff(192,plain,
c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(unit_resolution,[status(thm)],[191,174,107]) ).
tff(193,plain,
c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b),
inference(modus_ponens,[status(thm)],[192,93]) ).
tff(194,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(( ( c_lessequals(V_x,V_z,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)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(195,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,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) )
<=> ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,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) )
<=> ( ~ 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) ) )),
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_z,T_a) )
<=> ( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,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)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(198,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)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,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/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
tff(200,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[200,196]) ).
tff(202,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[201]) ).
tff(203,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[202,195]) ).
tff(204,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(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)
| c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(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)
| c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
( ( c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) )
<=> ( ~ class_Orderings_Oorder(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)
| c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(206,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,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(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(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)
| c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) ) ),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,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(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(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)
| c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) ) ),
inference(transitivity,[status(thm)],[206,204]) ).
tff(208,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,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(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),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_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(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)
| c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
( c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_0,t_b) ),
inference(unit_resolution,[status(thm)],[209,203,157,69]) ).
tff(211,plain,
$false,
inference(unit_resolution,[status(thm)],[210,193,91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ANA025-1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.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 : Thu Jun 19 11:21:33 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.19/1.36 % SZS status Unsatisfiable
% 1.19/1.36 % SZS output start Proof
% See solution above
% 1.26/1.46 % E exiting
%------------------------------------------------------------------------------