%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA027-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 04:59:13 AM UTC 2025
% Result : Unsatisfiable 0.90s 1.06s
% Output : Proof 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 54
% Syntax : Number of formulae : 129 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 614 ( 30 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 886 ( 418 ~; 406 |; 0 &)
% ( 62 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 337 ( 307 !; 0 ?; 337 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_b_type,type,
t_b: $i ).
tff(v_k_type,type,
v_k: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_g_type,type,
v_g: $i > $i ).
tff(c_plus_type,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(c_0_type,type,
c_0: $i ).
tff(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_minus_type,type,
c_minus: ( $i * $i * $i ) > $i ).
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_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [T: $i] :
rewrite(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
<=> ( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_23) ).
tff(10,plain,
! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [T_a: $i,V_y: $i] :
refl(( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
tff(22,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_k(v_x),t_b) = v_k(v_x) ) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_k(v_x),t_b) = v_k(v_x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_k(v_x),t_b) = v_k(v_x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_k(v_x),t_b) = v_k(v_x) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_plus(c_0,v_k(v_x),t_b) = v_k(v_x),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
v_k(v_x) = c_plus(c_0,v_k(v_x),t_b),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_g(v_x),t_b) = v_g(v_x) ) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_g(v_x),t_b) = v_g(v_x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_g(v_x),t_b) = v_g(v_x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ( c_plus(c_0,v_g(v_x),t_b) = v_g(v_x) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
c_plus(c_0,v_g(v_x),t_b) = v_g(v_x),
inference(unit_resolution,[status(thm)],[32,24,17]) ).
tff(34,plain,
v_g(v_x) = c_plus(c_0,v_g(v_x),t_b),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( c_lessequals(v_g(v_x),v_k(v_x),t_b)
<=> c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b) ),
inference(monotonicity,[status(thm)],[34,29]) ).
tff(36,plain,
( c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b)
<=> c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b)
<=> ~ c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,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(46,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(47,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)],[46]) ).
tff(48,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)],[47,45]) ).
tff(49,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(50,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)],[49,48]) ).
tff(51,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unit_resolution,[status(thm)],[50,44,3]) ).
tff(52,plain,
( ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
<=> ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(54,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
tff(61,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(unit_resolution,[status(thm)],[70,64,54]) ).
tff(72,plain,
~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[71,51]) ).
tff(73,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(74,axiom,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(75,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
tff(82,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ 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)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ),
inference(unit_resolution,[status(thm)],[91,85,75]) ).
tff(93,plain,
c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[92,51]) ).
tff(94,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(95,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)],[94]) ).
tff(96,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(97,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(98,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,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(102,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(103,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)],[102]) ).
tff(104,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)],[103,101]) ).
tff(105,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(106,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)],[105,104]) ).
tff(107,plain,
class_Orderings_Oorder(t_b),
inference(unit_resolution,[status(thm)],[106,100,3]) ).
tff(108,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(109,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)],[108]) ).
tff(110,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(111,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(112,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)],[111]) ).
tff(113,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(114,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)],[113,112]) ).
tff(115,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)],[114,110]) ).
tff(116,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)],[115]) ).
tff(117,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)],[116,109]) ).
tff(118,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_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),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_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ( c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b) )
<=> ( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,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(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),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_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,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(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),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_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,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(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,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_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),c_plus(c_0,v_k(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[123,117,107,93,72]) ).
tff(125,plain,
~ c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(modus_ponens,[status(thm)],[124,37]) ).
tff(126,plain,
( c_lessequals(v_g(v_x),v_k(v_x),t_b)
<=> c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,axiom,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(128,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
$false,
inference(unit_resolution,[status(thm)],[128,125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ANA027-1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 11:22:24 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.90/1.06 % SZS status Unsatisfiable
% 0.90/1.06 % SZS output start Proof
% See solution above
% 0.97/1.15 % E exiting
%------------------------------------------------------------------------------