%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA024-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.70s 0.92s
% Output : Proof 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 32
% Syntax : Number of formulae : 77 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 288 ( 20 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 382 ( 177 ~; 171 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 167 ( 153 !; 0 ?; 167 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_b_type,type,
t_b: $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_plus_type,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(v_g_type,type,
v_g: $i > $i ).
tff(c_minus_type,type,
c_minus: ( $i * $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_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $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/sandbox/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/sandbox/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_c: $i,V_b: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) )
<=> ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) )
<=> ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__11_0) ).
tff(22,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b) = v_k(v_x) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b) = v_k(v_x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b) = v_k(v_x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) )
| ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b) = v_k(v_x) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| ( c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b) = v_k(v_x) ) ),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,plain,
c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b) = v_k(v_x),
inference(unit_resolution,[status(thm)],[28,17]) ).
tff(30,plain,
( c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b)
<=> c_lessequals(v_k(v_x),v_f(v_x),t_b) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
<=> c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [V_U: $i] :
refl(( c_lessequals(v_k(V_U),v_f(V_U),t_b)
<=> c_lessequals(v_k(V_U),v_f(V_U),t_b) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(36,plain,
! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [V_U: $i] : c_lessequals(v_k(V_U),v_f(V_U),t_b)
| c_lessequals(v_k(v_x),v_f(v_x),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b),
inference(modus_ponens,[status(thm)],[40,31]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_54) ).
tff(46,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,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(50,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(51,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)],[50]) ).
tff(52,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)],[51,49]) ).
tff(53,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(54,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)],[53,52]) ).
tff(55,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unit_resolution,[status(thm)],[54,48,3]) ).
tff(56,plain,
( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
<=> ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(58,plain,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,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(60,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)],[59]) ).
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) )
<=> ! [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(62,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(63,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)],[62]) ).
tff(64,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
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) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,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)],[65,61]) ).
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) ),
inference(skolemize,[status(sab)],[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) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
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) )
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) )
<=> ( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,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_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,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_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,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_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,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_minus(v_k(v_x),v_g(v_x),t_b),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_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(unit_resolution,[status(thm)],[74,68,58]) ).
tff(76,plain,
~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[75,55]) ).
tff(77,plain,
$false,
inference(unit_resolution,[status(thm)],[76,41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : ANA024-1 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Jun 19 11:21:41 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.70/0.92 % SZS status Unsatisfiable
% 0.70/0.92 % SZS output start Proof
% See solution above
% 0.83/1.02 % E exiting
%------------------------------------------------------------------------------