%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA044-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 04:59:17 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.82s
% Output : Proof 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 36
% Syntax : Number of formulae : 84 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 362 ( 40 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 497 ( 233 ~; 227 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 153 ( 138 !; 0 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(t_b_type,type,
t_b: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(v_h_type,type,
v_h: $i > $i ).
tff(v_k_type,type,
v_k: ( $i * $i ) > $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_l_type,type,
v_l: ( $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_0_type,type,
c_0: $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(1,plain,
^ [V_V: $i,V_U: $i] :
refl(( c_lessequals(c_0,v_l(V_U,V_V),t_b)
<=> c_lessequals(c_0,v_l(V_U,V_V),t_b) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b)
<=> ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b)
<=> ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(5,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b)
| c_lessequals(c_0,v_l(v_x,v_xa),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_lessequals(c_0,v_l(v_x,v_xa),t_b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(12,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_40) ).
tff(17,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__cancel__semiring(t_b) )
<=> ( class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__cancel__semiring(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__cancel__semiring(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(unit_resolution,[status(thm)],[25,19,12]) ).
tff(27,plain,
^ [V_U: $i] :
refl(( c_lessequals(c_0,v_h(V_U),t_b)
<=> c_lessequals(c_0,v_h(V_U),t_b) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(31,plain,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b)
| c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) )),
rewrite(( ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
tff(42,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
| ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
inference(unit_resolution,[status(thm)],[48,45]) ).
tff(50,plain,
c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(unit_resolution,[status(thm)],[49,35,26,9]) ).
tff(51,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(52,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)],[51]) ).
tff(53,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(54,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(55,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,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(59,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(60,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)],[59,58]) ).
tff(61,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[60,57,12]) ).
tff(62,plain,
^ [T_a: $i,V_y: $i] :
refl(( ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
^ [T_a: $i,V_y: $i] :
rewrite(( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| ( c_HOL_Oabs(V_y,T_a) = V_y ) )
<=> ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| ( c_HOL_Oabs(V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| ( c_HOL_Oabs(V_y,T_a) = V_y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonneg_0) ).
tff(68,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
inference(unit_resolution,[status(thm)],[77,71,61]) ).
tff(79,plain,
c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),
inference(unit_resolution,[status(thm)],[78,50]) ).
tff(80,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) = c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ( c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) )
<=> ( c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(83,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
$false,
inference(unit_resolution,[status(thm)],[83,80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : ANA044-1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n006.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Jun 19 11:23:35 EDT 2025
% 0.09/0.31 % CPUTime :
% 0.61/0.82 % SZS status Unsatisfiable
% 0.61/0.82 % SZS output start Proof
% See solution above
% 0.73/0.90 % E exiting
%------------------------------------------------------------------------------