%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA043-2 : 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 04:59:16 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.54s
% Output : Proof 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 42
% Syntax : Number of formulae : 99 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 391 ( 20 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 530 ( 253 ~; 235 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 15 ( 15 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 : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 221 ( 202 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_b_type,type,
t_b: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $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 > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_x_type,type,
v_x: $i > $i ).
tff(v_l_type,type,
v_l: ( $i * $i ) > $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_0_type,type,
c_0: $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(1,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
tff(5,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(10,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__left__commute_0) ).
tff(19,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) = c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) = c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) = c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) = c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) = c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
<=> c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
<=> c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
<=> ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
^ [V_U: $i] :
refl(( ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b)
<=> ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(34,plain,
! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[38,29]) ).
tff(40,plain,
^ [V_U: $i] :
refl(( c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
<=> c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
<=> ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
<=> ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(44,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,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(50,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,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(52,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(53,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) )
<=> ( ~ ! [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(57,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
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) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[58,10,55]) ).
tff(60,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
tff(64,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b),
inference(unit_resolution,[status(thm)],[69,66,59]) ).
tff(71,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
tff(75,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(unit_resolution,[status(thm)],[80,10,77]) ).
tff(82,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
<=> ( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a) )
<=> ( ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) )),
rewrite(( ( ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) )
<=> ( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) )
<=> ( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
tff(88,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ( c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
<=> ( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_HOL_Oabs(v_f(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_h(v_k(v_x(v_c),v_xa(v_c))),t_b),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[97,91,81,70,48]) ).
tff(99,plain,
$false,
inference(unit_resolution,[status(thm)],[98,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : ANA043-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 11:24:09 EDT 2025
% 0.21/0.36 % CPUTime :
% 0.22/0.54 % SZS status Unsatisfiable
% 0.22/0.54 % SZS output start Proof
% See solution above
% 0.39/0.56 % E exiting
%------------------------------------------------------------------------------