TSTP Solution File: ANA039-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Tue Sep 6 16:23:37 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 59
% Syntax : Number of formulae : 116 ( 27 unt; 13 typ; 0 def)
% Number of atoms : 467 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 646 ( 305 ~; 296 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 241 ( 216 !; 0 ?; 241 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $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_f_type,type,
v_f: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_c_type,type,
v_c: $i ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(v_h_type,type,
v_h: $i > $i ).
tff(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $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(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
tff(5,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( class_Ring__and__Field_Oordered__idom(t_a)
<=> class_Ring__and__Field_Oordered__idom(t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(10,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
class_Orderings_Oorder(t_a),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [V_U: $i] :
refl(
( c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a)
<=> c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a)
<=> ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a)
<=> ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(19,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(
( ( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,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) )
<=> ( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(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_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_z,T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_z,T_a) )
<=> ( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(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)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(28,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)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
tff(30,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
<=> ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(36,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ class_Orderings_Oorder(t_a) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ class_Orderings_Oorder(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[39,36,33,23,14]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__semiring(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__semiring(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(unit_resolution,[status(thm)],[50,10,47]) ).
tff(52,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,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(58,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(unit_resolution,[status(thm)],[64,10,61]) ).
tff(66,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(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) )
<=> ! [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)],[66]) ).
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) )
<=> ! [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(69,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(70,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)],[69,68]) ).
tff(71,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)],[70]) ).
tff(72,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)],[71,67]) ).
tff(73,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_a)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),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) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,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_a)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,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_a)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a) ),
inference(unit_resolution,[status(thm)],[75,72]) ).
tff(77,plain,
c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a),
inference(unit_resolution,[status(thm)],[76,65]) ).
tff(78,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,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(V_a,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,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(V_a,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
tff(82,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ),
inference(unit_resolution,[status(thm)],[87,84]) ).
tff(89,plain,
c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a),
inference(unit_resolution,[status(thm)],[88,65]) ).
tff(90,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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_a,V_c,T_a),c_times(V_b,V_c,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(91,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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_a,V_c,T_a),c_times(V_b,V_c,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)],[90]) ).
tff(92,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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_a,V_c,T_a),c_times(V_b,V_c,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(93,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_a,V_c,T_a),c_times(V_b,V_c,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_a,V_c,T_a),c_times(V_b,V_c,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_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a) )
<=> ( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a) )
<=> ( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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(94,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_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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)],[93]) ).
tff(95,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_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
tff(96,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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)],[95,94]) ).
tff(97,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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)],[96,92]) ).
tff(98,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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)],[97]) ).
tff(99,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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)],[98,91]) ).
tff(100,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),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_a,V_c,T_a),c_times(V_b,V_c,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,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,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,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
$false,
inference(unit_resolution,[status(thm)],[102,99,89,77,51,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 19:41:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------