TSTP Solution File: ANA044-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA044-2 : 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 16:23:39 EDT 2022
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 49
% Syntax : Number of formulae : 97 ( 29 unt; 13 typ; 0 def)
% Number of atoms : 342 ( 30 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 456 ( 213 ~; 207 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 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 : 149 ( 133 !; 0 ?; 149 :)
% 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(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
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(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,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)],[4]) ).
tff(6,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(7,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(13,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
tff(22,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
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) )
<=> ( ~ ! [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(26,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(27,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)],[26]) ).
tff(28,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)],[27,25]) ).
tff(29,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(30,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)],[29,28]) ).
tff(31,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(unit_resolution,[status(thm)],[30,13,24]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,axiom,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(36,plain,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,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(40,plain,
c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,axiom,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(45,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,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(49,plain,
c_lessequals(c_0,v_l(v_x,v_xa),t_b),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( 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)
| ~ 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) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( 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) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( 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) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( 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) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( 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) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,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,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) ) )),
( ( ~ 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,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) ) )),
inference(bind,[status(th)],]) ).
tff(54,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,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) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
tff(56,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( 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) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( 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) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( 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) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( 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) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( 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_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ 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) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( 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_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ 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) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( 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_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ 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) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( 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_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ 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) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,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)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
inference(unit_resolution,[status(thm)],[62,59,49,40]) ).
tff(64,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)],[63,31]) ).
tff(65,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(66,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)],[65]) ).
tff(67,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(68,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(69,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)],[68]) ).
tff(70,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
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)],[70,69]) ).
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) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,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)],[72]) ).
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) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
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) )
| ( 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(rewrite,[status(thm)],]) ).
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) )
| ( 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(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)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(unit_resolution,[status(thm)],[77,74]) ).
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)],[78,64,17]) ).
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/sandbox/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
% 0.07/0.12 % Problem : ANA044-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 29 19:48:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------