TSTP Solution File: ANA044-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA044-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 0.96s 1.00s
% Output : Proof 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 56
% Syntax : Number of formulae : 112 ( 34 unt; 16 typ; 0 def)
% Number of atoms : 455 ( 49 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 609 ( 284 ~; 272 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 34 ( 34 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 185 ( 162 !; 0 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(t_b_type,type,
t_b: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(v_h_type,type,
v_h: $i > $i ).
tff(v_k_type,type,
v_k: ( $i * $i ) > $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_l_type,type,
v_l: ( $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Nat_Osize_type,type,
c_Nat_Osize: ( $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(c_Product__Type_OUnity_type,type,
c_Product__Type_OUnity: $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(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,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(3,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_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(5,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)],[4]) ).
tff(6,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(7,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_40) ).
tff(8,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,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(12,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(13,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)],[12]) ).
tff(14,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)],[13,11]) ).
tff(15,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(16,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)],[15,14]) ).
tff(17,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(unit_resolution,[status(thm)],[16,10,3]) ).
tff(18,plain,
^ [V_U: $i] :
refl(
( c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b)
<=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [V_U: $i] :
rewrite(
( c_lessequals(c_0,v_h(V_U),t_b)
<=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b)
<=> ! [V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,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(23,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(24,plain,
! [V_U: $i] : c_lessequals(c_0,v_h(V_U),t_b),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
! [V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ~ ! [V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_k(v_x,v_xa)),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_k(v_x,v_xa)),t_b),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
^ [V_V: $i,V_U: $i] :
refl(
( c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b)
<=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b)
<=> ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [V_V: $i,V_U: $i] :
rewrite(
( c_lessequals(c_0,v_l(V_U,V_V),t_b)
<=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b) )),
inference(bind,[status(th)],]) ).
tff(33,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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,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(35,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(36,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b),
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ~ ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(V_U,V_V),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(v_x,v_xa),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(v_x,v_xa),t_b),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ~ c_lessequals(c_0,V_a,T_a)
<=> ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a) )),
rewrite(
( ~ c_lessequals(c_0,V_b,T_a)
<=> ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a) )),
rewrite(
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
<=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ) )),
rewrite(
( ( ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ) )),
( ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) )),
rewrite(
( ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,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(50,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[51,45]) ).
tff(53,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[53,43]) ).
tff(55,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) )
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_k(v_x,v_xa)),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) )
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_k(v_x,v_xa)),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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(56,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) )
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_k(v_x,v_xa)),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_a,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_b,T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(V_a,V_b,T_a),T_a) )
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_k(v_x,v_xa)),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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)],[56,55]) ).
tff(58,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_k(v_x,v_xa)),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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)],[57,54]) ).
tff(59,plain,
c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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)],[58,41,29,17]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(63,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(64,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,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(68,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(69,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)],[68,67]) ).
tff(70,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[69,66,3]) ).
tff(71,plain,
^ [T_a: $i,V_y: $i] :
refl(
( ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) )
<=> ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) )
<=> ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
^ [T_a: $i,V_y: $i] :
trans(
monotonicity(
rewrite(
( ~ c_lessequals(c_0,V_y,T_a)
<=> ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,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) )
<=> ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) )),
rewrite(
( ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,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) )
<=> ( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
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) )
<=> ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ! [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(76,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(77,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)],[76]) ).
tff(78,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/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonneg_0) ).
tff(79,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)],[78,77]) ).
tff(80,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)],[79,75]) ).
tff(81,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) ),
inference(modus_ponens,[status(thm)],[80,74]) ).
tff(82,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) ),
inference(modus_ponens,[status(thm)],[82,72]) ).
tff(84,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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(85,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) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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)
| ( 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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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(86,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,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) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,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) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,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) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ( c_HOL_Oabs(V_y,T_a) = V_y )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_y,T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ( c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) = c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) )
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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)],[88,87]) ).
tff(90,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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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)],[89,83,70]) ).
tff(91,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)],[90,59]) ).
tff(92,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)],[91]) ).
tff(93,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(94,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(95,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)],[94,93]) ).
tff(96,plain,
$false,
inference(unit_resolution,[status(thm)],[95,92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ANA044-1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 20:05:43 EDT 2022
% 0.13/0.35 % 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.
% 0.96/1.00 % SZS status Unsatisfiable
% 0.96/1.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------