TSTP Solution File: ANA034-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA034-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 16:23:34 EDT 2022
% Result : Unsatisfiable 1.17s 1.10s
% Output : Proof 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 91
% Syntax : Number of formulae : 183 ( 42 unt; 21 typ; 0 def)
% Number of atoms : 966 ( 25 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1433 ( 686 ~; 655 |; 0 &)
% ( 92 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 57 ( 57 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 14 >; 8 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 392 ( 351 !; 0 ?; 392 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_b_type,type,
t_b: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(v_g_type,type,
v_g: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_ca_type,type,
v_ca: $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_b_type,type,
v_b: $i > $i ).
tff(v_a_type,type,
v_a: $i > $i ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $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_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(c_0_type,type,
c_0: $i ).
tff(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(c_less_type,type,
c_less: ( $i * $i * $i ) > $o ).
tff(1,plain,
( ( c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) )
<=> ( c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(3,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(7,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
tff(12,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ( c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ( c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ( c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ( c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b) = c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
<=> c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[19,4]) ).
tff(21,plain,
( c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
<=> c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
<=> ~ c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
<=> ~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(25,plain,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(31,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,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(35,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(36,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)],[35,34]) ).
tff(37,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[36,33,7]) ).
tff(38,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( ~ 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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(41,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_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,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(43,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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).
tff(44,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)],[43,42]) ).
tff(45,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[44,41]) ).
tff(46,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[50,47,37]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_42) ).
tff(56,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(unit_resolution,[status(thm)],[61,58,7]) ).
tff(63,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(64,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)],[63]) ).
tff(65,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(66,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_40) ).
tff(67,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,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(71,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(72,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)],[71]) ).
tff(73,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)],[72,70]) ).
tff(74,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(75,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)],[74,73]) ).
tff(76,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(unit_resolution,[status(thm)],[75,69,7]) ).
tff(77,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[79,47,37]) ).
tff(81,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(82,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)],[81]) ).
tff(83,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(84,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
tff(85,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Oorder(t_b) )
<=> ( class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Oorder(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Oorder(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Oorder(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
class_Orderings_Oorder(t_b),
inference(unit_resolution,[status(thm)],[93,87,7]) ).
tff(95,plain,
( c_less(c_0,v_c,t_b)
<=> c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( c_less(c_0,v_c,t_b)
<=> c_less(c_0,v_c,t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(98,plain,
c_less(c_0,v_c,t_b),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b),
inference(modus_ponens,[status(thm)],[98,95]) ).
tff(100,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
tff(106,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) )
<=> ( ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) ) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) ) ),
inference(transitivity,[status(thm)],[112,110]) ).
tff(114,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Oorder(t_b)
| ~ c_less(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b) ),
inference(unit_resolution,[status(thm)],[115,109,99]) ).
tff(117,plain,
c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b),
inference(unit_resolution,[status(thm)],[116,94]) ).
tff(118,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(119,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)],[118]) ).
tff(120,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(121,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)],[120]) ).
tff(122,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(123,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(124,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)],[123]) ).
tff(125,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
tff(126,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)],[125,124]) ).
tff(127,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)],[126,122]) ).
tff(128,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)],[127,121]) ).
tff(129,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)],[128]) ).
tff(130,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)],[129,119]) ).
tff(131,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_c,t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),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_c,t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,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_c,t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,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_c,t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_c,t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_f(v_x),t_b),t_b)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
inference(unit_resolution,[status(thm)],[133,130]) ).
tff(135,plain,
c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[134,117,80,76]) ).
tff(136,plain,
( c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
<=> c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(137,axiom,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(138,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
( c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
<=> c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(140,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(141,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
^ [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
<=> ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
^ [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
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,V_c,T_a)
<=> ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_c,T_a) )),
( ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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_d,T_a),T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),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_d,T_a),T_a)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),V_c,T_a)
| ~ c_lessequals(V_c,V_d,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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) ) )),
( ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(145,plain,
( ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) )
<=> ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) )
<=> ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
^ [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,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(V_c,V_d,T_a)
| ~ c_lessequals(c_0,V_c,T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,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_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,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_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(c_0,V_b,T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(c_0,V_b,T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(c_0,V_b,T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(c_0,V_b,T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a) )
<=> ( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(148,plain,
( ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a) )
<=> ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
tff(150,plain,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,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_d,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_c,V_d,T_a) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) ),
inference(modus_ponens,[status(thm)],[151,145]) ).
tff(153,plain,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) ),
inference(modus_ponens,[status(thm)],[153,143]) ).
tff(155,plain,
( ( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b) )
<=> ( ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
( ( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,plain,
( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ 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_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,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),V_c,T_a) )
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[160,154,141,138,135,62,51]) ).
tff(162,plain,
$false,
inference(unit_resolution,[status(thm)],[161,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA034-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.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 19:39:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.17/1.10 % SZS status Unsatisfiable
% 1.17/1.10 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------