TSTP Solution File: ANA031-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA031-2 : 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 16:23:33 EDT 2022
% Result : Unsatisfiable 0.68s 0.65s
% Output : Proof 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 71
% Syntax : Number of formulae : 147 ( 39 unt; 15 typ; 0 def)
% Number of atoms : 504 ( 60 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 676 ( 321 ~; 303 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 12 >; 5 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 297 ( 274 !; 0 ?; 297 :)
% 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 > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(v_b_type,type,
v_b: $i > $i ).
tff(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Osemigroup__mult_type,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
tff(c_0_type,type,
c_0: $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(1,plain,
( 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/sandbox2/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_OrderedGroup_Oab__semigroup__mult(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
tff(8,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
tff(19,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
tff(30,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Osemigroup__mult(t_b) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Osemigroup__mult(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(unit_resolution,[status(thm)],[35,32,3]) ).
tff(37,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
<=> ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
tff(41,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b) = c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b),t_b),
inference(unit_resolution,[status(thm)],[46,43,36]) ).
tff(48,plain,
c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b),t_b) = c_times(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),v_c,t_b),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b) = c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b) = c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b) = c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b) = c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b) = c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),
inference(unit_resolution,[status(thm)],[51,21,14]) ).
tff(53,plain,
c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(c_HOL_Oabs(v_g(v_x(v_c)),t_b),v_c,t_b),t_b),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),
inference(transitivity,[status(thm)],[54,48,25]) ).
tff(56,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b) = c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b) = c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b) = c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b) = c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b) = c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b),
inference(unit_resolution,[status(thm)],[58,21,14]) ).
tff(60,plain,
( c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b)
<=> c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[59,55]) ).
tff(61,plain,
( c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b)
<=> c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b)
<=> ~ c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
^ [V_U: $i] :
refl(
( ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b)
<=> ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(67,plain,
! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [V_U: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[71,62]) ).
tff(73,plain,
^ [V_U: $i] :
refl(
( c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b)
<=> c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b)
<=> ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b)
<=> ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(77,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ~ ! [V_U: $i] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,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(83,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)],[82]) ).
tff(84,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(85,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(86,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,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(90,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(91,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)],[90,89]) ).
tff(92,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[91,88,3]) ).
tff(93,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,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(96,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/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
tff(97,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)],[96,95]) ).
tff(98,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,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)],[98,94]) ).
tff(100,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b),
inference(unit_resolution,[status(thm)],[102,99,92]) ).
tff(104,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(105,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)],[104]) ).
tff(106,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(107,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
tff(108,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,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(112,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(113,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)],[112,111]) ).
tff(114,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(unit_resolution,[status(thm)],[113,110,3]) ).
tff(115,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
<=> ( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a) )
<=> ( ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) )),
rewrite(
( ( ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) )
<=> ( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) )
<=> ( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
tff(121,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
<=> ( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ) ),
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) )
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
c_lessequals(c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_HOL_Oabs(v_b(v_x(v_c)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(v_c)),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x(v_c)),t_b),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[130,124,114,103,81]) ).
tff(132,plain,
$false,
inference(unit_resolution,[status(thm)],[131,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : ANA031-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.31 % Computer : n002.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Mon Aug 29 19:43:13 EDT 2022
% 0.09/0.31 % CPUTime :
% 0.09/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.31 Usage: tptp [options] [-file:]file
% 0.09/0.31 -h, -? prints this message.
% 0.09/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.31 -m, -model generate model.
% 0.09/0.31 -p, -proof generate proof.
% 0.09/0.31 -c, -core generate unsat core of named formulas.
% 0.09/0.31 -st, -statistics display statistics.
% 0.09/0.31 -t:timeout set timeout (in second).
% 0.09/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.31 -<param>:<value> configuration parameter and value.
% 0.09/0.31 -o:<output-file> file to place output in.
% 0.68/0.65 % SZS status Unsatisfiable
% 0.68/0.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------