%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA035-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 04:59:15 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 39
% Syntax : Number of formulae : 97 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 310 ( 139 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 393 ( 185 ~; 181 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 239 ( 227 !; 0 ?; 239 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(t_b_type,type,
t_b: $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(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(1,plain,
^ [T: $i] :
refl(( ( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [T: $i] :
rewrite(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
<=> ( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
tff(7,plain,
! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(13,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__3_0) ).
tff(22,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(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(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(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(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(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(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(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(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(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(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,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(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[28,17]) ).
tff(30,plain,
c_times(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(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(symmetry,[status(thm)],[29]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34,33]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36,32]) ).
tff(38,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(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,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(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,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(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,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(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b) ) ),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),
inference(unit_resolution,[status(thm)],[41,17]) ).
tff(43,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[43]) ).
tff(45,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),t_b),v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),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_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,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),t_b),v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,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),t_b),v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),t_b),
inference(unit_resolution,[status(thm)],[47,37,17]) ).
tff(49,plain,
c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),t_b) = c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),t_b),
inference(monotonicity,[status(thm)],[42]) ).
tff(51,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[53,24,17]) ).
tff(55,plain,
c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[54]) ).
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),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),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),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),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),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),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),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[58,37,17]) ).
tff(60,plain,
c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,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),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),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),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,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),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,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),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[63,37,17]) ).
tff(65,plain,
c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[64,60,55,50,49,44]) ).
tff(66,plain,
c_times(v_ca,c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b) = c_times(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),c_times(v_ca,v_c,t_b),t_b) = c_times(v_ca,c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),c_times(v_ca,v_c,t_b),t_b) = c_times(v_ca,c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),c_times(v_ca,v_c,t_b),t_b) = c_times(v_ca,c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),c_times(v_ca,v_c,t_b),t_b) = c_times(v_ca,c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),c_times(v_ca,v_c,t_b),t_b) = c_times(v_ca,c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b),
inference(unit_resolution,[status(thm)],[69,24,17]) ).
tff(71,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(v_c,v_ca,t_b) = c_times(v_ca,v_c,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(v_c,v_ca,t_b) = c_times(v_ca,v_c,t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,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(v_c,v_ca,t_b) = c_times(v_ca,v_c,t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,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(v_c,v_ca,t_b) = c_times(v_ca,v_c,t_b) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ( c_times(v_c,v_ca,t_b) = c_times(v_ca,v_c,t_b) ) ),
inference(unit_resolution,[status(thm)],[73,37]) ).
tff(75,plain,
c_times(v_c,v_ca,t_b) = c_times(v_ca,v_c,t_b),
inference(unit_resolution,[status(thm)],[74,17]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,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(80,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)],[79,78]) ).
tff(81,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)],[80]) ).
tff(82,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)],[81,77]) ).
tff(83,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_f(v_x),v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(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_f(v_x),v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,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_f(v_x),v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,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_f(v_x),v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b) = c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[85,13,82]) ).
tff(87,plain,
c_times(c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),c_times(v_c,v_ca,t_b),t_b) = c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),c_times(v_ca,v_c,t_b),t_b),
inference(monotonicity,[status(thm)],[86,75]) ).
tff(88,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(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_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),c_times(v_c,v_ca,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(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_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),c_times(v_c,v_ca,t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,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(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_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),c_times(v_c,v_ca,t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,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(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_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),c_times(v_c,v_ca,t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(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_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),c_times(v_c,v_ca,t_b),t_b) ) ),
inference(unit_resolution,[status(thm)],[90,37]) ).
tff(92,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_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),c_times(v_c,v_ca,t_b),t_b),
inference(unit_resolution,[status(thm)],[91,17]) ).
tff(93,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(transitivity,[status(thm)],[92,87,70,66,30]) ).
tff(94,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(95,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(96,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)],[95,94]) ).
tff(97,plain,
$false,
inference(unit_resolution,[status(thm)],[96,93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA035-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.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 : Thu Jun 19 11:23:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% See solution above
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------