TSTP Solution File: SWW240+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW240+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 20:58:02 EDT 2022
% Result : Theorem 0.76s 0.80s
% Output : Proof 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 65
% Syntax : Number of formulae : 135 ( 32 unt; 15 typ; 0 def)
% Number of atoms : 396 ( 125 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 461 ( 199 ~; 195 |; 0 &)
% ( 46 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 11 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 296 ( 264 !; 0 ?; 296 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(v_p_type,type,
v_p: $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(c_Polynomial_Omonom_type,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(1,plain,
( class_Rings_Ocomm__ring__1(t_a)
<=> class_Rings_Ocomm__ring__1(t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Rings_Ocomm__ring__1(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
tff(3,plain,
class_Rings_Ocomm__ring__1(t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T: $i] :
refl(
( ( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [T: $i] :
rewrite(
( ( class_Rings_Ocomm__ring__1(T)
=> class_Rings_Ocomm__semiring__1(T) )
<=> ( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [T: $i] :
( class_Rings_Ocomm__ring__1(T)
=> class_Rings_Ocomm__semiring__1(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [T: $i] :
( class_Rings_Ocomm__ring__1(T)
=> class_Rings_Ocomm__semiring__1(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__1) ).
tff(10,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Rings_Ocomm__semiring__1(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) )
<=> ( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Rings_Ocomm__semiring__1(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Rings_Ocomm__semiring__1(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__1(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Rings_Ocomm__semiring__1(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_Rings_Ocomm__semiring__1(t_a),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(24,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(unit_resolution,[status(thm)],[31,17]) ).
tff(33,plain,
^ [T: $i] :
refl(
( ( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [T: $i] :
rewrite(
( ( class_Rings_Ocomm__ring__1(T)
=> class_Groups_Omonoid__mult(T) )
<=> ( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [T: $i] :
( class_Rings_Ocomm__ring__1(T)
=> class_Groups_Omonoid__mult(T) )
<=> ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [T: $i] :
( class_Rings_Ocomm__ring__1(T)
=> class_Groups_Omonoid__mult(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__ring__1__Groups_Omonoid__mult) ).
tff(39,plain,
! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Groups_Omonoid__mult(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) )
<=> ( ~ ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Groups_Omonoid__mult(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Groups_Omonoid__mult(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [T: $i] :
( class_Groups_Omonoid__mult(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Groups_Omonoid__mult(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
class_Groups_Omonoid__mult(t_a),
inference(unit_resolution,[status(thm)],[45,42,3]) ).
tff(47,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [V_a: $i,T_a: $i] :
( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [V_a: $i,T_a: $i] :
( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
tff(53,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
| ~ class_Groups_Omonoid__mult(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) = hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
| ~ class_Groups_Omonoid__mult(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) = hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
| ~ class_Groups_Omonoid__mult(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) = hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
| ~ class_Groups_Omonoid__mult(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) = hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ class_Groups_Omonoid__mult(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) = hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n) ) ),
inference(unit_resolution,[status(thm)],[59,56]) ).
tff(61,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) = hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n),
inference(unit_resolution,[status(thm)],[60,46]) ).
tff(62,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),c_Groups_Oone__class_Oone(t_a)),
inference(unit_resolution,[status(thm)],[64,27,17]) ).
tff(66,plain,
^ [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
<=> ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
<=> ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
<=> ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__monom) ).
tff(72,plain,
! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) ) )
<=> ( ~ ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [V_x: $i,V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),
inference(unit_resolution,[status(thm)],[78,75,17]) ).
tff(80,plain,
hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x) = hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n),
inference(transitivity,[status(thm)],[79,65,61]) ).
tff(81,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(t_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(unit_resolution,[status(thm)],[84,27,17]) ).
tff(86,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
^ [T: $i] :
refl(
( ( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
^ [T: $i] :
rewrite(
( ( class_Rings_Ocomm__ring__1(T)
=> class_Rings_Ocomm__semiring__0(T) )
<=> ( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [T: $i] :
( class_Rings_Ocomm__ring__1(T)
=> class_Rings_Ocomm__semiring__0(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [T: $i] :
( class_Rings_Ocomm__ring__1(T)
=> class_Rings_Ocomm__semiring__0(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__0) ).
tff(93,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Rings_Ocomm__semiring__0(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) )
<=> ( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Rings_Ocomm__semiring__0(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Rings_Ocomm__semiring__0(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Ocomm__ring__1(T) )
| class_Rings_Ocomm__semiring__0(t_a)
| ~ class_Rings_Ocomm__ring__1(t_a) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(unit_resolution,[status(thm)],[99,96,3]) ).
tff(101,plain,
^ [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
<=> ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
<=> ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
^ [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
<=> ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mult) ).
tff(107,plain,
! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) )
<=> ( ~ ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ~ ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(unit_resolution,[status(thm)],[113,110]) ).
tff(115,plain,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_x)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(unit_resolution,[status(thm)],[114,100]) ).
tff(116,plain,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(transitivity,[status(thm)],[115,86,81,32]) ).
tff(117,plain,
( ( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) )
<=> ( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,axiom,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(119,plain,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
$false,
inference(unit_resolution,[status(thm)],[119,116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW240+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 13:12:33 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.76/0.80 % SZS status Theorem
% 0.76/0.80 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------