%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW288+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:36:47 AM UTC 2025
% Result : Theorem 0.54s 0.72s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 60 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 331 ( 180 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 465 ( 205 ~; 177 |; 30 &)
% ( 32 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 92 ( 81 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(v_p_type,type,
v_p: $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
tff(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
tff(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
tff(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
tff(1,plain,
^ [T: $i] :
refl(( ( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) )
<=> ( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) )
<=> ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) )
<=> ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [T: $i] :
rewrite(( ( class_Int_Oring__char__0(T)
=> class_Groups_Ozero(T) )
<=> ( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T: $i] :
( class_Int_Oring__char__0(T)
=> class_Groups_Ozero(T) )
<=> ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [T: $i] :
( class_Int_Oring__char__0(T)
=> class_Groups_Ozero(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Int_Oring__char__0__Groups_Ozero) ).
tff(7,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Int_Oring__char__0(t_a)
<=> class_Int_Oring__char__0(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
class_Int_Oring__char__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
tff(13,plain,
class_Int_Oring__char__0(t_a),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) )
| class_Groups_Ozero(t_a)
| ~ class_Int_Oring__char__0(t_a) )
<=> ( ~ ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) )
| class_Groups_Ozero(t_a)
| ~ class_Int_Oring__char__0(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) )
| class_Groups_Ozero(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) )
| class_Groups_Ozero(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_Groups_Ozero(t_a),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_a: $i,V_p: $i,T_a: $i] :
refl(( ( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [V_a: $i,V_p: $i,T_a: $i] :
rewrite(( ( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
^ [V_a: $i,V_p: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) )
<=> ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )),
( ( class_Groups_Ozero(T_a)
=> ( ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ( class_Groups_Ozero(T_a)
=> ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) )),
rewrite(( ( class_Groups_Ozero(T_a)
=> ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) )),
( ( class_Groups_Ozero(T_a)
=> ( ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [V_a: $i,V_p: $i,T_a: $i] :
( class_Groups_Ozero(T_a)
=> ( ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
<=> ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [V_a: $i,V_p: $i,T_a: $i] :
( class_Groups_Ozero(T_a)
=> ( ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__eq__if) ).
tff(26,plain,
! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ),
inference(modus_ponens,[status(thm)],[29,19]) ).
tff(31,plain,
( ( ~ ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
| ~ class_Groups_Ozero(t_a)
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ( ~ ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
| ~ class_Groups_Ozero(t_a)
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ class_Groups_Ozero(t_a)
| ~ ( ~ ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ) ) )
<=> ( ~ class_Groups_Ozero(t_a)
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
| ~ class_Groups_Ozero(t_a)
| ~ ( ~ ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ) ) )
<=> ( ~ ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
| ~ class_Groups_Ozero(t_a)
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
| ~ class_Groups_Ozero(t_a)
| ~ ( ~ ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ) ) )
<=> ( ~ ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
| ~ class_Groups_Ozero(t_a)
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
| ~ class_Groups_Ozero(t_a)
| ~ ( ~ ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ~ ( ~ ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) )
| ~ class_Groups_Ozero(t_a)
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ class_Groups_Ozero(t_a)
| ( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(unit_resolution,[status(thm)],[36,30]) ).
tff(38,plain,
c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(unit_resolution,[status(thm)],[37,17]) ).
tff(39,plain,
( class_Rings_Oidom(t_a)
<=> class_Rings_Oidom(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_1) ).
tff(41,plain,
class_Rings_Oidom(t_a),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a)
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) )
<=> ( ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) )
| ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ~ ( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) )
<=> ( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
<=> ~ ( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
<=> ~ ~ ( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
<=> ( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) )
<=> ( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a)
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) )
<=> ( ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) )
| ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(transitivity,[status(thm)],[47,42]) ).
tff(49,plain,
( ( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) )
<=> ( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
=> ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) )
<=> ( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
=> ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096degree_Ap_A_061_Adegree_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096) ).
tff(52,plain,
( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ),
inference(modus_ponens,[status(thm)],[52,49]) ).
tff(54,plain,
( ( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) )
| ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(modus_ponens,[status(thm)],[53,48]) ).
tff(55,plain,
c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(unit_resolution,[status(thm)],[54,41,13]) ).
tff(56,plain,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(transitivity,[status(thm)],[55,38]) ).
tff(57,plain,
( ( c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
<=> ( c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(59,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW288+1 : TPTP v9.0.0. Released v5.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 11:23:24 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.54/0.72 % SZS status Theorem
% 0.54/0.72 % SZS output start Proof
% See solution above
% 0.61/0.79 % E exiting
%------------------------------------------------------------------------------