TSTP Solution File: SWW288+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW288+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 20:58:13 EDT 2022
% Result : Theorem 0.67s 0.74s
% Output : Proof 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of formulae : 75 ( 17 unt; 13 typ; 0 def)
% Number of atoms : 320 ( 180 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 426 ( 179 ~; 161 |; 30 &)
% ( 35 <=>; 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 : 15 ( 10 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 2 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,
( class_Int_Oring__char__0(t_a)
<=> class_Int_Oring__char__0(t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Int_Oring__char__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
tff(3,plain,
class_Int_Oring__char__0(t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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(8,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)],[7]) ).
tff(9,axiom,
! [T: $i] :
( class_Int_Oring__char__0(T)
=> class_Groups_Ozero(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Int_Oring__char__0__Groups_Ozero) ).
tff(10,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
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)],[16,13,3]) ).
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/sandbox2/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,
( ( v_p = 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))) )
<=> ( v_p = 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(40,plain,
( ( $false
| ( v_p = 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))) ) )
<=> ( v_p = 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(41,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( $true
& $true )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_1) ).
tff(44,plain,
( class_Rings_Oidom(t_a)
<=> $true ),
inference(iff_true,[status(thm)],[43]) ).
tff(45,plain,
( class_Int_Oring__char__0(t_a)
<=> $true ),
inference(iff_true,[status(thm)],[2]) ).
tff(46,plain,
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
<=> ( $true
& $true ) ),
inference(monotonicity,[status(thm)],[45,44]) ).
tff(47,plain,
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
<=> $true ),
inference(transitivity,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
<=> $false ),
inference(transitivity,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( v_p = 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))) ) )
<=> ( $false
| ( v_p = 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)],[49]) ).
tff(51,plain,
( ( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( v_p = 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))) ) )
<=> ( v_p = 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(transitivity,[status(thm)],[50,40]) ).
tff(52,plain,
( ( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
=> ( v_p = 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) )
| ( v_p = 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(53,axiom,
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
=> ( v_p = 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/sandbox2/benchmark/theBenchmark.p',fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096) ).
tff(54,plain,
( ~ ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
| ( v_p = 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)],[53,52]) ).
tff(55,plain,
v_p = 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)],[54,51]) ).
tff(56,plain,
v_p = 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)],[55,39]) ).
tff(57,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(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(transitivity,[status(thm)],[57,38]) ).
tff(59,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(60,axiom,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(61,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW288+1 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 14:05:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.67/0.74 % SZS status Theorem
% 0.67/0.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------