%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW186+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:36:35 AM UTC 2025
% Result : Theorem 0.49s 0.69s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 44
% Syntax : Number of formulae : 110 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 433 ( 265 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 551 ( 245 ~; 187 |; 19 &)
% ( 75 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 267 ( 234 !; 0 ?; 267 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(v_h_type,type,
v_h: $i ).
tff(v_p_type,type,
v_p: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
tff(1,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
<=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(3,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( class_Rings_Ocomm__semiring__0(t_a)
<=> class_Rings_Ocomm__semiring__0(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
tff(6,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
<=> ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
<=> ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
<=> ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
tff(13,plain,
! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) ) )
<=> ( ~ ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_h: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),
inference(unit_resolution,[status(thm)],[19,16,6]) ).
tff(21,plain,
^ [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
refl(( ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
<=> ( class_Rings_Ocomm__semiring__0(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) )),
rewrite(( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
<=> ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
<=> ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
<=> ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
tff(27,plain,
! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_a: $i,V_p: $i,V_c: $i,T_a: $i] :
( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(unit_resolution,[status(thm)],[33,30,3,6]) ).
tff(35,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
=> ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
=> ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(39,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(unit_resolution,[status(thm)],[40,34]) ).
tff(42,plain,
v_p = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h),
inference(transitivity,[status(thm)],[41,35]) ).
tff(43,plain,
c_Polynomial_OpCons(t_a,v_a,v_p) = c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Polynomial_OpCons(t_a,v_a,v_p),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(monotonicity,[status(thm)],[34]) ).
tff(46,plain,
c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_OpCons(t_a,v_a,v_p),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
^ [V_h: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
<=> ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
<=> ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [V_h: $i,V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [V_h: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
<=> ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [V_h: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__single) ).
tff(55,plain,
! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) = c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ) )
<=> ( ~ ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) = c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) = c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [V_h: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) = c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) = c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(unit_resolution,[status(thm)],[61,58,6]) ).
tff(63,plain,
c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(transitivity,[status(thm)],[45,63,48,20,3]) ).
tff(65,plain,
^ [T: $i] :
refl(( ( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) )
<=> ( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) )
<=> ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) )
<=> ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
^ [T: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__0(T)
=> class_Groups_Ozero(T) )
<=> ( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
=> class_Groups_Ozero(T) )
<=> ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
=> class_Groups_Ozero(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
tff(71,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) )
| class_Groups_Ozero(t_a)
| ~ class_Rings_Ocomm__semiring__0(t_a) )
<=> ( ~ ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) )
| class_Groups_Ozero(t_a)
| ~ class_Rings_Ocomm__semiring__0(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) )
| class_Groups_Ozero(t_a)
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [T: $i] :
( class_Groups_Ozero(T)
| ~ class_Rings_Ocomm__semiring__0(T) )
| class_Groups_Ozero(t_a)
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
class_Groups_Ozero(t_a),
inference(unit_resolution,[status(thm)],[77,74,6]) ).
tff(79,plain,
^ [V_pa_2: $i,V_a_2: $i,T_b: $i] :
refl(( ( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) )
<=> ( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) )
<=> ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
^ [V_pa_2: $i,V_a_2: $i,T_b: $i] :
rewrite(( ( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) )
<=> ( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) )
<=> ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) )
<=> ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
^ [V_pa_2: $i,V_a_2: $i,T_b: $i] :
rewrite(( ( class_Groups_Ozero(T_b)
=> ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) )
<=> ( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( class_Groups_Ozero(T_b)
=> ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) )
<=> ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( class_Groups_Ozero(T_b)
=> ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
tff(87,plain,
! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ( ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ),
inference(modus_ponens,[status(thm)],[90,80]) ).
tff(92,plain,
( ( ~ ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) )
| ~ class_Groups_Ozero(t_a)
| ~ ( ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) )
<=> ( ~ ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) )
| ~ class_Groups_Ozero(t_a)
| ~ ( ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) )
| ~ class_Groups_Ozero(t_a)
| ~ ( ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [V_pa_2: $i,V_a_2: $i,T_b: $i] :
( ~ class_Groups_Ozero(T_b)
| ~ ( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
| ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) )
<=> ( c_Polynomial_OpCons(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) )
| ~ class_Groups_Ozero(t_a)
| ~ ( ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ~ class_Groups_Ozero(t_a)
| ~ ( ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(unit_resolution,[status(thm)],[94,91]) ).
tff(96,plain,
~ ( ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(unit_resolution,[status(thm)],[95,78]) ).
tff(97,plain,
( ~ ~ ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ( ( v_a = c_Groups_Ozero__class_Ozero(t_a) )
& ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ~ ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ( ( v_a = c_Groups_Ozero__class_Ozero(t_a) )
& ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ~ ~ ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ~ ( ( v_a = c_Groups_Ozero__class_Ozero(t_a) )
& ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(transitivity,[status(thm)],[99,97]) ).
tff(101,plain,
( ~ ( ( v_a = c_Groups_Ozero__class_Ozero(t_a) )
& ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ~ ( ( v_a = c_Groups_Ozero__class_Ozero(t_a) )
& ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,axiom,
~ ( ( v_a = c_Groups_Ozero__class_Ozero(t_a) )
& ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(103,plain,
~ ( ( v_a = c_Groups_Ozero__class_Ozero(t_a) )
& ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[103,100]) ).
tff(105,plain,
v_a != c_Groups_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[104,41]) ).
tff(106,plain,
( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( v_a = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(107,plain,
( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
( ( ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
| ~ ( ( v_a != c_Groups_Ozero__class_Ozero(t_a) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
| ( c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(109,plain,
c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(unit_resolution,[status(thm)],[108,107,96]) ).
tff(110,plain,
$false,
inference(unit_resolution,[status(thm)],[109,64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWW186+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 11:16:27 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.49/0.69 % SZS status Theorem
% 0.49/0.69 % SZS output start Proof
% See solution above
% 0.60/0.77 % E exiting
%------------------------------------------------------------------------------