%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG347-1 : TPTP v9.0.0. Released v4.1.0.
% 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 04:58:57 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.66s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 27
% Syntax : Number of formulae : 63 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 132 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 316 ( 138 ~; 153 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 131 ( 117 !; 0 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_pa_type,type,
v_pa: $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_a_type,type,
v_a: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(class_HOL_Ozero_type,type,
class_HOL_Ozero: $i > $o ).
tff(1,plain,
( ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a) )
<=> ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_Polynomial_Odegree(v_pa,t_a) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
c_Suc(c_Polynomial_Odegree(v_pa,t_a)) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
<=> ( v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(9,plain,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( class_Ring__and__Field_Ocomm__semiring__0(t_a)
<=> class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(12,plain,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [T_a: $i,V_p: $i,V_h: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [T_a: $i,V_p: $i,V_h: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
tff(19,plain,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(unit_resolution,[status(thm)],[28,22,12,9]) ).
tff(30,plain,
^ [T: $i] :
refl(( ( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
<=> ( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
<=> ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
<=> ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [T: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_HOL_Ozero(T) )
<=> ( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_HOL_Ozero(T) )
<=> ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_HOL_Ozero(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_HOL_Ozero) ).
tff(36,plain,
! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
| class_HOL_Ozero(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) )
<=> ( ~ ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
| class_HOL_Ozero(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
| class_HOL_Ozero(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
| class_HOL_Ozero(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
class_HOL_Ozero(t_a),
inference(unit_resolution,[status(thm)],[42,12,39]) ).
tff(44,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
refl(( ( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
<=> ( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
rewrite(( ( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
tff(50,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ),
inference(unit_resolution,[status(thm)],[56,53]) ).
tff(58,plain,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)),
inference(unit_resolution,[status(thm)],[57,43,29]) ).
tff(59,plain,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
inference(transitivity,[status(thm)],[58,6]) ).
tff(60,plain,
( ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)) )
<=> ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(62,plain,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG347-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 11:07:54 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.48/0.66 % SZS status Unsatisfiable
% 0.48/0.66 % SZS output start Proof
% See solution above
% 0.54/0.72 % E exiting
%------------------------------------------------------------------------------