%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW246+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:36:41 AM UTC 2025
% Result : Theorem 0.71s 0.88s
% Output : Proof 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 65 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 275 ( 103 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 388 ( 193 ~; 147 |; 6 &)
% ( 34 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 178 ( 163 !; 0 ?; 178 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(tptp_fun_B_y_1_type,type,
tptp_fun_B_y_1: $i > $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
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(tptp_fun_B_x_2_type,type,
tptp_fun_B_x_2: $i > $i ).
tff(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [T: $i] :
refl(( ( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) )
<=> ( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [T: $i] :
rewrite(( ( class_Rings_Oidom(T)
=> class_Rings_Ocomm__semiring__0(T) )
<=> ( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T: $i] :
( class_Rings_Oidom(T)
=> class_Rings_Ocomm__semiring__0(T) )
<=> ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [T: $i] :
( class_Rings_Oidom(T)
=> class_Rings_Ocomm__semiring__0(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).
tff(7,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Rings_Oidom(t_a)
<=> class_Rings_Oidom(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
tff(13,plain,
class_Rings_Oidom(t_a),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) )
| class_Rings_Ocomm__semiring__0(t_a)
| ~ class_Rings_Oidom(t_a) )
<=> ( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) )
| class_Rings_Ocomm__semiring__0(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) )
| class_Rings_Ocomm__semiring__0(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_Rings_Ocomm__semiring__0(T)
| ~ class_Rings_Oidom(T) )
| class_Rings_Ocomm__semiring__0(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [V_x: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
tff(24,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
( ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) )
<=> ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) )
<=> ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) ),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = c_Groups_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[36,27,17]) ).
tff(38,plain,
hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
^ [V_f_2: $i,T_c: $i,T_b: $i] :
refl(( ~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
^ [V_f_2: $i,T_c: $i,T_b: $i] :
rewrite(( ~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
^ [V_f_2: $i,T_c: $i,T_b: $i] :
trans(monotonicity(rewrite(( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
<=> ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) ) )),
rewrite(( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) )
<=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )),
( ( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
& ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
& ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) )),
rewrite(( ( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
& ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) )),
( ( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
& ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [V_f_2: $i,T_c: $i,T_b: $i] :
( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
& ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
<=> ! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [V_f_2: $i,T_c: $i,T_b: $i] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
<=> ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
<=> ! [V_f_2: $i,T_c: $i,T_b: $i] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
<=> ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [V_f_2: $i,T_c: $i,T_b: $i] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
<=> ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_constant__def) ).
tff(48,plain,
! [V_f_2: $i,T_c: $i,T_b: $i] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
<=> ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [V_f_2: $i,T_c: $i,T_b: $i] :
( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
& ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( ~ ! [V_f_2: $i,T_c: $i,T_b: $i] :
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ! [B_x: $i,B_y: $i] : ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)
| ( hAPP(V_f_2,tptp_fun_B_x_2(V_f_2)) != hAPP(V_f_2,tptp_fun_B_y_1(V_f_2)) ) ) )
| ~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ! [B_x: $i,B_y: $i] : ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),B_x) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
~ ( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ! [B_x: $i,B_y: $i] : ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),B_x) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) ) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( ~ ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ! [B_x: $i,B_y: $i] : ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),B_x) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),B_y) ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) )
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(55,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) ),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) )
<=> ( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) )
<=> ( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C0_C) ).
tff(59,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(modus_ponens,[status(thm)],[59,56]) ).
tff(61,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(unit_resolution,[status(thm)],[60,13]) ).
tff(62,plain,
( ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) )
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
( ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) )
| ( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) ) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_x_2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),tptp_fun_B_y_1(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))),
inference(unit_resolution,[status(thm)],[63,55]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW246+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 11:20:38 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.71/0.88 % SZS status Theorem
% 0.71/0.88 % SZS output start Proof
% See solution above
% 0.77/0.95 % E exiting
%------------------------------------------------------------------------------