%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG348-1 : TPTP v9.0.0. Released v4.1.0.
% 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 04:58:57 AM UTC 2025
% Result : Unsatisfiable 0.44s 0.60s
% Output : Proof 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 54 ( 26 ~; 22 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 48 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(v_p_type,type,
v_p: $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(1,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
tff(3,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(6,plain,
c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset__poly_0) ).
tff(11,plain,
! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_x: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
$false,
inference(unit_resolution,[status(thm)],[16,13,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG348-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 11:07:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.44/0.60 % SZS status Unsatisfiable
% 0.44/0.60 % SZS output start Proof
% See solution above
% 0.47/0.65 % E exiting
%------------------------------------------------------------------------------