%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG398-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 04:59:02 AM UTC 2025
% Result : Unsatisfiable 0.49s 0.67s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 37
% Syntax : Number of formulae : 89 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 171 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 323 ( 128 ~; 166 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 198 ( 180 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
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_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(v_q_____type,type,
v_q____: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
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,
^ [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
tff(8,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
tff(18,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_a00_0) ).
tff(21,plain,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
tff(28,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[34,31,21,18]) ).
tff(36,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[37,15]) ).
tff(39,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tff(42,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
^ [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
<=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
<=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
tff(47,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[52,49,42]) ).
tff(54,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[36]) ).
tff(55,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).
tff(62,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[68,65,21,18]) ).
tff(70,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[70,55]) ).
tff(72,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
tff(77,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[82,79,42]) ).
tff(84,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[84,72,53,39]) ).
tff(86,plain,
( ( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(88,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
$false,
inference(unit_resolution,[status(thm)],[88,85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG398-1 : TPTP v9.0.0. Released v4.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 : Thu Jun 19 11:17:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.49/0.67 % SZS status Unsatisfiable
% 0.49/0.67 % SZS output start Proof
% See solution above
% 0.56/0.72 % E exiting
%------------------------------------------------------------------------------