TSTP Solution File: SWW271+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW271+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Thu Sep 29 20:58:09 EDT 2022
% Result : Theorem 0.78s 0.83s
% Output : Proof 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 41
% Syntax : Number of formulae : 80 ( 24 unt; 16 typ; 0 def)
% Number of atoms : 231 ( 74 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 283 ( 130 ~; 108 |; 0 &)
% ( 29 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 12 >; 6 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 110 ( 77 !; 23 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $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(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(v_qa_____type,type,
v_qa____: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
tff(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_Rings_Odvd__class_Odvd_type,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(1,plain,
^ [T_1: $i] :
refl(
( ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) )
<=> ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) )
<=> ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) )
<=> ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [T_1: $i] :
rewrite(
( ( class_Fields_Ofield(T_1)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T_1: $i] :
( class_Fields_Ofield(T_1)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [T_1: $i] :
( class_Fields_Ofield(T_1)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
tff(7,plain,
! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Fields_Ofield(tc_Complex_Ocomplex)
<=> class_Fields_Ofield(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
tff(13,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) )
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Fields_Ofield(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) )
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Fields_Ofield(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) )
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Fields_Ofield(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [T_1: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) )
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Fields_Ofield(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
<=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) )
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) )),
( ( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) )
<=> ( class_Divides_Osemiring__div(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) ) )),
rewrite(
( ( class_Divides_Osemiring__div(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) )
<=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ) )),
( ( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) )
<=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
tff(24,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096) ).
tff(30,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ ) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ ) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____))
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____ ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____,
inference(unit_resolution,[status(thm)],[36,30,27,17]) ).
tff(38,plain,
v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
^ [B_r: $i] :
refl(
( ( v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) )
<=> ( v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [B_r: $i] : ( v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) )
<=> ! [B_r: $i] : ( v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) )
<=> ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( $false
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) )
<=> ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(44,plain,
( v_thesis____
<=> $false ),
inference(iff_false,[status(thm)],[43]) ).
tff(45,plain,
( ( v_thesis____
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) )
<=> ( $false
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ) ),
inference(monotonicity,[status(thm)],[44,41]) ).
tff(46,plain,
( ( v_thesis____
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) )
<=> ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ),
inference(transitivity,[status(thm)],[45,42]) ).
tff(47,plain,
( ( v_thesis____
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) )
<=> ( v_thesis____
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(48,plain,
( ( ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) )
=> v_thesis____ )
<=> ( v_thesis____
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
( ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) )
=> v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(50,plain,
( v_thesis____
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( v_thesis____
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ),
inference(modus_ponens,[status(thm)],[50,47]) ).
tff(52,plain,
( v_thesis____
| ~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(modus_ponens,[status(thm)],[52,46]) ).
tff(54,plain,
~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(modus_ponens,[status(thm)],[53,41]) ).
tff(55,plain,
~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(modus_ponens,[status(thm)],[54,41]) ).
tff(56,plain,
~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(modus_ponens,[status(thm)],[55,41]) ).
tff(57,plain,
~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(modus_ponens,[status(thm)],[56,41]) ).
tff(58,plain,
~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(modus_ponens,[status(thm)],[57,41]) ).
tff(59,plain,
~ ? [B_r: $i] : ( v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(modus_ponens,[status(thm)],[58,41]) ).
tff(60,plain,
^ [B_r: $i] : refl($oeq(v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r),v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r))),
inference(bind,[status(th)],]) ).
tff(61,plain,
! [B_r: $i] : ( v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(nnf-neg,[status(sab)],[59,60]) ).
tff(62,plain,
! [B_r: $i] : ( v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(modus_ponens,[status(thm)],[61,40]) ).
tff(63,plain,
( ~ ! [B_r: $i] : ( v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) )
| ( v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_qa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,62,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW271+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n012.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 : Sun Sep 4 13:44:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.78/0.83 % SZS status Theorem
% 0.78/0.83 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------