%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW290+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:47 AM UTC 2025
% Result : Theorem 0.52s 0.74s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 47
% Syntax : Number of formulae : 110 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 369 ( 144 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 409 ( 162 ~; 158 |; 0 &)
% ( 71 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 216 ( 192 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $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(v_a_type,type,
v_a: $i ).
tff(v_q_type,type,
v_q: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
tff(1,plain,
( class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
tff(3,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
<=> ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
<=> ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
<=> ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
tff(10,plain,
! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) ) )
<=> ( ~ ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
^ [T_1: $i] :
refl(( ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
^ [T_1: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
tff(25,plain,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
tff(31,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[34,31,28]) ).
tff(36,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(42,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( class_Groups_Ozero(tc_Complex_Ocomplex)
<=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
tff(54,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
^ [T_a: $i] :
refl(( ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
^ [T_a: $i] :
rewrite(( ( class_Groups_Ozero(T_a)
=> ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [T_a: $i] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [T_a: $i] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__0__0) ).
tff(61,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[67,64,54]) ).
tff(69,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(transitivity,[status(thm)],[69,51]) ).
tff(71,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
^ [T_1: $i] :
refl(( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [T_1: $i] :
rewrite(( ( class_Rings_Oidom(T_1)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [T_1: $i] :
( class_Rings_Oidom(T_1)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [T_1: $i] :
( class_Rings_Oidom(T_1)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(78,plain,
! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
( class_Rings_Oidom(tc_Complex_Ocomplex)
<=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
tff(84,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ( ~ ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [T_1: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[87,84,81]) ).
tff(89,plain,
^ [V_aa_2: $i,V_b_2: $i,T_a: $i] :
refl(( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [V_aa_2: $i,V_b_2: $i,T_a: $i] :
rewrite(( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
tff(95,plain,
! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ) )
<=> ( ~ ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
<=> ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
<=> ( ~ ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
<=> ( ~ ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [V_aa_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) )
<=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(unit_resolution,[status(thm)],[104,98,88]) ).
tff(106,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(transitivity,[status(thm)],[105,71,18]) ).
tff(107,plain,
( ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) )
<=> ( c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,axiom,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(109,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
$false,
inference(unit_resolution,[status(thm)],[109,106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWW290+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 11:24:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.52/0.74 % SZS status Theorem
% 0.52/0.74 % SZS output start Proof
% See solution above
% 0.67/0.82 % E exiting
%------------------------------------------------------------------------------