TSTP Solution File: SWW255+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW255+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 20:58:05 EDT 2022
% Result : Theorem 1.70s 1.39s
% Output : Proof 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 69
% Syntax : Number of formulae : 132 ( 41 unt; 22 typ; 0 def)
% Number of atoms : 376 ( 234 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 385 ( 129 ~; 153 |; 0 &)
% ( 88 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 16 >; 10 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 255 ( 225 !; 0 ?; 255 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_k_____type,type,
v_k____: $i ).
tff(v_w_____type,type,
v_w____: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(v_q_____type,type,
v_q____: $i ).
tff(c_Rings_Oinverse__class_Oinverse_type,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(v_s_____type,type,
v_s____: $i ).
tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
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(1,plain,
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____))) )
<=> ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))) )
<=> ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))) )
<=> ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096poly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_A_061poly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Aw_A_094_Ak_A_K_Apoly_A_IpCons_Aa_As_J_Aw_096) ).
tff(5,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____))),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____))),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex)
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(11,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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(16,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)],[15]) ).
tff(17,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(18,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)],[17,16]) ).
tff(19,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)],[18,14]) ).
tff(20,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)],[19]) ).
tff(21,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)],[20,13]) ).
tff(22,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_Complex_Ocomplex)
| ( ( v_a____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) )
<=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(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_Complex_Ocomplex)
| ( ( v_a____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) )
<=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,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_Complex_Ocomplex)
| ( ( v_a____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) )
<=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,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_Complex_Ocomplex)
| ( ( v_a____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) )
<=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ( v_a____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) )
<=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(unit_resolution,[status(thm)],[24,21,11]) ).
tff(26,plain,
( class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
<=> class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
tff(28,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [V_b_2: $i,V_aa_2: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [V_b_2: $i,V_aa_2: $i,T_a: $i] :
rewrite(
( ( class_Rings_Oring__no__zero__divisors(T_a)
=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
tff(35,plain,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ) )
<=> ( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(unit_resolution,[status(thm)],[41,38,28]) ).
tff(43,plain,
( class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
tff(45,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
^ [V_x: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
^ [V_x: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
tff(52,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[58,55,45]) ).
tff(60,plain,
( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(tautology,[status(thm)],]) ).
tff(61,plain,
( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(63,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[62,61,42]) ).
tff(64,plain,
( ~ ( ( v_a____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) )
<=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
| ( v_a____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(tautology,[status(thm)],]) ).
tff(65,plain,
v_a____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))),
inference(unit_resolution,[status(thm)],[64,63,25]) ).
tff(66,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) = v_a____,
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
^ [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
<=> ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
<=> ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
^ [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
<=> ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,axiom,
! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pCons) ).
tff(73,plain,
! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ),
inference(modus_ponens,[status(thm)],[75,68]) ).
tff(77,plain,
( ( ~ ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) ) )
<=> ( ~ ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
( ~ ! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_w____))),
inference(unit_resolution,[status(thm)],[79,76,45]) ).
tff(81,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____) = v_a____,
inference(transitivity,[status(thm)],[80,66]) ).
tff(82,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
tff(86,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
^ [V_b: $i,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),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
^ [V_b: $i,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),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(93,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),
inference(unit_resolution,[status(thm)],[99,96,86]) ).
tff(101,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____)),
inference(transitivity,[status(thm)],[101,83]) ).
tff(103,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_w____))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____),
inference(transitivity,[status(thm)],[103,8]) ).
tff(105,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(109,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
$false,
inference(unit_resolution,[status(thm)],[109,106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW255+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Sep 4 13:28:53 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 1.70/1.39 % SZS status Theorem
% 1.70/1.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------