TSTP Solution File: SWW203+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW203+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 20:57:53 EDT 2022
% Result : Theorem 8.19s 5.58s
% Output : Proof 8.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 122
% Syntax : Number of formulae : 259 ( 110 unt; 28 typ; 0 def)
% Number of atoms : 628 ( 424 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 545 ( 173 ~; 163 |; 0 &)
% ( 194 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 20 >; 12 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-3 aty)
% Number of variables : 392 ( 343 !; 0 ?; 392 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Complex_OIm_type,type,
c_Complex_OIm: $i > $i ).
tff(v_y_type,type,
v_y: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Complex_ORe_type,type,
c_Complex_ORe: $i > $i ).
tff(c_NthRoot_Osqrt_type,type,
c_NthRoot_Osqrt: $i > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Complex_Oii_type,type,
c_Complex_Oii: $i ).
tff(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
tff(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
tff(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
tff(c_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
tff(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(class_Groups_Ogroup__add_type,type,
class_Groups_Ogroup__add: $i > $o ).
tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(c_Complex_Ocomplex_OComplex_type,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(1,plain,
^ [V_x: $i] :
refl(
( ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [V_x: $i] :
rewrite(
( ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [V_x: $i] :
rewrite(
( ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
tff(9,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
inference(modus_ponens,[status(thm)],[10,4]) ).
tff(12,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
inference(modus_ponens,[status(thm)],[12,2]) ).
tff(14,plain,
( ~ ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
| ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
^ [V_ya_2: $i,V_xa_2: $i] :
refl(
( ( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) )
<=> ( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) )
<=> ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) )
<=> ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__eq__iff) ).
tff(20,plain,
! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) )
| ( ( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( class_Groups_Oab__group__add(tc_RealDef_Oreal)
<=> class_Groups_Oab__group__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
tff(27,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [V_b_2: $i,V_a_2: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [V_b_2: $i,V_a_2: $i,T_a: $i] :
rewrite(
( ( class_Groups_Oab__group__add(T_a)
=> ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( class_Groups_Oab__group__add(T_a)
=> ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( class_Groups_Oab__group__add(T_a)
=> ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
tff(34,plain,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Groups_Oab__group__add(tc_RealDef_Oreal)
| ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
<=> ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Groups_Oab__group__add(tc_RealDef_Oreal)
| ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
<=> ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Groups_Oab__group__add(tc_RealDef_Oreal)
| ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
<=> ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oab__group__add(T_a)
| ( ( V_a_2 = V_b_2 )
<=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Groups_Oab__group__add(tc_RealDef_Oreal)
| ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
<=> ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
<=> ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[40,37,27]) ).
tff(42,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
<=> class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
tff(44,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
^ [V_a_2: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
^ [V_a_2: $i,T_a: $i] :
rewrite(
( ( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
^ [V_a_2: $i,T_a: $i] :
rewrite(
( ( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
^ [V_a_2: $i,T_a: $i] :
rewrite(
( ( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [V_a_2: $i,T_a: $i] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [V_a_2: $i,T_a: $i] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
tff(55,plain,
! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[56,50]) ).
tff(58,plain,
! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[57,48]) ).
tff(59,plain,
! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[59,46]) ).
tff(61,plain,
( ( ~ ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
| ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
| ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
| ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [V_a_2: $i,T_a: $i] :
( ~ class_Rings_Oring__1__no__zero__divisors(T_a)
| ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
| ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[63,60,44]) ).
tff(65,plain,
( ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__i) ).
tff(67,plain,
c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_Complex_ORe(c_Complex_Oii) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(tautology,[status(thm)],]) ).
tff(69,plain,
( ~ ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[69,64]) ).
tff(71,plain,
( class_Groups_Ogroup__add(tc_RealDef_Oreal)
<=> class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
tff(73,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
tff(80,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
| ~ class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
| ~ class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
| ~ class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )
| ~ class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(unit_resolution,[status(thm)],[86,83,73]) ).
tff(88,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[87,70]) ).
tff(89,plain,
( ~ ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
<=> ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
| ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
( ~ ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
<=> ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(unit_resolution,[status(thm)],[90,41]) ).
tff(92,plain,
( ~ ( ( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(93,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(unit_resolution,[status(thm)],[92,91,24]) ).
tff(94,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),
inference(transitivity,[status(thm)],[93,15]) ).
tff(95,plain,
( ~ ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
| ( c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),
inference(unit_resolution,[status(thm)],[95,13]) ).
tff(97,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(99,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
^ [V_a_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_a_2) )
<=> ( V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
^ [V_a_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_a_2) )
<=> ( V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
tff(106,plain,
! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( ( ~ ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ~ ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[112,109,99]) ).
tff(114,plain,
( ~ ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
| ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(tautology,[status(thm)],]) ).
tff(115,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(unit_resolution,[status(thm)],[114,70,113]) ).
tff(116,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),
inference(transitivity,[status(thm)],[117,96]) ).
tff(119,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)))),
inference(monotonicity,[status(thm)],[118,94]) ).
tff(120,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
^ [V_y: $i,V_x: $i] :
refl(
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) )
<=> ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
^ [V_y: $i,V_x: $i] :
rewrite(
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) )),
inference(bind,[status(th)],]) ).
tff(124,plain,
( ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) )
<=> ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
^ [V_y: $i,V_x: $i] :
rewrite(
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
<=> ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
<=> ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,axiom,
! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__norm) ).
tff(129,plain,
! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ),
inference(modus_ponens,[status(thm)],[129,126]) ).
tff(131,plain,
! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ),
inference(modus_ponens,[status(thm)],[130,124]) ).
tff(132,plain,
! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ),
inference(modus_ponens,[status(thm)],[132,122]) ).
tff(134,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) )
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
^ [V_z: $i] :
refl(
( ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
<=> ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
<=> ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
<=> ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,axiom,
! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__surj) ).
tff(140,plain,
! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
inference(skolemize,[status(sab)],[140]) ).
tff(142,plain,
! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
( ~ ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
| ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y),
inference(unit_resolution,[status(thm)],[143,142]) ).
tff(145,plain,
^ [V_y: $i,V_x: $i] :
refl(
( ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) )
<=> ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) ) )),
inference(bind,[status(th)],]) ).
tff(146,plain,
( ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) )
<=> ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) )
<=> ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,axiom,
! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im_Odiff) ).
tff(149,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)) )
| ( c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),
inference(unit_resolution,[status(thm)],[152,151]) ).
tff(154,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)) = c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(156,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
tff(157,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(159,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[158]) ).
tff(160,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(162,plain,
( ! [V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,axiom,
! [V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
tff(164,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[164,160]) ).
tff(166,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ),
inference(skolemize,[status(sab)],[165]) ).
tff(167,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[166,159]) ).
tff(168,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)) ) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),
inference(unit_resolution,[status(thm)],[170,167,157]) ).
tff(172,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),
inference(monotonicity,[status(thm)],[67]) ).
tff(173,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))) = c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),
inference(transitivity,[status(thm)],[172,171,154]) ).
tff(174,plain,
^ [V_y: $i,V_x: $i] :
refl(
( ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) )
<=> ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) ) )),
inference(bind,[status(th)],]) ).
tff(175,plain,
( ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) )
<=> ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) ) ),
inference(quant_intro,[status(thm)],[174]) ).
tff(176,plain,
( ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) )
<=> ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,axiom,
! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Odiff) ).
tff(178,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) ),
inference(skolemize,[status(sab)],[178]) ).
tff(180,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) ),
inference(modus_ponens,[status(thm)],[179,175]) ).
tff(181,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)) )
| ( c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),
inference(unit_resolution,[status(thm)],[181,180]) ).
tff(183,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
( ( ~ ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(185,plain,
( ~ ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
( ~ ! [V_a_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_a_2) )
<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
( ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[186,109,99]) ).
tff(188,plain,
( ~ ( ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) )
| ( c_Complex_ORe(c_Complex_Oii) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(tautology,[status(thm)],]) ).
tff(189,plain,
( ~ ( ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) )
<=> ( c_Complex_ORe(c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) ) ),
inference(unit_resolution,[status(thm)],[188,67]) ).
tff(190,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),
inference(unit_resolution,[status(thm)],[189,187]) ).
tff(191,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)) = c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),
inference(transitivity,[status(thm)],[191,183]) ).
tff(193,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)))) = c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),
inference(monotonicity,[status(thm)],[192,173]) ).
tff(194,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y),
inference(transitivity,[status(thm)],[193,144]) ).
tff(195,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
^ [V_z: $i] :
refl(
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) )),
inference(bind,[status(th)],]) ).
tff(198,plain,
( ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) )
<=> ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,plain,
^ [V_z: $i] :
rewrite(
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) )),
inference(bind,[status(th)],]) ).
tff(200,plain,
( ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) )
<=> ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,plain,
^ [V_z: $i] :
rewrite(
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ) )),
inference(bind,[status(th)],]) ).
tff(202,plain,
( ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
<=> ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
( ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
<=> ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(204,axiom,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cmod__def) ).
tff(205,plain,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ),
inference(modus_ponens,[status(thm)],[205,202]) ).
tff(207,plain,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ),
inference(modus_ponens,[status(thm)],[206,200]) ).
tff(208,plain,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ),
inference(skolemize,[status(sab)],[207]) ).
tff(209,plain,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ),
inference(modus_ponens,[status(thm)],[208,198]) ).
tff(210,plain,
( ~ ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) )
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(211,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
inference(unit_resolution,[status(thm)],[210,209]) ).
tff(212,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
inference(transitivity,[status(thm)],[212,196,135]) ).
tff(214,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))) ),
inference(monotonicity,[status(thm)],[213,120]) ).
tff(215,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))) ),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(217,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(218,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(219,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096sqrt_A_I_IRe_Ax_A_N_ARe_Ay_A_L_A0_J_A_094_A2_A_L_A_I0_A_L_A_IIm_Ax_A_N_AIm_Ay_J_J_A_094_A2_J_060_061_Asqrt_A_I_IRe_Ax_A_N_ARe_Ay_J_A_094_A2_A_L_A0_A_094_A2_J_A_L_Asqrt_A_I0_A_094_A2_A_L_A_IIm_Ax_A_N_AIm_Ay_J_A_094_A2_J_096) ).
tff(220,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))),
inference(modus_ponens,[status(thm)],[220,217]) ).
tff(222,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Complex_ORe(c_Complex_Oii)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Oii),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
inference(modus_ponens,[status(thm)],[221,216]) ).
tff(223,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(modus_ponens,[status(thm)],[222,215]) ).
tff(224,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)))))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))) ),
inference(rewrite,[status(thm)],]) ).
tff(225,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)))))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))) ),
inference(rewrite,[status(thm)],]) ).
tff(226,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)))))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))) ),
inference(rewrite,[status(thm)],]) ).
tff(227,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(228,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(modus_ponens,[status(thm)],[228,225]) ).
tff(230,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(modus_ponens,[status(thm)],[229,224]) ).
tff(231,plain,
$false,
inference(unit_resolution,[status(thm)],[230,223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWW203+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 12:39:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 8.19/5.58 % SZS status Theorem
% 8.19/5.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------