TSTP Solution File: ALG355-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG355-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 : Tue Sep 6 16:09:55 EDT 2022
% Result : Unsatisfiable 3.22s 2.39s
% Output : Proof 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 79
% Syntax : Number of formulae : 159 ( 62 unt; 24 typ; 0 def)
% Number of atoms : 383 ( 152 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 423 ( 185 ~; 195 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 19 >; 14 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 226 ( 207 !; 0 ?; 226 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
tff(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
tff(c_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_b_type,type,
v_b: $i ).
tff(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(c_HOL_Oabs__class_Oabs_type,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Complex_ORe_type,type,
c_Complex_ORe: $i > $i ).
tff(c_Complex_OIm_type,type,
c_Complex_OIm: $i > $i ).
tff(c_NthRoot_Osqrt_type,type,
c_NthRoot_Osqrt: $i > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(class_Ring__and__Field_Oabs__if_type,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(1,plain,
^ [V_z: $i] :
refl(
( ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) )
<=> ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) )
<=> ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) )
<=> ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cmod__def_0) ).
tff(5,plain,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) )
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
^ [V_u: $i,V_v: $i] :
refl(
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_realpow__two__le__add__order_0) ).
tff(16,plain,
! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [V_u: $i,V_v: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_x: $i] :
refl(
( ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
<=> ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
<=> ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [V_x: $i] :
rewrite(
( ( ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V_x: $i] :
( ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_x: $i] :
( ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__pow2_0) ).
tff(27,plain,
! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[35,11]) ).
tff(37,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
tff(40,plain,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).
tff(45,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[50,47,40]) ).
tff(52,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[54,47,40]) ).
tff(56,plain,
c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[55,51]) ).
tff(57,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
tff(60,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
tff(65,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[70,67,60]) ).
tff(72,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[72,57]) ).
tff(74,plain,
c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [V_z: $i] : ( c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(v_b),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(unit_resolution,[status(thm)],[76,7]) ).
tff(78,plain,
c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
^ [V_x: $i,V_y: $i] :
refl(
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__self__sum__ge__zero_0) ).
tff(85,plain,
! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ~ ! [V_x: $i,V_y: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
( ( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[92,30,89]) ).
tff(94,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
tff(97,plain,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) )
<=> ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
tff(102,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) )
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) )
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) )
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) )
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[107,104,97]) ).
tff(109,plain,
( class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(110,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
tff(111,plain,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
<=> ( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a )
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) )
<=> ( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a )
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a )
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
tff(118,plain,
! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[120,113]) ).
tff(122,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(transitivity,[status(thm)],[124,122]) ).
tff(126,plain,
( ~ ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [V_a: $i,T_a: $i] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a ) )
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[127,121,111,108]) ).
tff(129,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[128,94,80]) ).
tff(130,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[130,37]) ).
tff(132,plain,
( ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(134,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
$false,
inference(unit_resolution,[status(thm)],[134,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG355-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.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 : Mon Aug 29 16:03:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 3.22/2.39 % SZS status Unsatisfiable
% 3.22/2.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------