%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW210+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:29:15 PM UTC 2026
% Result : Theorem 115.00s 33.91s
% Output : CNFRefutation 115.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 145 ( 37 unt; 0 def)
% Number of atoms : 284 ( 56 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 251 ( 112 ~; 116 |; 9 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 11 con; 0-3 aty)
% Number of variables : 211 ( 0 sgn 197 !; 14 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IRe_A_Is_A_If_An_J_J_A_N_Ax_J_A_060_Ae_A_P_A2_096) ).
fof(f6,axiom,
? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_096) ).
fof(f263,axiom,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(f278,axiom,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(f281,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(f376,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f377,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f388,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f389,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f390,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f461,axiom,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(f468,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
fof(f496,axiom,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f1112,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1150,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1201,axiom,
( ? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
=> ( ? [X2] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
=> v_thesis____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1202,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f1203,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1202]) ).
fof(f1204,plain,
( ? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
=> ( ? [X2] :
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X3)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
=> v_thesis____ ) ),
inference(rectify,[],[f1201]) ).
fof(f1205,plain,
~ v_thesis____,
inference(flattening,[],[f1203]) ).
fof(f1207,plain,
( ! [X0] :
? [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
| ! [X2] :
? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X3)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
| v_thesis____ ),
inference(ennf_transformation,[],[f1204]) ).
fof(f1208,plain,
( ! [X0] :
? [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
| ! [X2] :
? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X3)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
| v_thesis____ ),
inference(flattening,[],[f1207]) ).
fof(f1270,plain,
? [X0] :
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f1321,plain,
? [X0] :
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f1344,plain,
! [X0,X1,X2] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(ennf_transformation,[],[f281]) ).
fof(f1497,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)) ),
inference(ennf_transformation,[],[f468]) ).
fof(f1499,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) ),
inference(ennf_transformation,[],[f461]) ).
fof(f1726,plain,
( ! [X2] :
? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X3))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
| ! [X0] :
? [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
| v_thesis____ ),
inference(rectify,[],[f1208]) ).
fof(f1727,plain,
( ! [X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,sK13(X2))
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
| ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0))
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
| v_thesis____ ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X3,sK13(X2))],[f1726]) ).
fof(f1774,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f1270]) ).
fof(f1780,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(nnf_transformation,[],[f263]) ).
fof(f1837,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f1321]) ).
fof(f2010,plain,
! [X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,sK13(X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0))
| v_thesis____ ),
inference(cnf_transformation,[],[f1727]) ).
fof(f2011,plain,
! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0))
| v_thesis____ ),
inference(cnf_transformation,[],[f1727]) ).
fof(f2012,plain,
! [X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,sK13(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| v_thesis____ ),
inference(cnf_transformation,[],[f1727]) ).
fof(f2013,plain,
! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| v_thesis____ ),
inference(cnf_transformation,[],[f1727]) ).
fof(f2014,plain,
~ v_thesis____,
inference(cnf_transformation,[],[f1205]) ).
fof(f2171,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(cnf_transformation,[],[f1774]) ).
fof(f2206,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1780]) ).
fof(f2272,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f389]) ).
fof(f2273,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f388]) ).
fof(f2324,plain,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f496]) ).
fof(f2361,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f390]) ).
fof(f2398,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(cnf_transformation,[],[f1837]) ).
fof(f2407,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1112]) ).
fof(f2421,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(cnf_transformation,[],[f1344]) ).
fof(f2430,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f278]) ).
fof(f2440,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
inference(cnf_transformation,[],[f377]) ).
fof(f2441,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
inference(cnf_transformation,[],[f376]) ).
fof(f2615,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1150]) ).
fof(f2638,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)) ),
inference(cnf_transformation,[],[f1497]) ).
fof(f2640,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) ),
inference(cnf_transformation,[],[f1499]) ).
fof(f3005,plain,
! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| v_thesis____ ),
inference(definition_unfolding,[],[f2013,f2361,f2324,f2361,f2324]) ).
fof(f3006,plain,
! [X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,sK13(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| v_thesis____ ),
inference(definition_unfolding,[],[f2012,f2361,f2324]) ).
fof(f3007,plain,
! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0))
| v_thesis____ ),
inference(definition_unfolding,[],[f2011,f2361,f2324]) ).
fof(f3012,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(definition_unfolding,[],[f2171,f2361,f2324]) ).
fof(f3115,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(definition_unfolding,[],[f2398,f2361,f2324]) ).
fof(f3152,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X0)) ),
inference(definition_unfolding,[],[f2638,f2324]) ).
fof(f3154,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ),
inference(definition_unfolding,[],[f2640,f2324]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(cnf_transformation,[],[f3005]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(cnf_transformation,[],[f3006]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK12(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(cnf_transformation,[],[f3007]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0)) ),
inference(cnf_transformation,[],[f2010]) ).
tcf(c_53,negated_conjecture,
~ v_thesis____,
inference(cnf_transformation,[],[f2014]) ).
tcf(c_202,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X0))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X0) ),
inference(cnf_transformation,[],[f3012]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f2206]) ).
tcf(c_303,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f2272]) ).
tcf(c_304,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f2273]) ).
tcf(c_424,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X0)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X0) ),
inference(cnf_transformation,[],[f3115]) ).
tcf(c_429,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f2407]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X2,X1)) )
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f2421]) ).
tcf(c_452,plain,
! [X0: $i] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f2430]) ).
tcf(c_462,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)),
inference(cnf_transformation,[],[f2440]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(cnf_transformation,[],[f2441]) ).
tcf(c_636,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f2615]) ).
tcf(c_659,plain,
! [X0: $i,X1: $i] :
( ( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X1)) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) )
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f3152]) ).
tcf(c_661,plain,
! [X0: $i] :
( ( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f3154]) ).
tcf(c_1640,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_53,c_50]) ).
tcf(c_1641,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(renaming,[status(thm)],[c_1640]) ).
tcf(c_1806,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(prop_impl_just,[status(thm)],[c_53,c_49]) ).
tcf(c_1808,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(prop_impl_just,[status(thm)],[c_1641]) ).
tcf(c_1812,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK12(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(prop_impl_just,[status(thm)],[c_53,c_51]) ).
tcf(c_1832,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X2,X1)) )
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(prop_impl_just,[status(thm)],[c_443]) ).
tcf(c_1970,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X0))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X0) ),
inference(prop_impl_just,[status(thm)],[c_202]) ).
tcf(c_2048,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X0)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X0) ),
inference(prop_impl_just,[status(thm)],[c_424]) ).
tcf(c_2110,plain,
! [X0: $i,X1: $i] :
( ( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X1)) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) )
| ~ class_Int_Onumber__ring(X0) ),
inference(prop_impl_just,[status(thm)],[c_659]) ).
tcf(c_2112,plain,
! [X0: $i] :
( ( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Int_Onumber__ring(X0) ),
inference(prop_impl_just,[status(thm)],[c_661]) ).
tcf(c_8658,plain,
! [X0: $i] :
( ( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Int_Onumber__ring(X0) ),
inference(demodulation,[status(thm)],[c_2112,c_303,c_304,c_462,c_463]) ).
tcf(c_10425,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)) )
| ~ class_Int_Onumber__ring(X0) ),
inference(demodulation,[status(thm)],[c_2110,c_304,c_462,c_463]) ).
tcf(c_11205,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X0))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X0) ),
inference(demodulation,[status(thm)],[c_1970,c_303,c_304,c_462,c_463]) ).
tcf(c_11212,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK12(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(demodulation,[status(thm)],[c_1812,c_303,c_304,c_462,c_463]) ).
tcf(c_11219,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X0)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X0) ),
inference(demodulation,[status(thm)],[c_2048,c_303,c_304,c_462,c_463]) ).
tcf(c_11226,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(demodulation,[status(thm)],[c_1808,c_303,c_304,c_462,c_463]) ).
tcf(c_11402,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(demodulation,[status(thm)],[c_1806,c_303,c_304,c_462,c_463]) ).
tcf(c_12140,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X2,X1)) )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1832,c_429]) ).
tcf(c_12141,plain,
! [X0: $i,X1: $i] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
inference(unflattening,[status(thm)],[c_12140]) ).
tcf(c_18543,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)) )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_10425,c_636]) ).
tcf(c_18544,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),
inference(unflattening,[status(thm)],[c_18543]) ).
tcf(c_18561,plain,
! [X0: $i] :
( ( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X0) )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_8658,c_636]) ).
tcf(c_18562,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_18561]) ).
tcf(c_21837,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X0))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X0) ),
inference(prop_impl_just,[status(thm)],[c_11205]) ).
tcf(c_21897,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X0)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X0) ),
inference(prop_impl_just,[status(thm)],[c_11219]) ).
tcf(c_21963,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1)) ),
inference(prop_impl_just,[status(thm)],[c_11226]) ).
tcf(c_21964,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(renaming,[status(thm)],[c_21963]) ).
tcf(c_22113,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK12(X1)) ),
inference(prop_impl_just,[status(thm)],[c_11212]) ).
tcf(c_22114,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK12(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(renaming,[status(thm)],[c_22113]) ).
tcf(c_22143,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(prop_impl_just,[status(thm)],[c_11402]) ).
tcf(c_27058,plain,
! [X0: $i,X1: $i] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
inference(demodulation,[status(thm)],[c_12141,c_452]) ).
tcf(c_28587,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,X0))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X0) ),
inference(demodulation,[status(thm)],[c_21837,c_18544,c_18562,c_27058]) ).
tcf(c_28717,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X0)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X0) ),
inference(demodulation,[status(thm)],[c_21897,c_18544,c_18562,c_27058]) ).
tcf(c_28724,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK12(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(demodulation,[status(thm)],[c_22114,c_18544,c_18562,c_27058]) ).
tcf(c_28785,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(demodulation,[status(thm)],[c_21964,c_18544,c_18562,c_27058]) ).
tcf(c_28870,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X1)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(demodulation,[status(thm)],[c_22143,c_18544,c_18562,c_27058]) ).
tcf(c_36501,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,X0))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,X0) ),
inference(prop_impl_just,[status(thm)],[c_28587]) ).
tcf(c_36567,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X0)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,X0) ),
inference(prop_impl_just,[status(thm)],[c_28717]) ).
tcf(c_36623,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0)) ),
inference(prop_impl_just,[status(thm)],[c_53,c_52]) ).
tcf(c_36627,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1)) ),
inference(prop_impl_just,[status(thm)],[c_28785]) ).
tcf(c_36628,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK13(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(renaming,[status(thm)],[c_36627]) ).
tcf(c_36761,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK12(X1)) ),
inference(prop_impl_just,[status(thm)],[c_28724]) ).
tcf(c_36762,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK12(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(renaming,[status(thm)],[c_36761]) ).
tcf(c_37005,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X1)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(prop_impl_just,[status(thm)],[c_28870]) ).
tcf(c_43035,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_37005]) ).
tcf(c_43036,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(X0))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_37005]) ).
tcf(c_43037,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_37005]) ).
tcf(c_43038,plain,
! [X0: $i] :
( ~ iPr_def_12
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK13(X0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_36628]) ).
tcf(c_43039,plain,
( iPr_def_12
| iPr_def_11 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_36628]) ).
tcf(c_43040,plain,
! [X0: $i] :
( ~ iPr_def_13
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_36762]) ).
tcf(c_43041,plain,
( iPr_def_13
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_36762]) ).
tcf(c_43042,plain,
( iPr_def_13
| iPr_def_12 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_36623]) ).
tcf(c_48271,plain,
! [X0: $i] :
( ~ iPr_def_13
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0)) ),
inference(prop_impl_just,[status(thm)],[c_43040]) ).
tcf(c_48272,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK12(X0))
| ~ iPr_def_13 ),
inference(renaming,[status(thm)],[c_48271]) ).
tcf(c_48671,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK13(X0))
| ~ iPr_def_12 ),
inference(prop_impl_just,[status(thm)],[c_43038]) ).
tcf(c_56987,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,sK12(sK21))
| ~ iPr_def_13 ),
inference(instantiation,[status(thm)],[c_48272]) ).
tcf(c_56988,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(sK21))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21,sK12(sK21)) ),
inference(instantiation,[status(thm)],[c_36567]) ).
tcf(c_71545,plain,
( ~ iPr_def_11
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK12(sK21))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(instantiation,[status(thm)],[c_43036]) ).
tcf(c_83536,plain,
! [X0: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,sK12(X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_43040,c_236]) ).
tcf(c_84345,plain,
! [X0: $i] :
( iPr_def_12
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,sK12(X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_43042,c_83536]) ).
tcf(c_84346,plain,
! [X0: $i] :
( iPr_def_10
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,sK12(X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_43041,c_83536]) ).
tcf(c_84423,plain,
iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_84345,c_43039,c_43042,c_56987,c_56988,c_71545]) ).
tcf(c_84425,plain,
iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_84346,c_43037,c_43041,c_56987,c_56988,c_71545]) ).
tcf(c_152912,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(X0)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,sK13(X0)) ),
inference(instantiation,[status(thm)],[c_36501]) ).
tcf(c_156356,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(sK19)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,sK13(sK19)) ),
inference(instantiation,[status(thm)],[c_152912]) ).
tcf(c_156357,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19,sK13(sK19))
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_48671]) ).
tcf(c_256492,plain,
( ~ iPr_def_10
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,sK13(sK19)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(instantiation,[status(thm)],[c_43035]) ).
tcf(c_256493,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_256492,c_156357,c_156356,c_84425,c_84423]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW210+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.39 % Computer : n015.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Thu Sep 24 21:48:37 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.44
% 0.15/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.44
% 0.15/10.44 % Detected problem language: tptp
% 0.15/10.46 % Proving...
% 115.00/33.91 % SZS status Started for theBenchmark.p
% 115.00/33.91 ERROR - "ProverProcess:heur/421498:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 115.00/33.91 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 115.00/33.91 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 8 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 128 --inst_lit_activity_flag false --inst_lit_sel "[+sign;+prop]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[+num_symb;-age;-age];[+num_symb;+conj_non_prolific_symb]]" --inst_passive_queues_freq "[512;10]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.006221608720445637 --inst_solver_per_active 32768 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+non_prol_conj_symb;+sign;-depth;-prop]" --inst_start_prop_sim_after_learn 9 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_irpzeedy/rg3lzmbr 2>> /export/starexec/sandbox2/tmp/iprover_out_irpzeedy/rg3lzmbr_error
% 115.00/33.91 % SZS status Theorem for theBenchmark.p
% 115.00/33.91
% 115.00/33.91 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 115.00/33.91
% 115.00/33.91 % ------ iProver source info
% 115.00/33.91
% 115.00/33.91 % git: date: 2026-07-19 20:42:38 +0200
% 115.00/33.91 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 115.00/33.91 % git: non_committed_changes: false
% 115.00/33.91
% 115.00/33.91 % ------ Parsing...
% 115.00/33.91 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 115.00/33.91
% 115.00/33.91 % ------ Preprocessing... sup_sim: 163 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 211 sf_s rm: 10 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e %
% 115.00/33.91
% 115.00/33.91 % ------ Preprocessing... gs_s sp: 8 0s gs_e snvd_s sp: 0 0s snvd_e %
% 115.00/33.91
% 115.00/33.91 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 115.00/33.91 % ------ Proving...
% 115.00/33.91 % ------ Problem Properties
% 115.00/33.91
% 115.00/33.91 %
% 115.00/33.91 % clauses 711
% 115.00/33.91 % conjectures 0
% 115.00/33.91 % EPR 30
% 115.00/33.91 % Horn 585
% 115.00/33.91 % unary 277
% 115.00/33.91 % binary 271
% 115.00/33.91 % lits 1352
% 115.00/33.91 % lits eq 423
% 115.00/33.91 % fd_pure 0
% 115.00/33.91 % fd_pseudo 0
% 115.00/33.91 % fd_cond 64
% 115.00/33.91 % fd_pseudo_cond 24
% 115.00/33.91 % AC symbols 0
% 115.00/33.91
% 115.00/33.91 % ------ Schedule dynamic 5 is on
% 115.00/33.91
% 115.00/33.91 % ------ no conjectures: strip conj schedule
% 115.00/33.91
% 115.00/33.91 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 115.00/33.91
% 115.00/33.91
% 115.00/33.91 % ------
% 115.00/33.91 % Current options:
% 115.00/33.91 % ------
% 115.00/33.91
% 115.00/33.91
% 115.00/33.91 %
% 115.00/33.91
% 115.00/33.91 % ------ Proving...
% 115.00/33.91 % Proof_search_loop: time out after: 6098 full_loop iterations
% 115.00/33.91
% 115.00/33.91 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" stripped conjectures Time Limit: 15.
% 115.00/33.91
% 115.00/33.91
% 115.00/33.91 % ------
% 115.00/33.91 % Current options:
% 115.00/33.91 % ------
% 115.00/33.91
% 115.00/33.91
% 115.00/33.91 %
% 115.00/33.91
% 115.00/33.91 % ------ Proving...
% 115.00/33.91 %
% 115.00/33.91
% 115.00/33.91 % SZS status Theorem for theBenchmark.p
% 115.00/33.91
% 115.00/33.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 115.00/33.91
% 115.00/33.91
%------------------------------------------------------------------------------