TSTP Solution File: SWW210+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW210+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 : Mon Jun 24 18:16:34 EDT 2024
% Result : Theorem 155.41s 21.31s
% Output : CNFRefutation 155.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 20
% Syntax : Number of formulae : 154 ( 44 unt; 0 def)
% Number of atoms : 301 ( 58 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 263 ( 116 ~; 113 |; 12 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 11 con; 0-3 aty)
% Number of variables : 232 ( 34 sgn 104 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
? [X3] :
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
=> 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____,X4))),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,
? [X3] :
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
=> 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____,X4)))),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(f278,axiom,
! [X29] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X29) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(f281,axiom,
! [X9,X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X5,X9)) = c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X9,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(f376,axiom,
! [X53,X54,X55] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,X54),X53) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f377,axiom,
! [X25,X14,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X25)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f388,axiom,
! [X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X16) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f389,axiom,
! [X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Int_OPls) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f390,axiom,
! [X16] : c_Int_OBit0(X16) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f462,axiom,
! [X6] :
( class_Int_Onumber__ring(X6)
=> c_Int_Onumber__class_Onumber__of(X6,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
fof(f468,axiom,
! [X31,X6] :
( class_Int_Onumber__ring(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oone__class_Oone(X6),c_Int_Onumber__class_Onumber__of(X6,X31)) = c_Int_Onumber__class_Onumber__of(X6,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
fof(f496,axiom,
! [X16] : c_Int_OBit1(X16) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16),X16),
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,
( ? [X80] :
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,X4)
=> 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____,X4))),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))))) )
=> ( ? [X81] :
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X81,X4)
=> 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____,X4)))),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,[],[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))))) ),
inference(rectify,[],[f5]) ).
fof(f1205,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(rectify,[],[f6]) ).
fof(f1458,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(rectify,[],[f278]) ).
fof(f1461,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(rectify,[],[f281]) ).
fof(f1556,plain,
! [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)),
inference(rectify,[],[f376]) ).
fof(f1557,plain,
! [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)),
inference(rectify,[],[f377]) ).
fof(f1568,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(rectify,[],[f388]) ).
fof(f1569,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(rectify,[],[f389]) ).
fof(f1570,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(rectify,[],[f390]) ).
fof(f1641,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(rectify,[],[f462]) ).
fof(f1647,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(rectify,[],[f468]) ).
fof(f1671,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(rectify,[],[f496]) ).
fof(f2159,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(f2160,plain,
~ v_thesis____,
inference(flattening,[],[f1203]) ).
fof(f2162,plain,
? [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f1204]) ).
fof(f2163,plain,
? [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f1205]) ).
fof(f2437,plain,
! [X0,X1,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))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(ennf_transformation,[],[f1461]) ).
fof(f2620,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f1641]) ).
fof(f2623,plain,
! [X0,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))
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f1647]) ).
fof(f3218,plain,
( v_thesis____
| ! [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)))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ! [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)))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
inference(ennf_transformation,[],[f2159]) ).
fof(f3219,plain,
( v_thesis____
| ! [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)))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ! [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)))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
inference(flattening,[],[f3218]) ).
fof(f3246,plain,
( ? [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
=> ! [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f3247,plain,
! [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f2162,f3246]) ).
fof(f3248,plain,
( ? [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
=> ! [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f3249,plain,
! [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f2163,f3248]) ).
fof(f3648,plain,
( v_thesis____
| ! [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)))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
| ! [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)))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) ),
inference(rectify,[],[f3219]) ).
fof(f3649,plain,
! [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)))))
& 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____,sK27(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)))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3650,plain,
! [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)))))
& 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____,sK28(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,X2,sK28(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3651,plain,
( v_thesis____
| ! [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____,sK27(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)))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(X0)) )
| ! [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____,sK28(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,X2,sK28(X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f3648,f3650,f3649]) ).
fof(f3656,plain,
! [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,X1) ),
inference(cnf_transformation,[],[f3247]) ).
fof(f3657,plain,
! [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,X1) ),
inference(cnf_transformation,[],[f3249]) ).
fof(f4070,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f1458]) ).
fof(f4073,plain,
! [X2,X0,X1] :
( 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))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(cnf_transformation,[],[f2437]) ).
fof(f4191,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,[],[f1556]) ).
fof(f4192,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,[],[f1557]) ).
fof(f4206,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f1568]) ).
fof(f4207,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f1569]) ).
fof(f4208,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f1570]) ).
fof(f4294,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f2620]) ).
fof(f4310,plain,
! [X0,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))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f2623]) ).
fof(f4348,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,[],[f1671]) ).
fof(f5270,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1112]) ).
fof(f5308,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1150]) ).
fof(f5359,plain,
! [X2,X0] :
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,sK28(X2)) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f5360,plain,
! [X2,X0] :
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(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____,sK28(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))))) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f5361,plain,
! [X2,X0] :
( 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_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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)))))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,sK28(X2)) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f5362,plain,
! [X2,X0] :
( 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_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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)))))
| ~ 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____,sK28(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))))) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f5363,plain,
~ v_thesis____,
inference(cnf_transformation,[],[f2160]) ).
fof(f5364,plain,
! [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,X1) ),
inference(definition_unfolding,[],[f3656,f4208,f4348]) ).
fof(f5365,plain,
! [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)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,X1) ),
inference(definition_unfolding,[],[f3657,f4208,f4348]) ).
fof(f5457,plain,
! [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))
| ~ class_Int_Onumber__ring(X0) ),
inference(definition_unfolding,[],[f4294,f4348]) ).
fof(f5458,plain,
! [X0,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))
| ~ class_Int_Onumber__ring(X1) ),
inference(definition_unfolding,[],[f4310,f4348]) ).
fof(f5550,plain,
! [X2,X0] :
( 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_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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(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____,sK28(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))))) ),
inference(definition_unfolding,[],[f5362,f4208,f4348,f4208,f4348]) ).
fof(f5551,plain,
! [X2,X0] :
( 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_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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,X2,sK28(X2)) ),
inference(definition_unfolding,[],[f5361,f4208,f4348]) ).
fof(f5552,plain,
! [X2,X0] :
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(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____,sK28(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))))) ),
inference(definition_unfolding,[],[f5360,f4208,f4348]) ).
cnf(c_53,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,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____,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,[],[f5364]) ).
cnf(c_54,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,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____,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,[],[f5365]) ).
cnf(c_444,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f4070]) ).
cnf(c_447,plain,
( ~ class_RealVector_Oreal__normed__vector(X0)
| 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)) ),
inference(cnf_transformation,[],[f4073]) ).
cnf(c_563,plain,
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,[],[f4191]) ).
cnf(c_564,plain,
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,[],[f4192]) ).
cnf(c_576,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f4206]) ).
cnf(c_577,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f4207]) ).
cnf(c_663,plain,
( ~ class_Int_Onumber__ring(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)) = c_Groups_Oone__class_Oone(X0) ),
inference(cnf_transformation,[],[f5457]) ).
cnf(c_679,plain,
( ~ class_Int_Onumber__ring(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_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)) ),
inference(cnf_transformation,[],[f5458]) ).
cnf(c_1607,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f5270]) ).
cnf(c_1645,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f5308]) ).
cnf(c_1696,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,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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(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____,sK28(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)))))
| v_thesis____ ),
inference(cnf_transformation,[],[f5550]) ).
cnf(c_1697,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,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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,sK28(X1))
| v_thesis____ ),
inference(cnf_transformation,[],[f5551]) ).
cnf(c_1698,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,c_Complex_ORe(v_s(hAPP(v_f____,sK28(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,X1,sK27(X1))
| v_thesis____ ),
inference(cnf_transformation,[],[f5552]) ).
cnf(c_1699,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK28(X1))
| v_thesis____ ),
inference(cnf_transformation,[],[f5359]) ).
cnf(c_1700,negated_conjecture,
~ v_thesis____,
inference(cnf_transformation,[],[f5363]) ).
cnf(c_2745,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,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____,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]) ).
cnf(c_2747,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,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____,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_54]) ).
cnf(c_2767,plain,
( ~ class_Int_Onumber__ring(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)) = c_Groups_Oone__class_Oone(X0) ),
inference(prop_impl_just,[status(thm)],[c_663]) ).
cnf(c_2769,plain,
( ~ class_Int_Onumber__ring(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_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)) ),
inference(prop_impl_just,[status(thm)],[c_679]) ).
cnf(c_3127,plain,
( ~ class_RealVector_Oreal__normed__vector(X0)
| 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)) ),
inference(prop_impl_just,[status(thm)],[c_447]) ).
cnf(c_4199,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK27(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____,sK28(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(global_subsumption_just,[status(thm)],[c_1698,c_1700,c_1698]) ).
cnf(c_4200,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,c_Complex_ORe(v_s(hAPP(v_f____,sK28(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,X1,sK27(X1)) ),
inference(renaming,[status(thm)],[c_4199]) ).
cnf(c_4202,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK28(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____,sK27(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(global_subsumption_just,[status(thm)],[c_1697,c_1700,c_1697]) ).
cnf(c_4203,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,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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,sK28(X1)) ),
inference(renaming,[status(thm)],[c_4202]) ).
cnf(c_4205,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,c_Complex_ORe(v_s(hAPP(v_f____,sK28(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____,sK27(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(global_subsumption_just,[status(thm)],[c_1696,c_1700,c_1696]) ).
cnf(c_4206,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,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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(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____,sK28(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(renaming,[status(thm)],[c_4205]) ).
cnf(c_11054,plain,
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X0) ),
inference(demodulation,[status(thm)],[c_2767,c_563,c_564,c_576,c_577]) ).
cnf(c_11097,plain,
( ~ class_Int_Onumber__ring(X0)
| 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)) ),
inference(demodulation,[status(thm)],[c_2769,c_563,c_564,c_576]) ).
cnf(c_11139,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,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____,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_2745,c_563,c_564,c_576,c_577]) ).
cnf(c_11141,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,c_Complex_ORe(v_s(hAPP(v_f____,sK28(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,sK27(X1)) ),
inference(demodulation,[status(thm)],[c_4200,c_563,c_564,c_576,c_577]) ).
cnf(c_11142,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,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____,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_2747,c_563,c_564,c_576,c_577]) ).
cnf(c_11143,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,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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,sK28(X1)) ),
inference(demodulation,[status(thm)],[c_4203,c_563,c_564,c_576,c_577]) ).
cnf(c_11180,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,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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(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____,sK28(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))))) ),
inference(demodulation,[status(thm)],[c_4206,c_563,c_564,c_576,c_577]) ).
cnf(c_15937,plain,
( X0 != tc_RealDef_Oreal
| 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)) ),
inference(resolution_lifted,[status(thm)],[c_3127,c_1607]) ).
cnf(c_15938,plain,
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_15937]) ).
cnf(c_26244,plain,
( X0 != tc_RealDef_Oreal
| 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)) ),
inference(resolution_lifted,[status(thm)],[c_11097,c_1645]) ).
cnf(c_26245,plain,
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_26244]) ).
cnf(c_26268,plain,
( X0 != tc_RealDef_Oreal
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X0) ),
inference(resolution_lifted,[status(thm)],[c_11054,c_1645]) ).
cnf(c_26269,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_26268]) ).
cnf(c_28888,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,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____,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(prop_impl_just,[status(thm)],[c_11139]) ).
cnf(c_28890,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,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____,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_11142]) ).
cnf(c_29298,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK28(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____,sK27(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_11143]) ).
cnf(c_29299,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,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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,sK28(X1)) ),
inference(renaming,[status(thm)],[c_29298]) ).
cnf(c_29558,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK27(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____,sK28(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(prop_impl_just,[status(thm)],[c_11141]) ).
cnf(c_29559,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,c_Complex_ORe(v_s(hAPP(v_f____,sK28(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,sK27(X1)) ),
inference(renaming,[status(thm)],[c_29558]) ).
cnf(c_29572,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,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,sK27(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(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____,sK28(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))))) ),
inference(prop_impl_just,[status(thm)],[c_11180]) ).
cnf(c_36336,plain,
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_15938,c_444]) ).
cnf(c_36582,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,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,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)))) ),
inference(demodulation,[status(thm)],[c_28888,c_36336,c_26245,c_26269]) ).
cnf(c_36590,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,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,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)))) ),
inference(demodulation,[status(thm)],[c_28890,c_36336,c_26245,c_26269]) ).
cnf(c_36591,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____,sK28(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,sK27(X1)) ),
inference(demodulation,[status(thm)],[c_29559,c_36336,c_26245,c_26269]) ).
cnf(c_36601,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____,sK27(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,sK28(X1)) ),
inference(demodulation,[status(thm)],[c_29299,c_36336,c_26245,c_26269]) ).
cnf(c_36627,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____,sK27(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(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____,sK28(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)))) ),
inference(demodulation,[status(thm)],[c_29572,c_36336,c_26245,c_26269]) ).
cnf(c_45051,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,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,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)))) ),
inference(prop_impl_just,[status(thm)],[c_36582]) ).
cnf(c_45053,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,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,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)))) ),
inference(prop_impl_just,[status(thm)],[c_36590]) ).
cnf(c_45439,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK28(X1)) ),
inference(prop_impl_just,[status(thm)],[c_1700,c_1699]) ).
cnf(c_45443,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK28(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____,sK27(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_36601]) ).
cnf(c_45444,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____,sK27(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,sK28(X1)) ),
inference(renaming,[status(thm)],[c_45443]) ).
cnf(c_45671,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK27(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____,sK28(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_36591]) ).
cnf(c_45672,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____,sK28(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,sK27(X1)) ),
inference(renaming,[status(thm)],[c_45671]) ).
cnf(c_46203,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____,sK27(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(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____,sK28(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)))) ),
inference(prop_impl_just,[status(thm)],[c_36627]) ).
cnf(c_52269,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____,sK28(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))))
| ~ sP0_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_46203]) ).
cnf(c_52270,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____,sK27(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))))
| ~ sP1_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP1_iProver_def])],[c_46203]) ).
cnf(c_52271,plain,
( sP0_iProver_def
| sP1_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_46203]) ).
cnf(c_52272,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK28(X0))
| ~ sP2_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP2_iProver_def])],[c_45444]) ).
cnf(c_52273,plain,
( sP1_iProver_def
| sP2_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_45444]) ).
cnf(c_52274,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(X0))
| ~ sP3_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP3_iProver_def])],[c_45672]) ).
cnf(c_52275,plain,
( sP0_iProver_def
| sP3_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_45672]) ).
cnf(c_52276,plain,
( sP2_iProver_def
| sP3_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_45439]) ).
cnf(c_60175,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(X0))
| ~ sP3_iProver_def ),
inference(prop_impl_just,[status(thm)],[c_52274]) ).
cnf(c_60176,plain,
( ~ sP3_iProver_def
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK27(X0)) ),
inference(renaming,[status(thm)],[c_60175]) ).
cnf(c_61027,plain,
( ~ sP2_iProver_def
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK28(X0)) ),
inference(prop_impl_just,[status(thm)],[c_52272]) ).
cnf(c_66860,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,sK28(sK13))
| 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____,sK28(sK13)))))),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_45051]) ).
cnf(c_66861,plain,
( ~ sP2_iProver_def
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK13,sK28(sK13)) ),
inference(instantiation,[status(thm)],[c_61027]) ).
cnf(c_75999,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____,sK28(sK13)))))),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))))
| ~ sP0_iProver_def ),
inference(instantiation,[status(thm)],[c_52269]) ).
cnf(c_78271,plain,
sP1_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_52271,c_52271,c_52273,c_66860,c_66861,c_75999]) ).
cnf(c_78273,plain,
sP3_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_52275,c_52275,c_52276,c_66860,c_66861,c_75999]) ).
cnf(c_128531,plain,
( ~ sP3_iProver_def
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,sK27(sK14)) ),
inference(instantiation,[status(thm)],[c_60176]) ).
cnf(c_128532,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK14,sK27(sK14))
| 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____,sK27(sK14))))))),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_45053]) ).
cnf(c_133122,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____,sK27(sK14))))))),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))))
| ~ sP1_iProver_def ),
inference(instantiation,[status(thm)],[c_52270]) ).
cnf(c_133123,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_133122,c_128532,c_128531,c_78273,c_78271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW210+1 : TPTP v8.2.0. Released v5.2.0.
% 0.06/0.11 % Command : run_iprover %s %d THM
% 0.10/0.32 % Computer : n027.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Jun 19 04:36:24 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 155.41/21.31 % SZS status Started for theBenchmark.p
% 155.41/21.31 % SZS status Theorem for theBenchmark.p
% 155.41/21.31
% 155.41/21.31 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 155.41/21.31
% 155.41/21.31 ------ iProver source info
% 155.41/21.31
% 155.41/21.31 git: date: 2024-06-12 09:56:46 +0000
% 155.41/21.31 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 155.41/21.31 git: non_committed_changes: false
% 155.41/21.31
% 155.41/21.31 ------ Parsing...
% 155.41/21.31 ------ Clausification by vclausify_rel & Parsing by iProver...
% 155.41/21.31
% 155.41/21.31 ------ Preprocessing... sup_sim: 177 sf_s rm: 22 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe:64:0s pe_e sup_sim: 398 sf_s rm: 61 0s sf_e pe_s pe_e sup_sim: 3 sf_s rm: 61 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 61 0s sf_e pe_s pe_e
% 155.41/21.31
% 155.41/21.31 ------ Preprocessing... gs_s sp: 8 0s gs_e snvd_s sp: 0 0s snvd_e
% 155.41/21.31
% 155.41/21.31 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 155.41/21.31 ------ Proving...
% 155.41/21.31 ------ Problem Properties
% 155.41/21.31
% 155.41/21.31
% 155.41/21.31 clauses 1330
% 155.41/21.31 conjectures 0
% 155.41/21.31 EPR 78
% 155.41/21.31 Horn 1115
% 155.41/21.31 unary 502
% 155.41/21.31 binary 432
% 155.41/21.31 lits 2674
% 155.41/21.31 lits eq 795
% 155.41/21.31 fd_pure 0
% 155.41/21.31 fd_pseudo 0
% 155.41/21.31 fd_cond 116
% 155.41/21.31 fd_pseudo_cond 56
% 155.41/21.31 AC symbols 0
% 155.41/21.31
% 155.41/21.31 ------ Input Options Time Limit: Unbounded
% 155.41/21.31
% 155.41/21.31
% 155.41/21.31 ------
% 155.41/21.31 Current options:
% 155.41/21.31 ------
% 155.41/21.31
% 155.41/21.31
% 155.41/21.31
% 155.41/21.31
% 155.41/21.31 ------ Proving...
% 155.41/21.31
% 155.41/21.31
% 155.41/21.31 % SZS status Theorem for theBenchmark.p
% 155.41/21.31
% 155.41/21.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 155.41/21.31
% 155.41/21.31
%------------------------------------------------------------------------------