%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW173+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 : Tue Sep 29 01:29:46 PM UTC 2026
% Result : Theorem 6.94s 1.83s
% Output : Refutation 8.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 47
% Syntax : Number of formulae : 233 ( 168 unt; 15 def)
% Number of atoms : 298 ( 222 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 124 ( 59 ~; 54 |; 0 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 21 con; 0-3 aty)
% Number of variables : 242 ( 242 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).
fof(f24,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
fof(f34,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(f73,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f80,axiom,
! [X0,X1,X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(f82,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/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f112,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/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
fof(f113,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I3_J) ).
fof(f116,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f117,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f118,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f119,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X0)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(f145,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(f159,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__num__one) ).
fof(f187,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(f207,axiom,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(f214,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f217,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(f226,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/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f252,axiom,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f314,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Min) ).
fof(f353,axiom,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X0)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit0) ).
fof(f409,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).
fof(f545,axiom,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(f944,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f948,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(f1034,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f1101,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(f1112,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f1125,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f1128,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1175,conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1176,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(negated_conjecture,[status(cth)],[f1175]) ).
fof(f1177,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(flattening,[],[f1176]) ).
fof(f1183,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f4]) ).
fof(f1193,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f1201,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f1230,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f73]) ).
fof(f1237,plain,
! [X0,X1,X2] :
( c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X0))
| ~ class_Int_Onumber__ring(X2) ),
inference(ennf_transformation,[],[f80]) ).
fof(f1277,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,[],[f112]) ).
fof(f1278,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f113]) ).
fof(f1344,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f187]) ).
fof(f1525,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f409]) ).
fof(f2014,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f944]) ).
fof(f2018,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f948]) ).
fof(f2534,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1183]) ).
fof(f2556,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f1193]) ).
fof(f2571,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f1201]) ).
fof(f2618,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(cnf_transformation,[],[f1230]) ).
fof(f2625,plain,
! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X0)) = c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ),
inference(cnf_transformation,[],[f1237]) ).
fof(f2629,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,[],[f82]) ).
fof(f2667,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,[],[f1277]) ).
fof(f2668,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f1278]) ).
fof(f2671,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f116]) ).
fof(f2672,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f117]) ).
fof(f2673,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f118]) ).
fof(f2674,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X0)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
inference(cnf_transformation,[],[f119]) ).
fof(f2713,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f145]) ).
fof(f2727,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f159]) ).
fof(f2777,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f1344]) ).
fof(f2802,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f207]) ).
fof(f2814,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
inference(cnf_transformation,[],[f214]) ).
fof(f2818,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f217]) ).
fof(f2832,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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(cnf_transformation,[],[f226]) ).
fof(f2870,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
inference(cnf_transformation,[],[f252]) ).
fof(f2959,plain,
c_Int_OBit1(c_Int_OPls) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin),
inference(cnf_transformation,[],[f314]) ).
fof(f3013,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X0)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f353]) ).
fof(f3123,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f1525]) ).
fof(f3397,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
inference(cnf_transformation,[],[f545]) ).
fof(f4016,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f2014]) ).
fof(f4023,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2018]) ).
fof(f4125,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1034]) ).
fof(f4192,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1101]) ).
fof(f4203,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1112]) ).
fof(f4216,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1125]) ).
fof(f4219,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1128]) ).
fof(f4266,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1177]) ).
fof(f4282,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(definition_unfolding,[],[f2556,f2629]) ).
fof(f4293,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(definition_unfolding,[],[f2571,f2673,f2629]) ).
fof(f4307,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,[],[f2667,f2629]) ).
fof(f4308,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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(X1) ),
inference(definition_unfolding,[],[f2668,f2629]) ).
fof(f4311,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
inference(definition_unfolding,[],[f2674,f2673,f2673,f2673]) ).
fof(f4322,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f2713,f2673,f2629]) ).
fof(f4330,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(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)),
inference(definition_unfolding,[],[f2727,f2629]) ).
fof(f4341,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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),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(X1) ),
inference(definition_unfolding,[],[f2777,f2673,f2629]) ).
fof(f4374,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin) = 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,[],[f2959,f2629]) ).
fof(f4390,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(definition_unfolding,[],[f3013,f2673,f2673]) ).
fof(f4424,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(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)))) ),
inference(definition_unfolding,[],[f3123,f2629]) ).
fof(f4635,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_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_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_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))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f4266,f2673,f2629,f2673,f2673,f2629,f2673,f2629,f2673,f2629]) ).
fof(f4853,definition,
sF22 = c_Power_Opower__class_Opower(tc_RealDef_Oreal),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f4854,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal) = sF22,
inference(reorient_equations,[],[f4853]) ).
fof(f4855,definition,
sF23 = hAPP(sF22,v_x),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f4856,plain,
hAPP(sF22,v_x) = sF23,
inference(reorient_equations,[],[f4855]) ).
fof(f4857,definition,
sF24 = c_Groups_Oone__class_Oone(tc_Int_Oint),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f4858,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = sF24,
inference(reorient_equations,[],[f4857]) ).
fof(f4859,definition,
sF25 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,c_Int_OPls),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f4860,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,c_Int_OPls) = sF25,
inference(reorient_equations,[],[f4859]) ).
fof(f4861,definition,
sF26 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF25,c_Int_OPls),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f4862,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF25,c_Int_OPls) = sF26,
inference(reorient_equations,[],[f4861]) ).
fof(f4863,definition,
sF27 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,sF26),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f4864,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,sF26) = sF27,
inference(reorient_equations,[],[f4863]) ).
fof(f4865,definition,
sF28 = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,sF27),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f4866,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,sF27) = sF28,
inference(reorient_equations,[],[f4865]) ).
fof(f4867,definition,
sF29 = hAPP(sF23,sF28),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f4868,plain,
hAPP(sF23,sF28) = sF29,
inference(reorient_equations,[],[f4867]) ).
fof(f4869,definition,
sF30 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,sF27),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f4870,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,sF27) = sF30,
inference(reorient_equations,[],[f4869]) ).
fof(f4871,definition,
sF31 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF30),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f4872,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF30) = sF31,
inference(reorient_equations,[],[f4871]) ).
fof(f4873,definition,
sF32 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF29,sF31),
introduced(definition,[new_symbols(definition,[sF32])],[function_definition]) ).
fof(f4874,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF29,sF31) = sF32,
inference(reorient_equations,[],[f4873]) ).
fof(f4875,definition,
sF33 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF27),
introduced(definition,[new_symbols(definition,[sF33])],[function_definition]) ).
fof(f4876,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF27) = sF33,
inference(reorient_equations,[],[f4875]) ).
fof(f4877,definition,
sF34 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,sF33),
introduced(definition,[new_symbols(definition,[sF34])],[function_definition]) ).
fof(f4878,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,sF33) = sF34,
inference(reorient_equations,[],[f4877]) ).
fof(f4879,definition,
sF35 = hAPP(sF22,sF34),
introduced(definition,[new_symbols(definition,[sF35])],[function_definition]) ).
fof(f4880,plain,
hAPP(sF22,sF34) = sF35,
inference(reorient_equations,[],[f4879]) ).
fof(f4881,definition,
sF36 = hAPP(sF35,sF28),
introduced(definition,[new_symbols(definition,[sF36])],[function_definition]) ).
fof(f4882,plain,
hAPP(sF35,sF28) = sF36,
inference(reorient_equations,[],[f4881]) ).
fof(f4883,plain,
sF32 != sF36,
inference(definition_folding,[],[f4635,f4882,f4866,f4864,f4862,f4860,f4858,f4862,f4860,f4858,f4880,f4878,f4876,f4864,f4862,f4860,f4858,f4862,f4860,f4858,f4854,f4874,f4872,f4870,f4864,f4862,f4860,f4858,f4862,f4860,f4858,f4864,f4862,f4860,f4858,f4862,f4860,f4858,f4868,f4866,f4864,f4862,f4860,f4858,f4862,f4860,f4858,f4856,f4854]) ).
fof(f4954,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0),
inference(forward_demodulation,[],[f2802,f2818]) ).
fof(f4969,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)))))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4341,f2832]) ).
fof(f4980,plain,
c_Groups_Oone__class_Oone(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),
inference(forward_demodulation,[],[f4330,f2870]) ).
fof(f4986,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_Groups_Oplus__class_Oplus(tc_Int_Oint,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(forward_demodulation,[],[f4322,f2832]) ).
fof(f4994,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))),
inference(forward_demodulation,[],[f4311,f2832]) ).
fof(f4996,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin)))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4308,f4374]) ).
fof(f4997,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_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0)))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4307,f2832]) ).
fof(f5009,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_Groups_Oplus__class_Oplus(tc_Int_Oint,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)))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f4293,f2832]) ).
fof(f5017,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin))) = X0 ),
inference(forward_demodulation,[],[f4282,f4374]) ).
fof(f5027,plain,
sF24 = sF25,
inference(forward_demodulation,[],[f4860,f2672]) ).
fof(f5028,plain,
sF25 = sF26,
inference(forward_demodulation,[],[f4862,f2672]) ).
fof(f5067,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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))))))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4969,f2832]) ).
fof(f5074,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin),
inference(forward_demodulation,[],[f4980,f4374]) ).
fof(f5080,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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(forward_demodulation,[],[f4986,f2832]) ).
fof(f5087,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,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,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0))),
inference(forward_demodulation,[],[f4994,f2832]) ).
fof(f5089,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Int_OMin)) ),
inference(forward_demodulation,[],[f4996,f2818]) ).
fof(f5090,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_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0))))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4997,f2832]) ).
fof(f5099,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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))))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5009,f2832]) ).
fof(f5113,plain,
sF24 = sF26,
inference(forward_demodulation,[],[f5028,f5027]) ).
fof(f5133,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)))))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5067,f2671]) ).
fof(f5140,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin) = sF24,
inference(forward_demodulation,[],[f5074,f4858]) ).
fof(f5146,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,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(forward_demodulation,[],[f5080,f2671]) ).
fof(f5152,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_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0)))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5090,f2671]) ).
fof(f5159,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5099,f2671]) ).
fof(f5182,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(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))))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5133,f2671]) ).
fof(f5189,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin) = sF26,
inference(forward_demodulation,[],[f5140,f5113]) ).
fof(f5195,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(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))),
inference(forward_demodulation,[],[f5146,f2671]) ).
fof(f5201,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_Oone__class_Oone(tc_Int_Oint),X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5152,f2671]) ).
fof(f5208,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(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))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5159,f2671]) ).
fof(f5230,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin))))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5182,f4374]) ).
fof(f5241,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin))),
inference(forward_demodulation,[],[f5195,f4374]) ).
fof(f5247,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,sF24,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5201,f4858]) ).
fof(f5254,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5208,f4374]) ).
fof(f5275,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OMin)))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5230,f2818]) ).
fof(f5286,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OMin)),
inference(forward_demodulation,[],[f5241,f2818]) ).
fof(f5292,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,sF26,X0)) ),
inference(forward_demodulation,[],[f5247,f5113]) ).
fof(f5299,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OMin)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5254,f2818]) ).
fof(f5320,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF24,c_Int_OMin)))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5275,f4858]) ).
fof(f5329,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF24,c_Int_OMin)),
inference(forward_demodulation,[],[f5286,f4858]) ).
fof(f5341,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF24,c_Int_OMin)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5299,f4858]) ).
fof(f5362,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF26,c_Int_OMin))) ),
inference(forward_demodulation,[],[f5320,f5113]) ).
fof(f5371,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF26,c_Int_OMin)),
inference(forward_demodulation,[],[f5329,f5113]) ).
fof(f5383,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF26,c_Int_OMin)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5341,f5113]) ).
fof(f5408,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(forward_demodulation,[],[f5383,f5371]) ).
fof(f5447,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,X0),
inference(superposition,[],[f2832,f4864]) ).
fof(f5448,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF30,X0),
inference(superposition,[],[f2832,f4870]) ).
fof(f5614,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),X1)),
inference(superposition,[],[f5087,f2814]) ).
fof(f5661,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,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,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))),
inference(forward_demodulation,[],[f5614,f2832]) ).
fof(f6414,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(resolution,[],[f4216,f4016]) ).
fof(f6645,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1)),X2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)),
inference(resolution,[],[f4192,f2534]) ).
fof(f6646,plain,
! [X2,X0,X1] : hAPP(hAPP(sF22,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1)),X2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(sF22,X0),X2),hAPP(hAPP(sF22,X1),X2)),
inference(forward_demodulation,[],[f6645,f4854]) ).
fof(f6647,plain,
! [X0,X1] : hAPP(hAPP(sF22,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,X0)),X1) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(sF23,X1),hAPP(hAPP(sF22,X0),X1)),
inference(superposition,[],[f6646,f4856]) ).
fof(f6651,plain,
! [X0] : hAPP(hAPP(sF22,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,X0)),sF28) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF29,hAPP(hAPP(sF22,X0),sF28)),
inference(superposition,[],[f6647,f4868]) ).
fof(f6864,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(resolution,[],[f4203,f5408]) ).
fof(f6866,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),
inference(resolution,[],[f4203,f2618]) ).
fof(f6867,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0) = hAPP(hAPP(sF22,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f6864,f4854]) ).
fof(f7134,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,sF26) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OMin,c_Int_OMin)),
inference(superposition,[],[f4390,f5189]) ).
fof(f7162,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,sF26) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin),c_Int_OMin),
inference(forward_demodulation,[],[f7134,f4954]) ).
fof(f7169,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,sF26) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF26,c_Int_OMin),
inference(forward_demodulation,[],[f7162,f5189]) ).
fof(f7171,plain,
sF27 = c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF26,c_Int_OMin),
inference(forward_demodulation,[],[f7169,f4864]) ).
fof(f7172,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,sF27),
inference(superposition,[],[f5371,f7171]) ).
fof(f7175,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = sF28,
inference(forward_demodulation,[],[f7172,f4866]) ).
fof(f7192,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0) = hAPP(hAPP(sF22,X0),sF28),
inference(superposition,[],[f6867,f7175]) ).
fof(f7216,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)),
inference(resolution,[],[f4219,f2625]) ).
fof(f7221,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin))) = X0,
inference(resolution,[],[f4219,f5017]) ).
fof(f7222,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Int_OMin)),
inference(resolution,[],[f4219,f5089]) ).
fof(f7223,plain,
! [X0] : 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,sF26,X0)),
inference(resolution,[],[f4219,f5292]) ).
fof(f7224,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF26,c_Int_OMin))),
inference(resolution,[],[f4219,f5362]) ).
fof(f7227,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF27)),
inference(forward_demodulation,[],[f7224,f7171]) ).
fof(f7228,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF26)) = X0,
inference(forward_demodulation,[],[f7221,f5189]) ).
fof(f7230,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),sF33),
inference(forward_demodulation,[],[f7227,f4876]) ).
fof(f7265,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF26),
inference(superposition,[],[f3397,f7228]) ).
fof(f7289,plain,
hAPP(hAPP(sF22,sF33),sF28) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,sF33),
inference(superposition,[],[f7192,f7230]) ).
fof(f7322,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,sF27)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),sF33),
inference(superposition,[],[f7223,f4876]) ).
fof(f7355,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Int_OMin)) = 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)),
inference(superposition,[],[f6866,f7222]) ).
fof(f7361,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Int_OMin)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,X0)),
inference(forward_demodulation,[],[f7355,f7223]) ).
fof(f7369,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)),
inference(superposition,[],[f7216,f4876]) ).
fof(f7372,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,sF27)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),sF33),
inference(superposition,[],[f7216,f4876]) ).
fof(f7471,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,sF27),c_Int_OMin)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),sF33),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(superposition,[],[f7222,f7322]) ).
fof(f7474,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),sF33),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF26,sF27))),
inference(forward_demodulation,[],[f7471,f7361]) ).
fof(f7479,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),sF33),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,sF27)),
inference(forward_demodulation,[],[f7474,f5447]) ).
fof(f7483,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),sF33),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF27),sF33),
inference(forward_demodulation,[],[f7479,f7372]) ).
fof(f7484,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,sF33) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),sF33),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f7483,f4876]) ).
fof(f7486,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,sF33) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(superposition,[],[f7484,f6866]) ).
fof(f7638,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(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)))),
inference(resolution,[],[f4424,f4219]) ).
fof(f7639,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,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(forward_demodulation,[],[f7638,f2818]) ).
fof(f7640,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OMin))),
inference(forward_demodulation,[],[f7639,f4374]) ).
fof(f7641,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,sF26)),
inference(forward_demodulation,[],[f7640,f5189]) ).
fof(f7648,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF30,sF26)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF31,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(superposition,[],[f7641,f4872]) ).
fof(f7763,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),X1) = X0,
inference(resolution,[],[f4125,f4016]) ).
fof(f7764,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) = X1,
inference(resolution,[],[f4125,f4023]) ).
fof(f7777,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)) = X0,
inference(superposition,[],[f2814,f7763]) ).
fof(f7826,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) = X0,
inference(superposition,[],[f7764,f2814]) ).
fof(f7843,plain,
sF26 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sF26),sF27),
inference(superposition,[],[f7764,f4864]) ).
fof(f8162,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0),
inference(superposition,[],[f7764,f7777]) ).
fof(f8193,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sF26),c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sF26)))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sF26),c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,sF26)),
inference(superposition,[],[f5661,f7843]) ).
fof(f8200,plain,
sF27 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sF26),c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sF26)))),
inference(forward_demodulation,[],[f8193,f7826]) ).
fof(f8208,plain,
sF27 = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sF26))),sF26),
inference(forward_demodulation,[],[f8200,f8162]) ).
fof(f8210,plain,
sF27 = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF30,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,sF26)),sF26),
inference(forward_demodulation,[],[f8208,f5448]) ).
fof(f8212,plain,
sF27 = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF30,sF26),sF26),
inference(forward_demodulation,[],[f8210,f2818]) ).
fof(f8216,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,sF26) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,sF30,sF26),
inference(superposition,[],[f7763,f8212]) ).
fof(f8422,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF27,sF26)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF31,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(superposition,[],[f7648,f8216]) ).
fof(f8427,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF26)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF31,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f8422,f7369]) ).
fof(f8429,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF31,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f8427,f7265]) ).
fof(f8433,plain,
sF31 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(superposition,[],[f6414,f8429]) ).
fof(f8434,plain,
sF31 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,sF33),
inference(forward_demodulation,[],[f8433,f7486]) ).
fof(f12709,plain,
hAPP(hAPP(sF22,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,sF33)),sF28) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF29,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF33,sF33)),
inference(superposition,[],[f6651,f7289]) ).
fof(f12722,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF29,sF31) = hAPP(hAPP(sF22,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,sF33)),sF28),
inference(forward_demodulation,[],[f12709,f8434]) ).
fof(f12729,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF29,sF31) = hAPP(hAPP(sF22,sF34),sF28),
inference(forward_demodulation,[],[f12722,f4878]) ).
fof(f12731,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF29,sF31) = hAPP(sF35,sF28),
inference(forward_demodulation,[],[f12729,f4880]) ).
fof(f12733,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF29,sF31) = sF36,
inference(forward_demodulation,[],[f12731,f4882]) ).
fof(f12735,plain,
sF32 = sF36,
inference(forward_demodulation,[],[f12733,f4874]) ).
fof(f12737,plain,
$false,
inference(forward_subsumption_resolution,[],[f12735,f4883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW173+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 13:12:31 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.94/1.83 % (3376720)Detected formulas, will run a generic FOF schedule.
% 6.94/1.83 % (3376725)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=752564161:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.94/1.83 % (3376730)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1440810818:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.94/1.83 % (3376728)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1198422833:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.94/1.83 % (3376726)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=271874184:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.94/1.83 % (3376727)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2144195526:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.94/1.83 % (3376729)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=178600231:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.94/1.83 % (3376731)dis-21_1_sil=8000:lcm=predicate:random_seed=1623552709:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.94/1.83 % (3376728)Refutation not found, incomplete strategy
% 6.94/1.83 % (3376728)------------------------------
% 6.94/1.83 % (3376728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376728)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376728)Termination reason: Refutation not found, incomplete strategy
% 6.94/1.83 % (3376728)Time elapsed: 0.016 s
% 6.94/1.83 % (3376728)Peak memory usage: 90 MB
% 6.94/1.83 % (3376728)Instructions burned: 26 (million)
% 6.94/1.83 % (3376731)Instruction limit reached!
% 6.94/1.83 % (3376731)------------------------------
% 6.94/1.83 % (3376731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376731)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376731)Termination reason: Instruction limit
% 6.94/1.83 % (3376731)Termination phase: Saturation
% 6.94/1.83 % (3376731)Time elapsed: 0.062 s
% 6.94/1.83 % (3376731)Peak memory usage: 90 MB
% 6.94/1.83 % (3376731)Instructions burned: 130 (million)
% 6.94/1.83 % (3376729)Instruction limit reached!
% 6.94/1.83 % (3376729)------------------------------
% 6.94/1.83 % (3376729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376729)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376729)Termination reason: Instruction limit
% 6.94/1.83 % (3376729)Termination phase: Saturation
% 6.94/1.83 % (3376729)Time elapsed: 0.073 s
% 6.94/1.83 % (3376729)Peak memory usage: 89 MB
% 6.94/1.83 % (3376729)Instructions burned: 120 (million)
% 6.94/1.83 % (3376730)Instruction limit reached!
% 6.94/1.83 % (3376730)------------------------------
% 6.94/1.83 % (3376730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376730)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376730)Termination reason: Instruction limit
% 6.94/1.83 % (3376730)Termination phase: Saturation
% 6.94/1.83 % (3376730)Time elapsed: 0.075 s
% 6.94/1.83 % (3376730)Peak memory usage: 91 MB
% 6.94/1.83 % (3376730)Instructions burned: 140 (million)
% 6.94/1.83 % (3376740)lrs+10_1_sil=32000:urr=on:br=off:random_seed=208766880:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.94/1.83 % (3376739)lrs+10_1_sil=8000:sp=occurrence:random_seed=609781625:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.94/1.83 % (3376741)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2352856067:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.94/1.83 % (3376728)------------------------------
% 6.94/1.83 % (3376728)------------------------------
% 6.94/1.83 % (3376740)Instruction limit reached!
% 6.94/1.83 % (3376740)------------------------------
% 6.94/1.83 % (3376740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376740)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376740)Termination reason: Instruction limit
% 6.94/1.83 % (3376740)Termination phase: Saturation
% 6.94/1.83 % (3376740)Time elapsed: 0.089 s
% 6.94/1.83 % (3376740)Peak memory usage: 91 MB
% 6.94/1.83 % (3376740)Instructions burned: 158 (million)
% 6.94/1.83 % (3376739)Instruction limit reached!
% 6.94/1.83 % (3376739)------------------------------
% 6.94/1.83 % (3376739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376739)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376739)Termination reason: Instruction limit
% 6.94/1.83 % (3376739)Termination phase: Saturation
% 6.94/1.83 % (3376739)Time elapsed: 0.177 s
% 6.94/1.83 % (3376739)Peak memory usage: 92 MB
% 6.94/1.83 % (3376739)Instructions burned: 285 (million)
% 6.94/1.83 % (3376745)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2382688267:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.94/1.83 % (3376741)Instruction limit reached!
% 6.94/1.83 % (3376741)------------------------------
% 6.94/1.83 % (3376741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376741)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376741)Termination reason: Instruction limit
% 6.94/1.83 % (3376741)Termination phase: Saturation
% 6.94/1.83 % (3376741)Time elapsed: 0.206 s
% 6.94/1.83 % (3376741)Peak memory usage: 93 MB
% 6.94/1.83 % (3376741)Instructions burned: 325 (million)
% 6.94/1.83 % (3376746)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=398430437:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.94/1.83 % (3376747)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1609145963:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.94/1.83 % (3376745)Instruction limit reached!
% 6.94/1.83 % (3376745)------------------------------
% 6.94/1.83 % (3376745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376745)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376745)Termination reason: Instruction limit
% 6.94/1.83 % (3376745)Termination phase: Saturation
% 6.94/1.83 % (3376745)Time elapsed: 0.141 s
% 6.94/1.83 % (3376745)Peak memory usage: 92 MB
% 6.94/1.83 % (3376745)Instructions burned: 248 (million)
% 6.94/1.83 % (3376749)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1435622665:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.94/1.83 % (3376746)Instruction limit reached!
% 6.94/1.83 % (3376746)------------------------------
% 6.94/1.83 % (3376746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376746)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376746)Termination reason: Instruction limit
% 6.94/1.83 % (3376746)Termination phase: Saturation
% 6.94/1.83 % (3376746)Time elapsed: 0.161 s
% 6.94/1.83 % (3376746)Peak memory usage: 92 MB
% 6.94/1.83 % (3376746)Instructions burned: 295 (million)
% 6.94/1.83 % (3376749)Instruction limit reached!
% 6.94/1.83 % (3376749)------------------------------
% 6.94/1.83 % (3376749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376749)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376749)Termination reason: Instruction limit
% 6.94/1.83 % (3376749)Termination phase: Saturation
% 6.94/1.83 % (3376749)Time elapsed: 0.056 s
% 6.94/1.83 % (3376749)Peak memory usage: 90 MB
% 6.94/1.83 % (3376749)Instructions burned: 114 (million)
% 6.94/1.83 % (3376753)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3066091268:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.94/1.83 % (3376755)lrs+10_1_sil=8000:sp=occurrence:random_seed=7355035:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.94/1.83 % (3376754)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=929852592:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.94/1.83 % (3376753)Instruction limit reached!
% 6.94/1.83 % (3376753)------------------------------
% 6.94/1.83 % (3376753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376753)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376753)Termination reason: Instruction limit
% 6.94/1.83 % (3376753)Termination phase: Property scanning
% 6.94/1.83 % (3376753)Time elapsed: 0.058 s
% 6.94/1.83 % (3376753)Peak memory usage: 89 MB
% 6.94/1.83 % (3376753)Instructions burned: 127 (million)
% 6.94/1.83 % (3376754)Instruction limit reached!
% 6.94/1.83 % (3376754)------------------------------
% 6.94/1.83 % (3376754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376754)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376754)Termination reason: Instruction limit
% 6.94/1.83 % (3376754)Termination phase: Saturation
% 6.94/1.83 % (3376754)Time elapsed: 0.054 s
% 6.94/1.83 % (3376754)Peak memory usage: 90 MB
% 6.94/1.83 % (3376754)Instructions burned: 114 (million)
% 6.94/1.83 % (3376725)First to succeed.
% 6.94/1.83 % (3376725)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3376720"
% 6.94/1.83 % (3376759)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1344069354:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.94/1.83 % (3376759)Refutation not found, incomplete strategy
% 6.94/1.83 % (3376759)------------------------------
% 6.94/1.83 % (3376759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/1.83 % (3376759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.83 % (3376759)CaDiCaL version: 2.1.3
% 6.94/1.83 % (3376759)Termination reason: Refutation not found, incomplete strategy
% 6.94/1.83 % (3376759)Time elapsed: 0.068 s
% 6.94/1.83 % (3376759)Peak memory usage: 91 MB
% 6.94/1.83 % (3376759)Instructions burned: 131 (million)
% 6.94/1.83 % (3376760)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2055906778:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.94/1.83 % (3376725)Refutation found. Thanks to Tanya!
% 6.94/1.83 % SZS status Theorem for theBenchmark
% 6.94/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 8.57/2.02 % (3376725)------------------------------
% 8.57/2.02 % (3376725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.57/2.02 % (3376725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.57/2.02 % (3376725)CaDiCaL version: 2.1.3
% 8.57/2.02 % (3376725)Termination reason: Refutation
% 8.57/2.02 % (3376725)Time elapsed: 0.849 s
% 8.57/2.02 % (3376725)Peak memory usage: 149 MB
% 8.57/2.02 % (3376725)Instructions burned: 2510 (million)
% 8.57/2.02 % (3376725)------------------------------
% 8.57/2.02 % (3376725)------------------------------
% 8.57/2.02 % (3376720)Success in time 1.181 s
% 8.57/2.02 % Vampire exiting
%------------------------------------------------------------------------------