TSTP Solution File: SWW179+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW179+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 18:16:22 EDT 2024
% Result : Theorem 32.27s 5.21s
% Output : CNFRefutation 32.27s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X3] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(f6,axiom,
! [X4,X5,X6,X3,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X3),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X5),X4)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,X3,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__add__less) ).
fof(f22,axiom,
! [X6] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X6) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(f98,axiom,
! [X16,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> c_RealVector_Onorm__class_Onorm(X7,X16) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(f124,axiom,
! [X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ozero__class_Ozero(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(f140,axiom,
! [X20,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oabs__class_Oabs(X7,X20))
<=> c_Groups_Ozero__class_Ozero(X7) != X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
fof(f152,axiom,
! [X16,X7] :
( class_Groups_Omonoid__add(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X16) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(f155,axiom,
! [X16,X7] :
( class_Groups_Omonoid__add(X7)
=> c_Groups_Oplus__class_Oplus(X7,X16,c_Groups_Ozero__class_Ozero(X7)) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(f1122,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(f1129,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1158,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(f1184,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1275,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1276,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(negated_conjecture,[],[f1275]) ).
fof(f1277,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(rectify,[],[f4]) ).
fof(f1279,plain,
! [X0,X1,X2,X3,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X3),X2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X1),X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0)) ) ) ),
inference(rectify,[],[f6]) ).
fof(f1295,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),
inference(rectify,[],[f22]) ).
fof(f1370,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)) ),
inference(rectify,[],[f98]) ).
fof(f1396,plain,
! [X0] :
( class_RealVector_Oreal__normed__vector(X0)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f124]) ).
fof(f1412,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 ) ),
inference(rectify,[],[f140]) ).
fof(f1424,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(rectify,[],[f152]) ).
fof(f1427,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f155]) ).
fof(f2323,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(flattening,[],[f1276]) ).
fof(f2328,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X3),X2)
| ~ class_RealVector_Oreal__normed__vector(X4) ),
inference(ennf_transformation,[],[f1279]) ).
fof(f2329,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X3),X2)
| ~ class_RealVector_Oreal__normed__vector(X4) ),
inference(flattening,[],[f2328]) ).
fof(f2446,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1370]) ).
fof(f2489,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(ennf_transformation,[],[f1396]) ).
fof(f2516,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1412]) ).
fof(f2531,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(ennf_transformation,[],[f1424]) ).
fof(f2534,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(ennf_transformation,[],[f1427]) ).
fof(f3481,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f2516]) ).
fof(f3913,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(cnf_transformation,[],[f1277]) ).
fof(f3915,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X3),X2)
| ~ class_RealVector_Oreal__normed__vector(X4) ),
inference(cnf_transformation,[],[f2329]) ).
fof(f3941,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f1295]) ).
fof(f4043,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f2446]) ).
fof(f4084,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f2489]) ).
fof(f4102,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3481]) ).
fof(f4119,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(cnf_transformation,[],[f2531]) ).
fof(f4123,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(cnf_transformation,[],[f2534]) ).
fof(f5478,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1122]) ).
fof(f5485,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1129]) ).
fof(f5514,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1158]) ).
fof(f5540,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1184]) ).
fof(f5631,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(cnf_transformation,[],[f2323]) ).
cnf(c_52,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(cnf_transformation,[],[f3913]) ).
cnf(c_54,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X3),X4)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X2)) ),
inference(cnf_transformation,[],[f3915]) ).
cnf(c_80,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f3941]) ).
cnf(c_180,plain,
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)) = c_RealVector_Onorm__class_Onorm(X0,X1) ),
inference(cnf_transformation,[],[f4043]) ).
cnf(c_221,plain,
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f4084]) ).
cnf(c_238,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X0)
| c_Groups_Ozero__class_Ozero(X0) = X1
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oabs__class_Oabs(X0,X1)) ),
inference(cnf_transformation,[],[f4102]) ).
cnf(c_250,plain,
( ~ class_Groups_Omonoid__add(X0)
| c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1 ),
inference(cnf_transformation,[],[f4119]) ).
cnf(c_254,plain,
( ~ class_Groups_Omonoid__add(X0)
| c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 ),
inference(cnf_transformation,[],[f4123]) ).
cnf(c_1573,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f5478]) ).
cnf(c_1580,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f5485]) ).
cnf(c_1609,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f5514]) ).
cnf(c_1635,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f5540]) ).
cnf(c_1726,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(cnf_transformation,[],[f5631]) ).
cnf(c_2729,plain,
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)) = c_RealVector_Onorm__class_Onorm(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_180]) ).
cnf(c_2731,plain,
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(prop_impl_just,[status(thm)],[c_221]) ).
cnf(c_3031,plain,
( ~ class_Groups_Omonoid__add(X0)
| c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1 ),
inference(prop_impl_just,[status(thm)],[c_250]) ).
cnf(c_3033,plain,
( ~ class_Groups_Omonoid__add(X0)
| c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 ),
inference(prop_impl_just,[status(thm)],[c_254]) ).
cnf(c_19445,plain,
( X0 != tc_RealDef_Oreal
| c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 ),
inference(resolution_lifted,[status(thm)],[c_3033,c_1609]) ).
cnf(c_19446,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0,
inference(unflattening,[status(thm)],[c_19445]) ).
cnf(c_19451,plain,
( X0 != tc_RealDef_Oreal
| c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1 ),
inference(resolution_lifted,[status(thm)],[c_3031,c_1609]) ).
cnf(c_19452,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = X0,
inference(unflattening,[status(thm)],[c_19451]) ).
cnf(c_27548,plain,
( X0 != tc_RealDef_Oreal
| c_Groups_Ozero__class_Ozero(X0) = X1
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oabs__class_Oabs(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_238,c_1573]) ).
cnf(c_27549,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) ),
inference(unflattening,[status(thm)],[c_27548]) ).
cnf(c_29830,plain,
( X0 != tc_RealDef_Oreal
| c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution_lifted,[status(thm)],[c_2731,c_1580]) ).
cnf(c_29831,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_29830]) ).
cnf(c_29835,plain,
( X0 != tc_RealDef_Oreal
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)) = c_RealVector_Onorm__class_Onorm(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_2729,c_1580]) ).
cnf(c_29836,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),
inference(unflattening,[status(thm)],[c_29835]) ).
cnf(c_29887,plain,
( X0 != tc_RealDef_Oreal
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X3),X4)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X2)) ),
inference(resolution_lifted,[status(thm)],[c_54,c_1580]) ).
cnf(c_29888,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2),X3)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1)) ),
inference(unflattening,[status(thm)],[c_29887]) ).
cnf(c_30250,plain,
( X0 != tc_Complex_Ocomplex
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)) = c_RealVector_Onorm__class_Onorm(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_2729,c_1635]) ).
cnf(c_30251,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),
inference(unflattening,[status(thm)],[c_30250]) ).
cnf(c_49489,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_29831,c_80]) ).
cnf(c_49522,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(light_normalisation,[status(thm)],[c_29836,c_80]) ).
cnf(c_53161,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X3)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)) ),
inference(light_normalisation,[status(thm)],[c_29888,c_80]) ).
cnf(c_53162,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X3)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)) ),
inference(light_normalisation,[status(thm)],[c_53161,c_80]) ).
cnf(c_53163,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X3)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)) ),
inference(demodulation,[status(thm)],[c_53162,c_80]) ).
cnf(c_73044,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) ),
inference(prop_impl_just,[status(thm)],[c_27549]) ).
cnf(c_103355,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = sP0_iProver_def,
definition ).
cnf(c_103356,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = sP1_iProver_def,
definition ).
cnf(c_103357,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____) = sP2_iProver_def,
definition ).
cnf(c_103358,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sP1_iProver_def,sP2_iProver_def) = sP3_iProver_def,
definition ).
cnf(c_103359,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = sP4_iProver_def,
definition ).
cnf(c_103360,plain,
hAPP(sP4_iProver_def,v_r) = sP5_iProver_def,
definition ).
cnf(c_103361,plain,
hAPP(sP5_iProver_def,v_m____) = sP6_iProver_def,
definition ).
cnf(c_103362,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sP6_iProver_def) = sP7_iProver_def,
definition ).
cnf(c_103363,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sP3_iProver_def,sP7_iProver_def) = sP8_iProver_def,
definition ).
cnf(c_103364,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP8_iProver_def),
inference(demodulation,[status(thm)],[c_1726,c_103359,c_103360,c_103361,c_103362,c_103357,c_103356,c_103358,c_103363,c_103355]) ).
cnf(c_125392,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),sP3_iProver_def)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),sP7_iProver_def)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)),sP8_iProver_def) ),
inference(superposition,[status(thm)],[c_103363,c_53163]) ).
cnf(c_125629,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,sP0_iProver_def) = X0,
inference(light_normalisation,[status(thm)],[c_19446,c_103355]) ).
cnf(c_125665,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sP0_iProver_def,X0) = X0,
inference(light_normalisation,[status(thm)],[c_19452,c_103355]) ).
cnf(c_125686,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sP0_iProver_def) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_49489,c_103355]) ).
cnf(c_126042,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sP1_iProver_def,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(light_normalisation,[status(thm)],[c_52,c_103355,c_103356]) ).
cnf(c_126159,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sP2_iProver_def) = sP2_iProver_def,
inference(superposition,[status(thm)],[c_103357,c_30251]) ).
cnf(c_126181,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sP1_iProver_def,sP2_iProver_def)),
inference(superposition,[status(thm)],[c_126159,c_126042]) ).
cnf(c_126186,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP3_iProver_def),
inference(light_normalisation,[status(thm)],[c_126181,c_103358]) ).
cnf(c_126279,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sP7_iProver_def) = sP7_iProver_def,
inference(superposition,[status(thm)],[c_103362,c_49522]) ).
cnf(c_126336,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),sP7_iProver_def)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sP0_iProver_def),sP3_iProver_def)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),sP8_iProver_def) ),
inference(superposition,[status(thm)],[c_125665,c_125392]) ).
cnf(c_126338,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),sP7_iProver_def)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP3_iProver_def)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),sP8_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_126336,c_125686]) ).
cnf(c_126339,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),sP7_iProver_def)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),sP8_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_126338,c_126186]) ).
cnf(c_129699,plain,
( X0 = sP0_iProver_def
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) ),
inference(light_normalisation,[status(thm)],[c_73044,c_103355]) ).
cnf(c_129713,plain,
( sP0_iProver_def = sP7_iProver_def
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP7_iProver_def) ),
inference(superposition,[status(thm)],[c_126279,c_129699]) ).
cnf(c_139669,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP7_iProver_def)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sP0_iProver_def),sP8_iProver_def) ),
inference(superposition,[status(thm)],[c_125686,c_126339]) ).
cnf(c_139678,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP7_iProver_def)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP8_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_139669,c_125686]) ).
cnf(c_139679,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP7_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_139678,c_103364]) ).
cnf(c_139717,plain,
sP0_iProver_def = sP7_iProver_def,
inference(backward_subsumption_resolution,[status(thm)],[c_129713,c_139679]) ).
cnf(c_139800,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sP3_iProver_def,sP0_iProver_def) = sP8_iProver_def,
inference(demodulation,[status(thm)],[c_103363,c_139717]) ).
cnf(c_140517,plain,
sP3_iProver_def = sP8_iProver_def,
inference(demodulation,[status(thm)],[c_139800,c_125629]) ).
cnf(c_140518,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sP0_iProver_def,sP3_iProver_def),
inference(demodulation,[status(thm)],[c_103364,c_140517]) ).
cnf(c_140519,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_140518,c_126186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW179+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 05:23:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 32.27/5.21 % SZS status Started for theBenchmark.p
% 32.27/5.21 % SZS status Theorem for theBenchmark.p
% 32.27/5.21
% 32.27/5.21 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 32.27/5.21
% 32.27/5.21 ------ iProver source info
% 32.27/5.21
% 32.27/5.21 git: date: 2024-06-12 09:56:46 +0000
% 32.27/5.21 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 32.27/5.21 git: non_committed_changes: false
% 32.27/5.21
% 32.27/5.21 ------ Parsing...
% 32.27/5.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 32.27/5.21
% 32.27/5.21 ------ Preprocessing... sup_sim: 101 sf_s rm: 54 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 96 sf_s rm: 20 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 21 0s sf_e pe_s pe_e
% 32.27/5.21
% 32.27/5.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 32.27/5.21
% 32.27/5.21 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 32.27/5.21 ------ Proving...
% 32.27/5.21 ------ Problem Properties
% 32.27/5.21
% 32.27/5.21
% 32.27/5.21 clauses 1401
% 32.27/5.21 conjectures 1
% 32.27/5.21 EPR 222
% 32.27/5.21 Horn 1215
% 32.27/5.21 unary 424
% 32.27/5.21 binary 507
% 32.27/5.21 lits 3075
% 32.27/5.21 lits eq 727
% 32.27/5.21 fd_pure 0
% 32.27/5.21 fd_pseudo 0
% 32.27/5.21 fd_cond 89
% 32.27/5.21 fd_pseudo_cond 78
% 32.27/5.21 AC symbols 0
% 32.27/5.21
% 32.27/5.21 ------ Schedule dynamic 5 is on
% 32.27/5.21
% 32.27/5.21 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 32.27/5.21
% 32.27/5.21
% 32.27/5.21 ------
% 32.27/5.21 Current options:
% 32.27/5.21 ------
% 32.27/5.21
% 32.27/5.21
% 32.27/5.21
% 32.27/5.21
% 32.27/5.21 ------ Proving...
% 32.27/5.21
% 32.27/5.21
% 32.27/5.21 % SZS status Theorem for theBenchmark.p
% 32.27/5.21
% 32.27/5.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.27/5.22
% 32.27/5.22
%------------------------------------------------------------------------------