%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW234+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:29:18 PM UTC 2026
% Result : Theorem 246.73s 37.95s
% Output : CNFRefutation 246.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 22
% Syntax : Number of formulae : 126 ( 42 unt; 0 def)
% Number of atoms : 252 ( 40 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 221 ( 95 ~; 98 |; 10 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 197 ( 0 sgn 197 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
c_Orderings_Oord__class_Oless__eq(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,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_h) ).
fof(f8,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(f9,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(f10,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(f18,axiom,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(f40,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(f157,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
<=> ( X1 = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(f185,axiom,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(f517,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f521,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(f546,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(f629,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(f632,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(f636,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(f897,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(f906,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f917,axiom,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f937,axiom,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(f989,axiom,
! [X0,X1] :
( ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) )
& ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(f1122,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(f1127,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1274,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1275,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(negated_conjecture,[status(cth)],[f1274]) ).
fof(f1281,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(flattening,[],[f1275]) ).
fof(f1288,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f1289,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ),
inference(flattening,[],[f1288]) ).
fof(f1290,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| X1 = X0 ),
inference(ennf_transformation,[],[f10]) ).
fof(f1291,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| X1 = X0 ),
inference(flattening,[],[f1290]) ).
fof(f1324,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f1325,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ),
inference(flattening,[],[f1324]) ).
fof(f1537,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ),
inference(ennf_transformation,[],[f185]) ).
fof(f1912,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(ennf_transformation,[],[f546]) ).
fof(f1972,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0)) ),
inference(ennf_transformation,[],[f629]) ).
fof(f1979,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(ennf_transformation,[],[f636]) ).
fof(f2300,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 ) ),
inference(ennf_transformation,[],[f989]) ).
fof(f2430,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X1 = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) )
& ( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f157]) ).
fof(f2431,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X1 = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) )
& ( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f2430]) ).
fof(f2561,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(nnf_transformation,[],[f521]) ).
fof(f2608,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ) ),
inference(nnf_transformation,[],[f632]) ).
fof(f2695,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f897]) ).
fof(f2711,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f937]) ).
fof(f2746,plain,
c_Orderings_Oord__class_Oless__eq(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,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cnf_transformation,[],[f6]) ).
fof(f2748,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f2749,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ),
inference(cnf_transformation,[],[f1289]) ).
fof(f2750,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1291]) ).
fof(f2760,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f18]) ).
fof(f2793,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ),
inference(cnf_transformation,[],[f1325]) ).
fof(f2950,plain,
! [X0,X1] :
( X0 != X1
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2431]) ).
fof(f2986,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f3472,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f517]) ).
fof(f3478,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2561]) ).
fof(f3517,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(cnf_transformation,[],[f1912]) ).
fof(f3633,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0)) ),
inference(cnf_transformation,[],[f1972]) ).
fof(f3636,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f2608]) ).
fof(f3637,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ),
inference(cnf_transformation,[],[f2608]) ).
fof(f3642,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f1979]) ).
fof(f3991,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2695]) ).
fof(f4013,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f906]) ).
fof(f4028,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(cnf_transformation,[],[f917]) ).
fof(f4053,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
inference(cnf_transformation,[],[f2711]) ).
fof(f4054,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2711]) ).
fof(f4126,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 ),
inference(cnf_transformation,[],[f2300]) ).
fof(f4264,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1122]) ).
fof(f4269,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1127]) ).
fof(f4416,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cnf_transformation,[],[f1281]) ).
fof(f4437,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f3991,f4013]) ).
fof(f4472,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0),
inference(definition_unfolding,[],[f4028,f4013]) ).
fof(f4497,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4054,f4013]) ).
fof(f4498,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(definition_unfolding,[],[f4053,f4013]) ).
fof(f4610,plain,
! [X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_resolution,[],[f2950]) ).
fof(f4757,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(equality_resolution,[],[f4126]) ).
tcf(c_54,plain,
c_Orderings_Oord__class_Oless__eq(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,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cnf_transformation,[],[f2746]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f2748]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f2749]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f2750]) ).
tcf(c_66,plain,
! [X0: $i] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f2760]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Oplus__class_Oplus(X0,X3,X1))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f2793]) ).
tcf(c_242,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[],[f4610]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X1))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f2986]) ).
tcf(c_748,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f3472]) ).
tcf(c_755,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f3478]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(cnf_transformation,[],[f3517]) ).
tcf(c_907,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X0),c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f3633]) ).
tcf(c_910,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3637]) ).
tcf(c_911,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ),
inference(cnf_transformation,[],[f3636]) ).
tcf(c_916,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3642]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4437]) ).
tcf(c_1298,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0),
inference(cnf_transformation,[],[f4472]) ).
tcf(c_1322,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4497]) ).
tcf(c_1323,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4498]) ).
tcf(c_1392,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f4757]) ).
tcf(c_1531,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f4264]) ).
tcf(c_1536,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f4269]) ).
tcf(c_1683,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cnf_transformation,[],[f4416]) ).
tcf(c_2546,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_1323,c_1263]) ).
tcf(c_2547,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_2546]) ).
tcf(c_2734,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X1))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(prop_impl_just,[status(thm)],[c_278]) ).
tcf(c_3360,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_1323,c_916,c_1263]) ).
tcf(c_3361,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(renaming,[status(thm)],[c_3360]) ).
tcf(c_24661,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X1))
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_2734,c_1536]) ).
tcf(c_24662,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),
inference(unflattening,[status(thm)],[c_24661]) ).
tcf(c_42998,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),
inference(demodulation,[status(thm)],[c_24662,c_66]) ).
tcf(c_60861,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2547]) ).
tcf(c_60862,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_60861]) ).
tcf(c_61523,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_3361]) ).
tcf(c_61524,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(renaming,[status(thm)],[c_61523]) ).
tcf(c_121222,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_748,c_1298]) ).
tcf(c_122220,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_1392,c_61524]) ).
tcf(c_122430,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_60862,c_791]) ).
tcf(c_122573,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_122430,c_1322]) ).
tcf(c_122903,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_122220,c_122573]) ).
tcf(c_122937,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X0),X1) ),
inference(superposition,[status(thm)],[c_122903,c_911]) ).
tcf(c_123227,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),X0),
inference(superposition,[status(thm)],[c_122937,c_1683]) ).
tcf(c_123238,plain,
c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_123227,c_755]) ).
tcf(c_123250,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(superposition,[status(thm)],[c_123238,c_907]) ).
tcf(c_123348,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_54,c_123250]) ).
tcf(c_123576,plain,
c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_123348,c_755]) ).
tcf(c_124153,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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,v_r____))) ),
inference(superposition,[status(thm)],[c_123576,c_910]) ).
tcf(c_124161,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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,v_r____))),
inference(forward_subsumption_resolution,[status(thm)],[c_124153,c_121222]) ).
tcf(c_267732,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(superposition,[status(thm)],[c_56,c_1683]) ).
tcf(c_272698,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(superposition,[status(thm)],[c_267732,c_57]) ).
tcf(c_272928,plain,
c_Orderings_Oord__class_Oless__eq(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,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(superposition,[status(thm)],[c_54,c_272698]) ).
tcf(c_272955,plain,
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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,v_r____))) ),
inference(superposition,[status(thm)],[c_272928,c_58]) ).
tcf(c_273626,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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,v_r____))),
inference(global_subsumption_just,[status(thm)],[c_272955,c_124161]) ).
tcf(c_380032,plain,
( ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ),
inference(superposition,[status(thm)],[c_95,c_273626]) ).
tcf(c_380034,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_380032,c_1531,c_242,c_42998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW234+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 21:44:31 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 246.73/37.95 % SZS status Started for theBenchmark.p
% 246.73/37.95 ERROR - "ProverProcess:heur/469571:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 246.73/37.95 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 246.73/37.95 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 6 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3.0 --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 32 --inst_dismatching false --inst_eager_unprocessed_to_passive false --inst_eq_res_simp false --inst_learning_factor 10 --inst_learning_loop_flag true --inst_learning_start 256 --inst_lit_activity_flag true --inst_lit_sel "[+sign;-ground;-non_prol_conj_symb;-num_var]" --inst_lit_sel_side num_lit --inst_orphan_elimination true --inst_passive_queue_type list --inst_passive_queues "[[-ground;-epr]]" --inst_passive_queues_freq "[2]" --inst_prop_sim_given false --inst_prop_sim_new false --inst_restr_to_given true --inst_sel_renew solver --inst_solver_calls_frac 0.6939020527068606 --inst_solver_per_active 8 --inst_sos_flag false --inst_start_prop_sim_after_learn 9 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 2048 --prop_solver_per_cl 128 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[DemodLightNormLoopTriv;ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 640 --sup_share_score_frac 0.1 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_t0yu0tfz/hqwq9ph1 2>> /export/starexec/sandbox2/tmp/iprover_out_t0yu0tfz/hqwq9ph1_error
% 246.73/37.95 % SZS status Theorem for theBenchmark.p
% 246.73/37.95
% 246.73/37.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 246.73/37.95
% 246.73/37.95 % ------ iProver source info
% 246.73/37.95
% 246.73/37.95 % git: date: 2026-07-19 20:42:38 +0200
% 246.73/37.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 246.73/37.95 % git: non_committed_changes: false
% 246.73/37.95
% 246.73/37.95 % ------ Parsing...
% 246.73/37.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 246.73/37.95
% 246.73/37.95 % ------ Preprocessing... sup_sim: 72 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 59 sf_s rm: 12 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe_e %
% 246.73/37.95
% 246.73/37.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 246.73/37.95
% 246.73/37.95 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 246.73/37.95 % ------ Proving...
% 246.73/37.95 % ------ Problem Properties
% 246.73/37.95
% 246.73/37.95 %
% 246.73/37.95 % clauses 1346
% 246.73/37.95 % conjectures 1
% 246.73/37.95 % EPR 231
% 246.73/37.95 % Horn 1192
% 246.73/37.95 % unary 406
% 246.73/37.95 % binary 456
% 246.73/37.95 % lits 3003
% 246.73/37.95 % lits eq 646
% 246.73/37.95 % fd_pure 0
% 246.73/37.95 % fd_pseudo 0
% 246.73/37.95 % fd_cond 69
% 246.73/37.95 % fd_pseudo_cond 87
% 246.73/37.95 % AC symbols 0
% 246.73/37.95
% 246.73/37.95 % ------ Input Options Time Limit: Unbounded
% 246.73/37.95
% 246.73/37.95
% 246.73/37.95 % ------
% 246.73/37.95 % Current options:
% 246.73/37.95 % ------
% 246.73/37.95
% 246.73/37.95
% 246.73/37.95 %
% 246.73/37.95
% 246.73/37.95 % ------ Proving...
% 246.73/37.95 %
% 246.73/37.95
% 246.73/37.95 % SZS status Theorem for theBenchmark.p
% 246.73/37.95
% 246.73/37.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 246.73/37.96
% 246.73/37.96
%------------------------------------------------------------------------------