%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW178+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 03:29:12 PM UTC 2026
% Result : Theorem 35.18s 8.52s
% Output : CNFRefutation 35.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 82 ( 50 unt; 5 def)
% Number of atoms : 138 ( 56 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 65 ( 33 ~; 27 |; 0 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 126 ( 0 sgn 126 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(f29,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(f34,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(f38,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
fof(f102,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(f334,axiom,
! [X0,X1] : c_RealVector_Odist__class_Odist(tc_Complex_Ocomplex,X1,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dist__complex__def) ).
fof(f1137,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f1149,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f1169,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1180,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1189,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f1200,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1201,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
inference(negated_conjecture,[status(cth)],[f1200]) ).
fof(f1208,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
inference(flattening,[],[f1201]) ).
fof(f1259,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(ennf_transformation,[],[f28]) ).
fof(f1260,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(ennf_transformation,[],[f29]) ).
fof(f1265,plain,
! [X0,X1,X2] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f1269,plain,
! [X0,X1,X2] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))) ),
inference(ennf_transformation,[],[f38]) ).
fof(f1346,plain,
! [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) ),
inference(ennf_transformation,[],[f102]) ).
fof(f2580,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f1259]) ).
fof(f2581,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,[],[f1260]) ).
fof(f2586,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(cnf_transformation,[],[f1265]) ).
fof(f2590,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))) ),
inference(cnf_transformation,[],[f1269]) ).
fof(f2666,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,[],[f1346]) ).
fof(f2980,plain,
! [X0,X1] : c_RealVector_Odist__class_Odist(tc_Complex_Ocomplex,X1,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)),
inference(cnf_transformation,[],[f334]) ).
fof(f4053,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1137]) ).
fof(f4065,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1149]) ).
fof(f4085,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1169]) ).
fof(f4096,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1180]) ).
fof(f4105,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1189]) ).
fof(f4116,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
inference(cnf_transformation,[],[f1208]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X2) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f2580]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),X2) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f2581]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X2,X1)) )
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f2586]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2)))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f2590]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2666]) ).
tcf(c_465,plain,
! [X0: $i,X1: $i] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_RealVector_Odist__class_Odist(tc_Complex_Ocomplex,X0,X1),
inference(cnf_transformation,[],[f2980]) ).
tcf(c_1517,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f4053]) ).
tcf(c_1529,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f4065]) ).
tcf(c_1549,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4085]) ).
tcf(c_1560,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4096]) ).
tcf(c_1569,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4105]) ).
tcf(c_1580,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
inference(cnf_transformation,[],[f4116]) ).
tcf(c_2442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X2,X1)) )
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(prop_impl_just,[status(thm)],[c_91]) ).
tcf(c_2450,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2)))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(prop_impl_just,[status(thm)],[c_95]) ).
tcf(c_2548,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X2) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_2550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),X2) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
tcf(c_2620,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_163]) ).
tcf(c_21000,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),X2) = X1 )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_2550,c_1529]) ).
tcf(c_21001,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(unflattening,[status(thm)],[c_21000]) ).
tcf(c_21006,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X2) = X1 )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_2548,c_1529]) ).
tcf(c_21007,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(unflattening,[status(thm)],[c_21006]) ).
tcf(c_21113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X2) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2548,c_1569]) ).
tcf(c_21114,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X1) = X0,
inference(unflattening,[status(thm)],[c_21113]) ).
tcf(c_23230,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_2620,c_1517]) ).
tcf(c_23231,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),
inference(unflattening,[status(thm)],[c_23230]) ).
tcf(c_23330,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2620,c_1560]) ).
tcf(c_23331,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),
inference(unflattening,[status(thm)],[c_23330]) ).
tcf(c_24728,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2)))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2450,c_1549]) ).
tcf(c_24729,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(unflattening,[status(thm)],[c_24728]) ).
tcf(c_24752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X2,X1)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2442,c_1549]) ).
tcf(c_24753,plain,
! [X0: $i,X1: $i] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)),
inference(unflattening,[status(thm)],[c_24752]) ).
tcf(c_38809,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_21001,c_23231]) ).
tcf(c_39652,plain,
! [X0: $i,X1: $i] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_RealVector_Odist__class_Odist(tc_Complex_Ocomplex,X1,X0),
inference(light_normalisation,[status(thm)],[c_24753,c_465]) ).
tcf(c_40026,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Odist__class_Odist(tc_Complex_Ocomplex,X0,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0))),
inference(light_normalisation,[status(thm)],[c_24729,c_39652]) ).
tcf(c_40240,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,v_w)))),
inference(demodulation,[status(thm)],[c_1580,c_23231,c_23331]) ).
tcf(c_78336,definition,
iPr_def_10 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_78337,definition,
iPr_def_11 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_78338,definition,
iPr_def_12 = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,v_w),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_78339,definition,
iPr_def_13 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_78340,definition,
iPr_def_14 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_78341,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,iPr_def_10,iPr_def_14),
inference(demodulation,[status(thm)],[c_40240,c_78338,c_78339,c_78337,c_78340,c_78336]) ).
tcf(c_97140,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_23231,c_21007]) ).
tcf(c_97269,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_23331,c_21114]) ).
tcf(c_110068,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,iPr_def_14,iPr_def_11) = iPr_def_13,
inference(superposition,[status(thm)],[c_78340,c_97140]) ).
tcf(c_110089,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,iPr_def_11,iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_110068,c_38809]) ).
tcf(c_117442,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_12,v_z) = v_w,
inference(superposition,[status(thm)],[c_78338,c_97269]) ).
tcf(c_117447,plain,
c_RealVector_Odist__class_Odist(tc_Complex_Ocomplex,iPr_def_12,v_z) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),
inference(superposition,[status(thm)],[c_117442,c_465]) ).
tcf(c_117448,plain,
c_RealVector_Odist__class_Odist(tc_Complex_Ocomplex,iPr_def_12,v_z) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_117447,c_78336]) ).
tcf(c_117461,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,iPr_def_10,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,iPr_def_12))),
inference(superposition,[status(thm)],[c_117448,c_40026]) ).
tcf(c_117477,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,iPr_def_10,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_117461,c_78337,c_78339,c_110089]) ).
tcf(c_117478,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_117477,c_78341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW178+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 % Computer : n019.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Thu Sep 24 21:39:49 UTC 2026
% 0.05/0.41 % CPUTime :
% 0.05/0.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.05/0.47 Running first-order theorem proving
% 0.05/0.47 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.49
% 0.05/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.05/0.49
% 0.05/0.49 % Detected problem language: tptp
% 0.21/0.52 % Proving...
% 35.18/8.52 % SZS status Started for theBenchmark.p
% 35.18/8.52 ERROR - "ProverProcess:heur/346297:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.18/8.52 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.18/8.52 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode time_based --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 2.7380125131254 --demod_completeness_check full --demod_use_ground true --eq_ax_congr_red false --extra_neg_conj none --inst_activity_threshold 16 --inst_dismatching false --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 6 --inst_learning_loop_flag true --inst_learning_start 1024 --inst_lit_activity_flag true --inst_lit_sel "[+depth;+sign;+num_symb;-split;-eq]" --inst_lit_sel_side cnt --inst_orphan_elimination true --inst_passive_queue_type list --inst_passive_queues "[[-num_lits];[-max_atom_input_occur;-ground]]" --inst_passive_queues_freq "[8;50]" --inst_prop_sim_given false --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 0.21724605765256222 --inst_solver_per_active 256 --inst_sos_flag true --inst_sos_phase true --inst_sos_sth_lit_sel "[-depth;+non_prol_conj_symb;-split;-ground;+num_var]" --inst_start_prop_sim_after_learn 8 --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 false --prep_def_merge_prop_impl true --prep_def_merge_tr_cl true --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim false --prep_sem_filter none --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten false --prep_upred true --preprocessing_flag true --prolific_symb_bound 2048 --prop_solver_per_cl 32 --pure_diseq_elim false --resolution_flag false --schedule none --share_sel_clauses false --smt_ac_axioms full --smt_preprocessing true --splitting_cvd true --splitting_cvd_svl false --splitting_grd true --splitting_mode full --splitting_nvd 128 --stats_out none --sub_typing true --subs_bck_mult 0 --sup_full_bw "[Demod]" --sup_full_fw "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;DemodLightNormLoopTriv;ACJoinability;ACNormalisation]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;Demod;ACJoinability]" --sup_immed_fw_main "[SubsumptionRes;DemodLoopTriv;DemodLightNormLoopTriv;ACJoinability;ACNormalisation]" --sup_immed_triv "[]" --sup_indices_passive "[UnitSubsumption;NonunitSubsumption;Subsumption;FwDemod;BwDemod;LightNorm]" --sup_input_bw "[]" --sup_input_fw "[]" --sup_input_triv "[PropSubs;Unflattening]" --sup_iter_deepening 4 --sup_passive_queue_type queue --sup_passive_queues "[[+num_symb]]" --sup_passive_queues_freq "[5]" --sup_prop_simpl_given true --sup_prop_simpl_new false --sup_restarts_mult 4 --sup_smt_interval 10000 --sup_symb_ordering arity_random --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.4432297345384799 --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/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_c8mtq0gq/3_4paq8i 2>> /export/starexec/sandbox/tmp/iprover_out_c8mtq0gq/3_4paq8i_error
% 35.18/8.52 ERROR - "ProverProcess:heur/397442:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.18/8.52 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.18/8.52 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 64 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 4 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 2 --inst_lit_activity_flag false --inst_lit_sel "[-split]" --inst_lit_sel_side num_lit --inst_orphan_elimination false --inst_passive_queue_type priority_queues --inst_passive_queues "[[+conj_symb]]" --inst_passive_queues_freq "[50]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 0.8199321230744955 --inst_solver_per_active 4 --inst_sos_flag false --inst_start_prop_sim_after_learn 7 --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 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_c8mtq0gq/gxvsxyhf 2>> /export/starexec/sandbox/tmp/iprover_out_c8mtq0gq/gxvsxyhf_error
% 35.18/8.52 ERROR - "ProverProcess:heur/421498:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.18/8.52 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.18/8.52 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 8 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 128 --inst_lit_activity_flag false --inst_lit_sel "[+sign;+prop]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[+num_symb;-age;-age];[+num_symb;+conj_non_prolific_symb]]" --inst_passive_queues_freq "[512;10]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.006221608720445637 --inst_solver_per_active 32768 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+non_prol_conj_symb;+sign;-depth;-prop]" --inst_start_prop_sim_after_learn 9 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_c8mtq0gq/ca7hg4tc 2>> /export/starexec/sandbox/tmp/iprover_out_c8mtq0gq/ca7hg4tc_error
% 35.18/8.52 % SZS status Theorem for theBenchmark.p
% 35.18/8.52
% 35.18/8.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.18/8.52
% 35.18/8.52 % ------ iProver source info
% 35.18/8.52
% 35.18/8.52 % git: date: 2026-07-19 20:42:38 +0200
% 35.18/8.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.18/8.52 % git: non_committed_changes: false
% 35.18/8.52
% 35.18/8.52 % ------ Parsing...
% 35.18/8.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.18/8.52
% 35.18/8.52 % ------ Preprocessing... sup_sim: 147 sf_s rm: 28 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e sup_sim: 358 sf_s rm: 56 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 56 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 56 0s sf_e pe_s pe_e %
% 35.18/8.52
% 35.18/8.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.18/8.52
% 35.18/8.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 35.18/8.52 % ------ Proving...
% 35.18/8.52 % ------ Problem Properties
% 35.18/8.52
% 35.18/8.52 %
% 35.18/8.52 % clauses 1306
% 35.18/8.52 % conjectures 0
% 35.18/8.52 % EPR 79
% 35.18/8.52 % Horn 1139
% 35.18/8.52 % unary 517
% 35.18/8.52 % binary 420
% 35.18/8.52 % lits 2579
% 35.18/8.52 % lits eq 689
% 35.18/8.52 % fd_pure 0
% 35.18/8.52 % fd_pseudo 0
% 35.18/8.52 % fd_cond 87
% 35.18/8.52 % fd_pseudo_cond 68
% 35.18/8.52 % AC symbols 0
% 35.18/8.52
% 35.18/8.52 % ------ Schedule dynamic 5 is on
% 35.18/8.52
% 35.18/8.52 % ------ no conjectures: strip conj schedule
% 35.18/8.52
% 35.18/8.52 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 35.18/8.52
% 35.18/8.52
% 35.18/8.52 % ------
% 35.18/8.52 % Current options:
% 35.18/8.52 % ------
% 35.18/8.52
% 35.18/8.52
% 35.18/8.52 %
% 35.18/8.52
% 35.18/8.52 % ------ Proving...
% 35.18/8.52 %
% 35.18/8.52
% 35.18/8.52 % SZS status Theorem for theBenchmark.p
% 35.18/8.52
% 35.18/8.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.18/8.52
% 35.18/8.52
%------------------------------------------------------------------------------