%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP642+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 01:34:59 PM UTC 2026
% Result : Theorem 1.18s 6.29s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 87 ( 29 unt; 2 def)
% Number of atoms : 387 ( 55 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 499 ( 208 ~; 217 |; 59 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 82 !; 6 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m1_group_2(X1,X0)
& v1_group_1(X1) )
=> k1_funct_1(k1_latsubgr(X0),X1) != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_latsubgr) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m1_group_2(X1,X0)
& v1_group_1(X1) )
=> k1_funct_1(k1_latsubgr(X0),X1) != k1_xboole_0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_1(X1) )
=> ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( ( m1_group_2(X2,X0)
& v1_group_1(X2) )
=> k1_funct_1(X1,X2) = u1_struct_0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(f13,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_1(k1_latsubgr(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(f17,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f19,axiom,
! [X0] :
( ( l1_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_group_2) ).
fof(f32,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f34,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f60,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_group_2(X1,X0)
& v1_group_1(X1)
& k1_funct_1(k1_latsubgr(X0),X1) = k1_xboole_0 ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f61,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_group_2(X1,X0)
& v1_group_1(X1)
& k1_funct_1(k1_latsubgr(X0),X1) = k1_xboole_0 ) ),
inference(flattening,[],[f60]) ).
fof(f71,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| k1_funct_1(X1,X2) = u1_struct_0(X2) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f72,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| k1_funct_1(X1,X2) = u1_struct_0(X2) ) ) ) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_1(k1_latsubgr(X0)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f76,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_1(k1_latsubgr(X0)) ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f78,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f79,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) ) ) ),
inference(flattening,[],[f78]) ).
fof(f86,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f32]) ).
fof(f87,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f86]) ).
fof(f105,plain,
( l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0)
& m1_group_2(sK1,sK0)
& v1_group_1(sK1)
& k1_xboole_0 = k1_funct_1(k1_latsubgr(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f61]) ).
fof(f106,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( ( k1_latsubgr(X0) != X1
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| k1_funct_1(X1,X2) = u1_struct_0(X2) ) )
& ( ? [X2] :
( m1_group_2(X2,X0)
& v1_group_1(X2)
& k1_funct_1(X1,X2) != u1_struct_0(X2) )
| X1 = k1_latsubgr(X0) ) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f107,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( ( k1_latsubgr(X0) != X1
| ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| k1_funct_1(X1,X3) = u1_struct_0(X3) ) )
& ( ? [X2] :
( m1_group_2(X2,X0)
& v1_group_1(X2)
& k1_funct_1(X1,X2) != u1_struct_0(X2) )
| X1 = k1_latsubgr(X0) ) ) ) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( ( k1_latsubgr(X0) != X1
| ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| k1_funct_1(X1,X3) = u1_struct_0(X3) ) )
& ( ( m1_group_2(sK2(X0,X1),X0)
& v1_group_1(sK2(X0,X1))
& k1_funct_1(X1,sK2(X0,X1)) != u1_struct_0(sK2(X0,X1)) )
| X1 = k1_latsubgr(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f107]) ).
fof(f124,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f125,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f126,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f127,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f128,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f129,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f105]) ).
fof(f130,plain,
k1_xboole_0 = k1_funct_1(k1_latsubgr(sK0),sK1),
inference(cnf_transformation,[],[f105]) ).
fof(f142,plain,
! [X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| k1_latsubgr(X0) != X1
| ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| k1_funct_1(X1,X3) = u1_struct_0(X3) ),
inference(cnf_transformation,[],[f108]) ).
fof(f148,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f149,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f150,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_funct_1(k1_latsubgr(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f151,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f152,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| l1_group_1(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f154,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ v3_struct_0(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f166,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f168,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f34]) ).
fof(f198,plain,
! [X3,X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(k1_latsubgr(X0))
| ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3) ),
inference(equality_resolution,[],[f142]) ).
tcf(c_49,negated_conjecture,
k1_funct_1(k1_latsubgr(sK0),sK1) = k1_xboole_0,
inference(cnf_transformation,[],[f130]) ).
tcf(c_50,negated_conjecture,
v1_group_1(sK1),
inference(cnf_transformation,[],[f129]) ).
tcf(c_51,negated_conjecture,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f127]) ).
tcf(c_53,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
tcf(c_54,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f125]) ).
tcf(c_55,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f124]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X1)
| ~ v1_funct_1(k1_latsubgr(X0))
| ~ m1_group_2(X1,X0)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_68,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_funct_1(k1_latsubgr(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_69,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_70,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_71,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v3_struct_0(X0)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( l1_group_1(X0)
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_86,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_88,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f168]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_65,c_68,c_70,c_69,c_65]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k1_funct_1(k1_latsubgr(X1),X0) = u1_struct_0(X0) )
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,X1) ),
inference(renaming,[status(thm)],[c_167]) ).
tcf(c_174,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_71]) ).
tcf(c_1078,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v1_xboole_0(u1_struct_0(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_174,c_86]) ).
tcf(c_1079,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_1078]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k1_funct_1(k1_latsubgr(X1),X0) = u1_struct_0(X0) )
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X0,X1)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_168]) ).
tcf(c_1154,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( k1_funct_1(k1_latsubgr(X0),sK1) = u1_struct_0(sK1) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(sK1,X0) ),
inference(unflattening,[status(thm)],[c_1153]) ).
tcf(c_1155,plain,
( v3_struct_0(sK0)
| ( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1) )
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_group_2(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_1154]) ).
tcf(c_1367,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) )
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_168]) ).
tcf(c_1368,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k1_funct_1(k1_latsubgr(sK0),X0) = u1_struct_0(X0) )
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_1367]) ).
tcf(c_1370,plain,
! [X0: $i] :
( ~ m1_group_2(X0,sK0)
| ~ v1_group_1(X0)
| ( k1_funct_1(k1_latsubgr(sK0),X0) = u1_struct_0(X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1368,c_55,c_53,c_52,c_1368]) ).
tcf(c_1371,plain,
! [X0: $i] :
( ( k1_funct_1(k1_latsubgr(sK0),X0) = u1_struct_0(X0) )
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_1370]) ).
tcf(c_1883,plain,
! [X0: $i,X1: $i] :
( l1_group_1(X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_74]) ).
tcf(c_1884,plain,
( l1_group_1(sK1)
| v3_struct_0(sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_1883]) ).
tcf(c_1885,plain,
l1_group_1(sK1),
inference(global_subsumption_just,[status(thm)],[c_1884,c_55,c_53,c_52,c_1884]) ).
tcf(c_1897,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v3_struct_0(X1)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_72]) ).
tcf(c_1898,plain,
( v3_struct_0(sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v3_struct_0(sK1) ),
inference(unflattening,[status(thm)],[c_1897]) ).
tcf(c_1899,plain,
~ v3_struct_0(sK1),
inference(global_subsumption_just,[status(thm)],[c_1898,c_55,c_53,c_52,c_1898]) ).
tcf(c_1904,plain,
! [X0: $i] :
( ( k1_funct_1(k1_latsubgr(sK0),X0) = u1_struct_0(X0) )
| ~ v1_group_1(X0)
| ( sK0 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_1371]) ).
tcf(c_1905,plain,
( ( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1) )
| ~ v1_group_1(sK1) ),
inference(unflattening,[status(thm)],[c_1904]) ).
tcf(c_1906,plain,
k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1),
inference(global_subsumption_just,[status(thm)],[c_1905,c_55,c_54,c_53,c_52,c_51,c_1155]) ).
tcf(c_4086,definition,
iPr_def_17 = k1_funct_1(iPr_def_11,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_4087,definition,
iPr_def_18 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_4092,plain,
~ v3_struct_0(sK1),
inference(demodulation,[status(thm)],[c_1899]) ).
tcf(c_4094,plain,
l1_group_1(sK1),
inference(demodulation,[status(thm)],[c_1885]) ).
tcf(c_4096,plain,
iPr_def_17 = iPr_def_18,
inference(demodulation,[status(thm)],[c_1906,c_4087,c_4086]) ).
tcf(c_4107,negated_conjecture,
iPr_def_17 = k1_xboole_0,
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_5528,plain,
v1_xboole_0(iPr_def_17),
inference(light_normalisation,[status(thm)],[c_88,c_4107]) ).
tcf(c_5595,plain,
u1_struct_0(sK1) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_4087,c_4096]) ).
tcf(c_6340,plain,
( v3_struct_0(sK1)
| ~ v1_xboole_0(iPr_def_17)
| ~ l1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_5595,c_1079]) ).
tcf(c_6345,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6340,c_4092,c_5528,c_4094]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/5.37 % Computer : n003.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Wed Sep 23 15:26:40 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 1.18/6.29 % SZS status Started for theBenchmark.p
% 1.18/6.29 % SZS status Theorem for theBenchmark.p
% 1.18/6.29
% 1.18/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.18/6.29
% 1.18/6.29 % ------ iProver source info
% 1.18/6.29
% 1.18/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.18/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.18/6.29 % git: non_committed_changes: false
% 1.18/6.29
% 1.18/6.29 % ------ Parsing...
% 1.18/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.18/6.29
% 1.18/6.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 1.18/6.29
% 1.18/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.18/6.29
% 1.18/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.18/6.29 % ------ Proving...
% 1.18/6.29 % ------ Problem Properties
% 1.18/6.29
% 1.18/6.29 %
% 1.18/6.29 % clauses 81
% 1.18/6.29 % conjectures 5
% 1.18/6.29 % EPR 28
% 1.18/6.29 % Horn 69
% 1.18/6.29 % unary 42
% 1.18/6.29 % binary 16
% 1.18/6.29 % lits 167
% 1.18/6.29 % lits eq 27
% 1.18/6.29 % fd_pure 0
% 1.18/6.29 % fd_pseudo 0
% 1.18/6.29 % fd_cond 7
% 1.18/6.29 % fd_pseudo_cond 3
% 1.18/6.29 % AC symbols 0
% 1.18/6.29
% 1.18/6.29 % ------ Schedule dynamic 5 is on
% 1.18/6.29
% 1.18/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.18/6.29
% 1.18/6.29
% 1.18/6.29 % ------
% 1.18/6.29 % Current options:
% 1.18/6.29 % ------
% 1.18/6.29
% 1.18/6.29
% 1.18/6.29 %
% 1.18/6.29
% 1.18/6.29 % ------ Proving...
% 1.18/6.29 %
% 1.18/6.29
% 1.18/6.29 % SZS status Theorem for theBenchmark.p
% 1.18/6.29
% 1.18/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.18/6.29
% 1.18/6.29
%------------------------------------------------------------------------------