%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT289+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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:58:54 PM UTC 2026
% Result : Theorem 4.19s 1.27s
% Output : CNFRefutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 105 ( 32 unt; 3 def)
% Number of atoms : 476 ( 34 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 572 ( 226 ~; 255 |; 72 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 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 : 23 ( 21 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 135 ( 0 sgn 129 !; 6 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_filter_0(X2,X0)
=> ~ ( r2_hidden(X1,X2)
& ~ r2_hidden(X2,k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),X1))
& v1_filter_0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_lopclset) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_filter_0(X2,X0)
=> ~ ( r2_hidden(X1,X2)
& ~ r2_hidden(X2,k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),X1))
& v1_filter_0(X2,X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f36,axiom,
! [X0] :
( l1_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f52,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(f67,axiom,
! [X0,X1,X2,X3] :
( ( m1_subset_1(X3,X0)
& m1_relset_1(X2,X0,X1)
& v1_funct_2(X2,X0,X1)
& v1_funct_1(X2)
& ~ v1_xboole_0(X0) )
=> k8_funct_2(X0,X1,X2,X3) = k1_funct_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
fof(f68,axiom,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k9_lopclset(X0) = k8_lopclset(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_lopclset) ).
fof(f74,axiom,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( m2_relset_1(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)))
& v1_funct_2(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)))
& v1_funct_1(k9_lopclset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_lopclset) ).
fof(f75,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l2_lattices(X0)
& l1_lattices(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f88,axiom,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_filter_0(X2,X0)
=> ( r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1))
<=> ( r2_hidden(X1,X2)
& v1_filter_0(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lopclset) ).
fof(f112,plain,
? [X0] :
( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ? [X2] :
( m1_filter_0(X2,X0)
& r2_hidden(X1,X2)
& ~ r2_hidden(X2,k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),X1))
& v1_filter_0(X2,X0) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f113,plain,
? [X0] :
( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ? [X2] :
( m1_filter_0(X2,X0)
& r2_hidden(X1,X2)
& ~ r2_hidden(X2,k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),X1))
& v1_filter_0(X2,X0) ) ) ),
inference(flattening,[],[f112]) ).
fof(f130,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f152,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f52]) ).
fof(f153,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f152]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,X0)
| ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2)
| v1_xboole_0(X0)
| k8_funct_2(X0,X1,X2,X3) = k1_funct_1(X2,X3) ),
inference(ennf_transformation,[],[f67]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,X0)
| ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2)
| v1_xboole_0(X0)
| k8_funct_2(X0,X1,X2,X3) = k1_funct_1(X2,X3) ),
inference(flattening,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k9_lopclset(X0) = k8_lopclset(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f170,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k9_lopclset(X0) = k8_lopclset(X0) ),
inference(flattening,[],[f169]) ).
fof(f177,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)))
& v1_funct_2(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)))
& v1_funct_1(k9_lopclset(X0)) ) ),
inference(ennf_transformation,[],[f74]) ).
fof(f178,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)))
& v1_funct_2(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)))
& v1_funct_1(k9_lopclset(X0)) ) ),
inference(flattening,[],[f177]) ).
fof(f179,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f195,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_filter_0(X2,X0)
| ( r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1))
<=> ( r2_hidden(X1,X2)
& v1_filter_0(X2,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f88]) ).
fof(f196,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_filter_0(X2,X0)
| ( r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1))
<=> ( r2_hidden(X1,X2)
& v1_filter_0(X2,X0) ) ) ) ) ),
inference(flattening,[],[f195]) ).
fof(f197,plain,
( l3_lattices(sK0)
& ~ v3_realset2(sK0)
& v17_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0)
& m1_subset_1(sK1,u1_struct_0(sK0))
& m1_filter_0(sK2,sK0)
& r2_hidden(sK1,sK2)
& ~ r2_hidden(sK2,k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),sK1))
& v1_filter_0(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f113]) ).
fof(f208,plain,
! [X0,X1,X2] :
( ( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) )
& ( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f221,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_filter_0(X2,X0)
| ( ( ~ r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1))
| ( r2_hidden(X1,X2)
& v1_filter_0(X2,X0) ) )
& ( ~ r2_hidden(X1,X2)
| ~ v1_filter_0(X2,X0)
| r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1)) ) ) ) ) ),
inference(nnf_transformation,[],[f196]) ).
fof(f222,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_filter_0(X2,X0)
| ( ( ~ r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1))
| ( r2_hidden(X1,X2)
& v1_filter_0(X2,X0) ) )
& ( ~ r2_hidden(X1,X2)
| ~ v1_filter_0(X2,X0)
| r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1)) ) ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f223,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f197]) ).
fof(f224,plain,
~ v3_realset2(sK0),
inference(cnf_transformation,[],[f197]) ).
fof(f225,plain,
v17_lattices(sK0),
inference(cnf_transformation,[],[f197]) ).
fof(f226,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f197]) ).
fof(f227,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f197]) ).
fof(f228,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f197]) ).
fof(f229,plain,
m1_filter_0(sK2,sK0),
inference(cnf_transformation,[],[f197]) ).
fof(f230,plain,
r2_hidden(sK1,sK2),
inference(cnf_transformation,[],[f197]) ).
fof(f231,plain,
~ r2_hidden(sK2,k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),sK1)),
inference(cnf_transformation,[],[f197]) ).
fof(f232,plain,
v1_filter_0(sK2,sK0),
inference(cnf_transformation,[],[f197]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f208]) ).
fof(f300,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f336,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f360,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X3,X0)
| ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2)
| v1_xboole_0(X0)
| k8_funct_2(X0,X1,X2,X3) = k1_funct_1(X2,X3) ),
inference(cnf_transformation,[],[f168]) ).
fof(f361,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k9_lopclset(X0) = k8_lopclset(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f365,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_relset_1(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0))) ),
inference(cnf_transformation,[],[f178]) ).
fof(f366,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v1_funct_2(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0))) ),
inference(cnf_transformation,[],[f178]) ).
fof(f367,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v1_funct_1(k9_lopclset(X0)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f369,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f397,plain,
! [X2,X0,X1] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_filter_0(X2,X0)
| ~ r2_hidden(X1,X2)
| ~ v1_filter_0(X2,X0)
| r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1)) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_49,negated_conjecture,
v1_filter_0(sK2,sK0),
inference(cnf_transformation,[],[f232]) ).
tcf(c_50,negated_conjecture,
~ r2_hidden(sK2,k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),sK1)),
inference(cnf_transformation,[],[f231]) ).
tcf(c_51,negated_conjecture,
r2_hidden(sK1,sK2),
inference(cnf_transformation,[],[f230]) ).
tcf(c_52,negated_conjecture,
m1_filter_0(sK2,sK0),
inference(cnf_transformation,[],[f229]) ).
tcf(c_53,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f228]) ).
tcf(c_54,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f227]) ).
tcf(c_55,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f226]) ).
tcf(c_56,negated_conjecture,
v17_lattices(sK0),
inference(cnf_transformation,[],[f225]) ).
tcf(c_57,negated_conjecture,
~ v3_realset2(sK0),
inference(cnf_transformation,[],[f224]) ).
tcf(c_58,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f223]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_125,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_151,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f336]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| ( k8_funct_2(X1,X2,X0,X3) = k1_funct_1(X0,X3) )
| ~ v1_funct_1(X0)
| ~ m1_subset_1(X3,X1)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f360]) ).
tcf(c_176,plain,
! [X0: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| ( k9_lopclset(X0) = k8_lopclset(X0) )
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_180,plain,
! [X0: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| v1_funct_1(k9_lopclset(X0))
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f367]) ).
tcf(c_181,plain,
! [X0: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| v1_funct_2(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)))
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f366]) ).
tcf(c_182,plain,
! [X0: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| m2_relset_1(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)))
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f365]) ).
tcf(c_183,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f369]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_realset2(X1)
| v3_struct_0(X1)
| r2_hidden(X2,k1_funct_1(k8_lopclset(X1),X0))
| ~ l3_lattices(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_0(X2,X1)
| ~ r2_hidden(X0,X2)
| ~ v1_filter_0(X2,X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_124]) ).
tcf(c_356,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(prop_impl_just,[status(thm)],[c_125]) ).
tcf(c_358,plain,
! [X0: $i] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(prop_impl_just,[status(thm)],[c_183]) ).
tcf(c_359,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(renaming,[status(thm)],[c_358]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| ( k8_funct_2(X1,X2,X0,X3) = k1_funct_1(X0,X3) )
| ~ v1_funct_1(X0)
| ~ m1_subset_1(X3,X1)
| ~ m2_relset_1(X0,X1,X2)
| ~ v1_funct_2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_175,c_306]) ).
tcf(c_2228,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_359,c_356]) ).
tcf(c_2229,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_2228]) ).
tcf(c_2525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v1_xboole_0(X2)
| v3_realset2(X0)
| v3_struct_0(X0)
| ( k8_funct_2(X2,X3,X1,X4) = k1_funct_1(X1,X4) )
| ~ v1_funct_1(X1)
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X4,X2)
| ~ m2_relset_1(X1,X2,X3)
| ( k9_lopclset(X0) != X1 )
| ( u1_struct_0(X0) != X2 )
| ( k1_zfmisc_1(k7_lopclset(X0)) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_617,c_181]) ).
tcf(c_2526,plain,
! [X0: $i,X1: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| v1_xboole_0(u1_struct_0(X0))
| ( k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),X1) = k1_funct_1(k9_lopclset(X0),X1) )
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| ~ v1_funct_1(k9_lopclset(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m2_relset_1(k9_lopclset(X0),u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0))) ),
inference(unflattening,[status(thm)],[c_2525]) ).
tcf(c_2528,plain,
! [X0: $i,X1: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v10_lattices(X0)
| ~ v17_lattices(X0)
| ~ l3_lattices(X0)
| ( k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),X1) = k1_funct_1(k9_lopclset(X0),X1) ) ),
inference(global_subsumption_just,[status(thm)],[c_2526,c_151,c_180,c_182,c_2229,c_2526]) ).
tcf(c_2529,plain,
! [X0: $i,X1: $i] :
( v3_realset2(X1)
| v3_struct_0(X1)
| ( k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X0) = k1_funct_1(k9_lopclset(X1),X0) )
| ~ l3_lattices(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(renaming,[status(thm)],[c_2528]) ).
tcf(c_3258,plain,
! [X0: $i,X1: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| ( k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),X1) = k1_funct_1(k9_lopclset(X0),X1) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_2529]) ).
tcf(c_3259,plain,
! [X0: $i] :
( v3_realset2(sK0)
| v3_struct_0(sK0)
| ( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),X0) = k1_funct_1(k9_lopclset(sK0),X0) )
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_3258]) ).
tcf(c_3261,plain,
! [X0: $i] :
( ( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),X0) = k1_funct_1(k9_lopclset(sK0),X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_3259,c_58,c_55,c_57,c_54,c_3259]) ).
tcf(c_3318,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| r2_hidden(X2,k1_funct_1(k8_lopclset(X0),X1))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_filter_0(X2,X0)
| ~ r2_hidden(X1,X2)
| ~ v1_filter_0(X2,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_208]) ).
tcf(c_3319,plain,
! [X0: $i,X1: $i] :
( v3_realset2(sK0)
| v3_struct_0(sK0)
| r2_hidden(X1,k1_funct_1(k8_lopclset(sK0),X0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_filter_0(X1,sK0)
| ~ v1_filter_0(X1,sK0)
| ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_3318]) ).
tcf(c_3320,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,k1_funct_1(k8_lopclset(sK0),X0))
| ~ m1_filter_0(X1,sK0)
| ~ v1_filter_0(X1,sK0)
| ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_3319,c_58,c_55,c_57,c_54,c_3319]) ).
tcf(c_3423,plain,
! [X0: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| ( k9_lopclset(X0) = k8_lopclset(X0) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_176]) ).
tcf(c_3424,plain,
( v3_realset2(sK0)
| v3_struct_0(sK0)
| ( k9_lopclset(sK0) = k8_lopclset(sK0) )
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0) ),
inference(unflattening,[status(thm)],[c_3423]) ).
tcf(c_3425,plain,
k9_lopclset(sK0) = k8_lopclset(sK0),
inference(global_subsumption_just,[status(thm)],[c_3424,c_58,c_55,c_57,c_54,c_3424]) ).
tcf(c_6052,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,k1_funct_1(k9_lopclset(sK0),X0))
| ~ m1_filter_0(X1,sK0)
| ~ v1_filter_0(X1,sK0)
| ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(light_normalisation,[status(thm)],[c_3320,c_3425]) ).
tcf(c_7708,definition,
iPr_def_10 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_7709,definition,
iPr_def_11 = k9_lopclset(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_7720,definition,
iPr_def_22 = k8_funct_2(iPr_def_10,iPr_def_19,iPr_def_11,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_7721,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,k1_funct_1(iPr_def_11,X0))
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m1_filter_0(X1,sK0)
| ~ v1_filter_0(X1,sK0)
| ~ r2_hidden(X0,X1) ),
inference(demodulation,[status(thm)],[c_6052,c_7709,c_7708]) ).
tcf(c_7741,plain,
! [X0: $i] :
( ( k8_funct_2(iPr_def_10,iPr_def_19,iPr_def_11,X0) = k1_funct_1(iPr_def_11,X0) )
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3261]) ).
tcf(c_7743,negated_conjecture,
m1_subset_1(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_7744,negated_conjecture,
m1_filter_0(sK2,sK0),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_7745,negated_conjecture,
r2_hidden(sK1,sK2),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_7746,negated_conjecture,
~ r2_hidden(sK2,iPr_def_22),
inference(demodulation,[status(thm)],[c_50,c_7720]) ).
tcf(c_7747,negated_conjecture,
v1_filter_0(sK2,sK0),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_8761,plain,
k8_funct_2(iPr_def_10,iPr_def_19,iPr_def_11,sK1) = k1_funct_1(iPr_def_11,sK1),
inference(superposition,[status(thm)],[c_7743,c_7741]) ).
tcf(c_8762,plain,
k1_funct_1(iPr_def_11,sK1) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_8761,c_7720]) ).
tcf(c_8923,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_22)
| ~ m1_subset_1(sK1,iPr_def_10)
| ~ m1_filter_0(X0,sK0)
| ~ r2_hidden(sK1,X0)
| ~ v1_filter_0(X0,sK0) ),
inference(superposition,[status(thm)],[c_8762,c_7721]) ).
tcf(c_8926,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_22)
| ~ m1_filter_0(X0,sK0)
| ~ r2_hidden(sK1,X0)
| ~ v1_filter_0(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8923,c_7743]) ).
tcf(c_8940,plain,
( r2_hidden(sK2,iPr_def_22)
| ~ r2_hidden(sK1,sK2)
| ~ v1_filter_0(sK2,sK0) ),
inference(superposition,[status(thm)],[c_7744,c_8926]) ).
tcf(c_8946,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8940,c_7746,c_7745,c_7747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT289+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 20:51:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 4.19/1.27 % SZS status Started for theBenchmark.p
% 4.19/1.27 % SZS status Theorem for theBenchmark.p
% 4.19/1.27
% 4.19/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.19/1.27
% 4.19/1.27 % ------ iProver source info
% 4.19/1.27
% 4.19/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.19/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.19/1.27 % git: non_committed_changes: false
% 4.19/1.27
% 4.19/1.27 % ------ Parsing...
% 4.19/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.19/1.27
% 4.19/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 56 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 14 sf_s rm: 32 0s sf_e pe_s pe_e %
% 4.19/1.27
% 4.19/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.19/1.27
% 4.19/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.19/1.27 % ------ Proving...
% 4.19/1.27 % ------ Problem Properties
% 4.19/1.27
% 4.19/1.27 %
% 4.19/1.27 % clauses 105
% 4.19/1.27 % conjectures 6
% 4.19/1.27 % EPR 31
% 4.19/1.27 % Horn 94
% 4.19/1.27 % unary 54
% 4.19/1.27 % binary 34
% 4.19/1.27 % lits 181
% 4.19/1.27 % lits eq 26
% 4.19/1.27 % fd_pure 0
% 4.19/1.27 % fd_pseudo 0
% 4.19/1.27 % fd_cond 1
% 4.19/1.27 % fd_pseudo_cond 3
% 4.19/1.27 % AC symbols 0
% 4.19/1.27
% 4.19/1.27 % ------ Schedule dynamic 5 is on
% 4.19/1.27
% 4.19/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.19/1.27
% 4.19/1.27
% 4.19/1.27 % ------
% 4.19/1.27 % Current options:
% 4.19/1.27 % ------
% 4.19/1.27
% 4.19/1.27
% 4.19/1.27 %
% 4.19/1.27
% 4.19/1.27 % ------ Proving...
% 4.19/1.27 %
% 4.19/1.27
% 4.19/1.27 % SZS status Theorem for theBenchmark.p
% 4.19/1.27
% 4.19/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.19/1.27
% 4.19/1.27
%------------------------------------------------------------------------------