%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT313+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 : n012.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 01:59:14 PM UTC 2026
% Result : Theorem 0.61s 0.95s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 147 ( 31 unt; 3 def)
% Number of atoms : 566 ( 56 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 626 ( 263 ~; 285 |; 53 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 18 ( 16 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 147 !; 4 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( ( r2_hidden(k6_lattices(X0),X1)
& v14_lattices(X0) )
=> ( X1 = u1_struct_0(X0)
& r1_filter_2(u1_struct_0(X0),X1,k17_filter_2(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( ( r2_hidden(k6_lattices(X0),X1)
& v14_lattices(X0) )
=> ( X1 = u1_struct_0(X0)
& r1_filter_2(u1_struct_0(X0),X1,k17_filter_2(X0)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k17_filter_2(X0) = u1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_2) ).
fof(f8,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m2_filter_2(k17_filter_2(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_filter_2) ).
fof(f13,axiom,
! [X0] :
( l1_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f15,axiom,
! [X0] :
( l2_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f16,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l2_lattices(X0)
& l1_lattices(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f18,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( m2_lattice4(X1,X0)
& ~ v1_xboole_0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(f19,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_lattice4(X1,X0)
=> m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(f28,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(f38,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(X0))
& m1_subset_1(X1,k1_zfmisc_1(X0))
& ~ v1_xboole_0(X0) )
=> ( r1_filter_2(X0,X1,X2)
<=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(f44,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_filter_2) ).
fof(f46,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1) )
=> ( ( r2_hidden(k6_lattices(X0),X1)
& v14_lattices(X0) )
=> ( k19_filter_2(X0,X1) = u1_struct_0(X0)
& r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),k17_filter_2(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_filter_2) ).
fof(f50,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f55,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_filter_2(X1,X0)
& r2_hidden(k6_lattices(X0),X1)
& v14_lattices(X0)
& ( u1_struct_0(X0) != X1
| ~ r1_filter_2(u1_struct_0(X0),X1,k17_filter_2(X0)) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f56,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_filter_2(X1,X0)
& r2_hidden(k6_lattices(X0),X1)
& v14_lattices(X0)
& ( u1_struct_0(X0) != X1
| ~ r1_filter_2(u1_struct_0(X0),X1,k17_filter_2(X0)) ) ) ),
inference(flattening,[],[f55]) ).
fof(f62,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k17_filter_2(X0) = u1_struct_0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f63,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k17_filter_2(X0) = u1_struct_0(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k17_filter_2(X0),X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k17_filter_2(X0),X0) ),
inference(flattening,[],[f64]) ).
fof(f70,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f71,plain,
! [X0] :
( ~ l2_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f72,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f73,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| ( m2_lattice4(X1,X0)
& ~ v1_xboole_0(X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f74,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| ( m2_lattice4(X1,X0)
& ~ v1_xboole_0(X1) ) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_lattice4(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f76,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_lattice4(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(flattening,[],[f75]) ).
fof(f81,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f82,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f81]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0)
| ( r1_filter_2(X0,X1,X2)
<=> X1 = X2 ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0)
| ( r1_filter_2(X0,X1,X2)
<=> X1 = X2 ) ),
inference(flattening,[],[f88]) ).
fof(f97,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f98,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1) ) ),
inference(flattening,[],[f97]) ).
fof(f100,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ v14_lattices(X0)
| ( k19_filter_2(X0,X1) = u1_struct_0(X0)
& r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),k17_filter_2(X0)) ) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f101,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ v14_lattices(X0)
| ( k19_filter_2(X0,X1) = u1_struct_0(X0)
& r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),k17_filter_2(X0)) ) ) ),
inference(flattening,[],[f100]) ).
fof(f106,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f108,plain,
( l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0)
& m2_filter_2(sK1,sK0)
& r2_hidden(k6_lattices(sK0),sK1)
& v14_lattices(sK0)
& ( sK1 != u1_struct_0(sK0)
| ~ r1_filter_2(u1_struct_0(sK0),sK1,k17_filter_2(sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f56]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0)
| ( ( ~ r1_filter_2(X0,X1,X2)
| X1 = X2 )
& ( X1 != X2
| r1_filter_2(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f124,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f125,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f126,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f127,plain,
m2_filter_2(sK1,sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f128,plain,
r2_hidden(k6_lattices(sK0),sK1),
inference(cnf_transformation,[],[f108]) ).
fof(f129,plain,
v14_lattices(sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f130,plain,
( sK1 != u1_struct_0(sK0)
| ~ r1_filter_2(u1_struct_0(sK0),sK1,k17_filter_2(sK0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f141,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| u1_struct_0(X0) = k17_filter_2(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f142,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k17_filter_2(X0),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f145,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f146,plain,
! [X0] :
( ~ l2_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f147,plain,
! [X0] :
( ~ l3_lattices(X0)
| l2_lattices(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f148,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f149,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(X1,X0)
| m2_lattice4(X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f151,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_lattice4(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f159,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0)
| ~ r1_filter_2(X0,X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f181,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(X1,X0)
| r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f183,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ v14_lattices(X0)
| u1_struct_0(X0) = k19_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f184,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ v14_lattices(X0)
| r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),k17_filter_2(X0)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f188,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_49,negated_conjecture,
( ~ r1_filter_2(u1_struct_0(sK0),sK1,k17_filter_2(sK0))
| ( u1_struct_0(sK0) != sK1 ) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_50,negated_conjecture,
v14_lattices(sK0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_51,negated_conjecture,
r2_hidden(k6_lattices(sK0),sK1),
inference(cnf_transformation,[],[f128]) ).
tcf(c_52,negated_conjecture,
m2_filter_2(sK1,sK0),
inference(cnf_transformation,[],[f127]) ).
tcf(c_53,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f126]) ).
tcf(c_54,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f125]) ).
tcf(c_55,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f124]) ).
tcf(c_64,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( u1_struct_0(X0) = k17_filter_2(X0) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_65,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m2_filter_2(k17_filter_2(X0),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_68,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_69,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_70,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_71,plain,
! [X0: $i] :
( l2_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_lattice4(X0,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_lattice4(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_82,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X0)
| ( X1 = X2 )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ r1_filter_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X0),X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| v3_struct_0(X1)
| r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X0),k17_filter_2(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ r2_hidden(k6_lattices(X1),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| v3_struct_0(X1)
| ( k19_filter_2(X1,X0) = u1_struct_0(X1) )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ r2_hidden(k6_lattices(X1),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_118,plain,
( l2_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_120,plain,
( l1_struct_0(sK0)
| ~ l2_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_131,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_146,plain,
( v3_struct_0(sK0)
| m2_filter_2(k17_filter_2(sK0),sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_147,plain,
( v3_struct_0(sK0)
| ( u1_struct_0(sK0) = k17_filter_2(sK0) )
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k19_filter_2(X1,X0) = u1_struct_0(X1) )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ r2_hidden(k6_lattices(X1),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_107,c_111]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X0),k17_filter_2(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ r2_hidden(k6_lattices(X1),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_106,c_111]) ).
tcf(c_859,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_68]) ).
tcf(c_860,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_859]) ).
tcf(c_911,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),k17_filter_2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_235]) ).
tcf(c_912,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| r1_filter_2(u1_struct_0(sK0),k19_filter_2(sK0,X0),k17_filter_2(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ r2_hidden(k6_lattices(sK0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_911]) ).
tcf(c_914,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ r2_hidden(k6_lattices(sK0),X0)
| r1_filter_2(u1_struct_0(sK0),k19_filter_2(sK0,X0),k17_filter_2(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_912,c_55,c_54,c_53,c_912]) ).
tcf(c_915,plain,
! [X0: $i] :
( r1_filter_2(u1_struct_0(sK0),k19_filter_2(sK0,X0),k17_filter_2(sK0))
| ~ r2_hidden(k6_lattices(sK0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_914]) ).
tcf(c_926,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k19_filter_2(X0,X1) = u1_struct_0(X0) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_234]) ).
tcf(c_927,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k19_filter_2(sK0,X0) = u1_struct_0(sK0) )
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ r2_hidden(k6_lattices(sK0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_926]) ).
tcf(c_929,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ r2_hidden(k6_lattices(sK0),X0)
| ( k19_filter_2(sK0,X0) = u1_struct_0(sK0) ) ),
inference(global_subsumption_just,[status(thm)],[c_927,c_55,c_54,c_53,c_927]) ).
tcf(c_930,plain,
! [X0: $i] :
( ( k19_filter_2(sK0,X0) = u1_struct_0(sK0) )
| ~ r2_hidden(k6_lattices(sK0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_929]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X3)
| v3_struct_0(X2)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X3)))
| ~ l3_lattices(X3)
| ~ l3_lattices(X2)
| ~ v10_lattices(X3)
| ~ v10_lattices(X2)
| ~ m2_filter_2(X0,X2)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_74]) ).
tcf(c_948,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X0,X1) ),
inference(unflattening,[status(thm)],[c_947]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(u1_struct_0(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_860,c_82]) ).
tcf(c_1033,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_1032]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ m2_filter_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_948]) ).
tcf(c_1168,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0)
| ~ m2_filter_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_1167]) ).
tcf(c_1170,plain,
! [X0: $i] :
( ~ m2_filter_2(X0,sK0)
| m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_1168,c_55,c_53,c_1168]) ).
tcf(c_1171,plain,
! [X0: $i] :
( m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m2_filter_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_1170]) ).
tcf(c_1179,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1)
| ~ l3_lattices(X0)
| ~ m2_filter_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_104]) ).
tcf(c_1180,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| r1_filter_2(u1_struct_0(sK0),k19_filter_2(sK0,X0),X0)
| ~ l3_lattices(sK0)
| ~ m2_filter_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_1179]) ).
tcf(c_1182,plain,
! [X0: $i] :
( ~ m2_filter_2(X0,sK0)
| r1_filter_2(u1_struct_0(sK0),k19_filter_2(sK0,X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_1180,c_55,c_53,c_1180]) ).
tcf(c_1183,plain,
! [X0: $i] :
( r1_filter_2(u1_struct_0(sK0),k19_filter_2(sK0,X0),X0)
| ~ m2_filter_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_1182]) ).
tcf(c_1246,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m2_filter_2(k17_filter_2(X0),X0)
| ~ l3_lattices(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_65]) ).
tcf(c_1247,plain,
( v3_struct_0(sK0)
| m2_filter_2(k17_filter_2(sK0),sK0)
| ~ l3_lattices(sK0) ),
inference(unflattening,[status(thm)],[c_1246]) ).
tcf(c_1248,plain,
m2_filter_2(k17_filter_2(sK0),sK0),
inference(global_subsumption_just,[status(thm)],[c_1247,c_55,c_54,c_53,c_146]) ).
tcf(c_1253,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( u1_struct_0(X0) = k17_filter_2(X0) )
| ~ l3_lattices(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_64]) ).
tcf(c_1254,plain,
( v3_struct_0(sK0)
| ( u1_struct_0(sK0) = k17_filter_2(sK0) )
| ~ l3_lattices(sK0) ),
inference(unflattening,[status(thm)],[c_1253]) ).
tcf(c_1255,plain,
u1_struct_0(sK0) = k17_filter_2(sK0),
inference(global_subsumption_just,[status(thm)],[c_1254,c_55,c_54,c_53,c_147]) ).
tcf(c_1275,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_1033]) ).
tcf(c_1276,plain,
( v3_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1275]) ).
tcf(c_1277,plain,
~ v1_xboole_0(u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_1276,c_55,c_53,c_118,c_120,c_131]) ).
tcf(c_1918,plain,
m2_filter_2(u1_struct_0(sK0),sK0),
inference(demodulation,[status(thm)],[c_1248,c_1255]) ).
tcf(c_2039,plain,
( ~ r1_filter_2(u1_struct_0(sK0),sK1,u1_struct_0(sK0))
| ( u1_struct_0(sK0) != sK1 ) ),
inference(light_normalisation,[status(thm)],[c_49,c_1255]) ).
tcf(c_2052,plain,
! [X0: $i] :
( r1_filter_2(u1_struct_0(sK0),k19_filter_2(sK0,X0),u1_struct_0(sK0))
| ~ r2_hidden(k6_lattices(sK0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(light_normalisation,[status(thm)],[c_915,c_1255]) ).
tcf(c_2441,definition,
iPr_def_10 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2442,definition,
iPr_def_11 = k1_zfmisc_1(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2443,definition,
iPr_def_12 = k6_lattices(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2449,plain,
! [X0: $i] :
( r1_filter_2(iPr_def_10,k19_filter_2(sK0,X0),iPr_def_10)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ r2_hidden(iPr_def_12,X0) ),
inference(demodulation,[status(thm)],[c_2052,c_2443,c_2441,c_2442]) ).
tcf(c_2450,plain,
( ~ r1_filter_2(iPr_def_10,sK1,iPr_def_10)
| ( iPr_def_10 != sK1 ) ),
inference(demodulation,[status(thm)],[c_2039]) ).
tcf(c_2451,plain,
m2_filter_2(iPr_def_10,sK0),
inference(demodulation,[status(thm)],[c_1918]) ).
tcf(c_2455,plain,
~ v1_xboole_0(iPr_def_10),
inference(demodulation,[status(thm)],[c_1277]) ).
tcf(c_2463,plain,
! [X0: $i] :
( r1_filter_2(iPr_def_10,k19_filter_2(sK0,X0),X0)
| ~ m2_filter_2(X0,sK0) ),
inference(demodulation,[status(thm)],[c_1183]) ).
tcf(c_2464,plain,
! [X0: $i] :
( m1_subset_1(X0,iPr_def_11)
| ~ m2_filter_2(X0,sK0) ),
inference(demodulation,[status(thm)],[c_1171]) ).
tcf(c_2465,plain,
! [X0: $i] :
( ( k19_filter_2(sK0,X0) = iPr_def_10 )
| ~ m1_subset_1(X0,iPr_def_11)
| ~ r2_hidden(iPr_def_12,X0) ),
inference(demodulation,[status(thm)],[c_930]) ).
tcf(c_2467,negated_conjecture,
m2_filter_2(sK1,sK0),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_2468,negated_conjecture,
r2_hidden(iPr_def_12,sK1),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_3154,plain,
m1_subset_1(sK1,iPr_def_11),
inference(superposition,[status(thm)],[c_2467,c_2464]) ).
tcf(c_3155,plain,
m1_subset_1(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_2451,c_2464]) ).
tcf(c_3189,plain,
( ( k19_filter_2(sK0,sK1) = iPr_def_10 )
| ~ m1_subset_1(sK1,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2468,c_2465]) ).
tcf(c_3190,plain,
k19_filter_2(sK0,sK1) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_3189,c_3154]) ).
tcf(c_3192,plain,
( r1_filter_2(iPr_def_10,iPr_def_10,sK1)
| ~ m2_filter_2(sK1,sK0) ),
inference(superposition,[status(thm)],[c_3190,c_2463]) ).
tcf(c_3193,plain,
r1_filter_2(iPr_def_10,iPr_def_10,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_3192,c_2467]) ).
tcf(c_3214,plain,
( r1_filter_2(iPr_def_10,iPr_def_10,iPr_def_10)
| ~ m1_subset_1(sK1,iPr_def_11)
| ~ r2_hidden(iPr_def_12,sK1) ),
inference(superposition,[status(thm)],[c_3190,c_2449]) ).
tcf(c_3215,plain,
r1_filter_2(iPr_def_10,iPr_def_10,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3214,c_3154,c_2468]) ).
tcf(c_3518,plain,
( v1_xboole_0(iPr_def_10)
| ( sK1 = iPr_def_10 )
| ~ m1_subset_1(iPr_def_10,k1_zfmisc_1(iPr_def_10))
| ~ m1_subset_1(sK1,k1_zfmisc_1(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3193,c_98]) ).
tcf(c_3522,plain,
( v1_xboole_0(iPr_def_10)
| ( sK1 = iPr_def_10 )
| ~ m1_subset_1(iPr_def_10,iPr_def_11)
| ~ m1_subset_1(sK1,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_3518,c_2442]) ).
tcf(c_3523,plain,
sK1 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_3522,c_2455,c_3155,c_3154]) ).
tcf(c_3536,plain,
( ~ r1_filter_2(iPr_def_10,iPr_def_10,iPr_def_10)
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_2450,c_3523]) ).
tcf(c_3541,plain,
~ r1_filter_2(iPr_def_10,iPr_def_10,iPr_def_10),
inference(equality_resolution_simp,[status(thm)],[c_3536]) ).
tcf(c_3542,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3541,c_3215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Wed Sep 23 21:01:21 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.31 Running first-order theorem proving
% 0.02/0.31 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
% 0.02/0.32
% 0.02/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.32
% 0.02/0.32 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 0.61/0.95 % SZS status Started for theBenchmark.p
% 0.61/0.95 % SZS status Theorem for theBenchmark.p
% 0.61/0.95
% 0.61/0.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.61/0.95
% 0.61/0.95 % ------ iProver source info
% 0.61/0.95
% 0.61/0.95 % git: date: 2026-07-19 20:42:38 +0200
% 0.61/0.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.61/0.95 % git: non_committed_changes: false
% 0.61/0.95
% 0.61/0.95 % ------ Parsing...
% 0.61/0.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.61/0.95
% 0.61/0.95 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 3 sf_s rm: 8 0s sf_e pe_s pe_e %
% 0.61/0.95
% 0.61/0.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.61/0.95
% 0.61/0.95 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.61/0.95 % ------ Proving...
% 0.61/0.95 % ------ Problem Properties
% 0.61/0.95
% 0.61/0.95 %
% 0.61/0.95 % clauses 67
% 0.61/0.95 % conjectures 3
% 0.61/0.95 % EPR 26
% 0.61/0.95 % Horn 55
% 0.61/0.95 % unary 33
% 0.61/0.95 % binary 24
% 0.61/0.95 % lits 115
% 0.61/0.95 % lits eq 14
% 0.61/0.95 % fd_pure 0
% 0.61/0.95 % fd_pseudo 0
% 0.61/0.95 % fd_cond 1
% 0.61/0.95 % fd_pseudo_cond 2
% 0.61/0.95 % AC symbols 0
% 0.61/0.95
% 0.61/0.95 % ------ Schedule dynamic 5 is on
% 0.61/0.95
% 0.61/0.95 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.61/0.95
% 0.61/0.95
% 0.61/0.95 % ------
% 0.61/0.95 % Current options:
% 0.61/0.95 % ------
% 0.61/0.95
% 0.61/0.95
% 0.61/0.95 %
% 0.61/0.95
% 0.61/0.95 % ------ Proving...
% 0.61/0.95 %
% 0.61/0.95
% 0.61/0.95 % SZS status Theorem for theBenchmark.p
% 0.61/0.95
% 0.61/0.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.61/0.96
% 0.61/0.96
%------------------------------------------------------------------------------