%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT330+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 : n015.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 01:59:21 PM UTC 2026
% Result : Theorem 29.64s 5.83s
% Output : CNFRefutation 29.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 121 ( 13 unt; 0 def)
% Number of atoms : 654 ( 0 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 905 ( 372 ~; 420 |; 73 &)
% ( 10 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 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 : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 209 ( 0 sgn 202 !; 7 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( v13_lattices(X0)
=> r1_filter_2(u1_struct_0(X0),k18_filter_2(X0,X1),k22_filter_2(X0,k5_lattices(X0),X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( v13_lattices(X0)
=> r1_filter_2(u1_struct_0(X0),k18_filter_2(X0,X1),k22_filter_2(X0,k5_lattices(X0),X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ( r1_filter_2(X0,X1,X2)
<=> ! [X3] :
( m1_subset_1(X3,X0)
=> ( r2_hidden(X3,X1)
<=> r2_hidden(X3,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).
fof(f9,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m2_filter_2(k18_filter_2(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_filter_2) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( m2_lattice4(k22_filter_2(X0,X1,X2),X0)
& ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k22_filter_2) ).
fof(f13,axiom,
! [X0] :
( ( l1_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k5_lattices(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
fof(f16,axiom,
! [X0] :
( l2_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f17,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l2_lattices(X0)
& l1_lattices(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f19,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(f20,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(f29,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(f47,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r2_hidden(X1,k18_filter_2(X0,X2))
<=> r3_lattices(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_2) ).
fof(f51,axiom,
! [X0] :
( ( l3_lattices(X0)
& v13_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> r3_lattices(X0,k5_lattices(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattices) ).
fof(f53,axiom,
! [X0,X1,X2] :
~ ( v1_xboole_0(X2)
& m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f54,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( r3_lattices(X0,X1,X2)
=> ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
fof(f61,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& v13_lattices(X0)
& ~ r1_filter_2(u1_struct_0(X0),k18_filter_2(X0,X1),k22_filter_2(X0,k5_lattices(X0),X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f62,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& v13_lattices(X0)
& ~ r1_filter_2(u1_struct_0(X0),k18_filter_2(X0,X1),k22_filter_2(X0,k5_lattices(X0),X1)) ) ),
inference(flattening,[],[f61]) ).
fof(f68,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( r1_filter_2(X0,X1,X2)
<=> ! [X3] :
( ~ m1_subset_1(X3,X0)
| ( r2_hidden(X3,X1)
<=> r2_hidden(X3,X2) ) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f71,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k18_filter_2(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f72,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k18_filter_2(X0,X1),X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( m2_lattice4(k22_filter_2(X0,X1,X2),X0)
& ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( m2_lattice4(k22_filter_2(X0,X1,X2),X0)
& ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f76,plain,
! [X0] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f75]) ).
fof(f78,plain,
! [X0] :
( ~ l2_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f79,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f80,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,[],[f19]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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,[],[f20]) ).
fof(f83,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,[],[f82]) ).
fof(f88,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f89,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f88]) ).
fof(f108,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r2_hidden(X1,k18_filter_2(X0,X2))
<=> r3_lattices(X0,X1,X2) ) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f109,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r2_hidden(X1,k18_filter_2(X0,X2))
<=> r3_lattices(X0,X1,X2) ) ) ) ),
inference(flattening,[],[f108]) ).
fof(f114,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v13_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| r3_lattices(X0,k5_lattices(X0),X1) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f115,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v13_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| r3_lattices(X0,k5_lattices(X0),X1) ) ),
inference(flattening,[],[f114]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f119,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f120,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ),
inference(flattening,[],[f119]) ).
fof(f124,plain,
( l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0)
& m1_subset_1(sK1,u1_struct_0(sK0))
& v13_lattices(sK0)
& ~ r1_filter_2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f62]) ).
fof(f125,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( ( ~ r1_filter_2(X0,X1,X2)
| ! [X3] :
( ~ m1_subset_1(X3,X0)
| ( ( ~ r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1) ) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,X0)
& ( r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| r1_filter_2(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f126,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( ( ~ r1_filter_2(X0,X1,X2)
| ! [X3] :
( ~ m1_subset_1(X3,X0)
| ( ( ~ r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1) ) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,X0)
& ( r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| r1_filter_2(X0,X1,X2) ) ) ) ) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( ( ~ r1_filter_2(X0,X1,X2)
| ! [X4] :
( ~ m1_subset_1(X4,X0)
| ( ( ~ r2_hidden(X4,X1)
| r2_hidden(X4,X2) )
& ( ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,X0)
& ( r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| r1_filter_2(X0,X1,X2) ) ) ) ) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( ( ~ r1_filter_2(X0,X1,X2)
| ! [X4] :
( ~ m1_subset_1(X4,X0)
| ( ( ~ r2_hidden(X4,X1)
| r2_hidden(X4,X2) )
& ( ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ) )
& ( ( m1_subset_1(sK2(X0,X1,X2),X0)
& ( r2_hidden(sK2(X0,X1,X2),X1)
| r2_hidden(sK2(X0,X1,X2),X2) )
& ( ~ r2_hidden(sK2(X0,X1,X2),X1)
| ~ r2_hidden(sK2(X0,X1,X2),X2) ) )
| r1_filter_2(X0,X1,X2) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f127]) ).
fof(f148,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( ( ~ r2_hidden(X1,k18_filter_2(X0,X2))
| r3_lattices(X0,X1,X2) )
& ( ~ r3_lattices(X0,X1,X2)
| r2_hidden(X1,k18_filter_2(X0,X2)) ) ) ) ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f151,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( ( ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) )
& ( ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f152,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( ( ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) )
& ( ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ) ) ) ) ) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f124]) ).
fof(f154,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f124]) ).
fof(f155,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f124]) ).
fof(f156,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f124]) ).
fof(f157,plain,
v13_lattices(sK0),
inference(cnf_transformation,[],[f124]) ).
fof(f158,plain,
~ r1_filter_2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),
inference(cnf_transformation,[],[f124]) ).
fof(f171,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| m1_subset_1(sK2(X0,X1,X2),X0)
| r1_filter_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f128]) ).
fof(f172,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| r2_hidden(sK2(X0,X1,X2),X1)
| r2_hidden(sK2(X0,X1,X2),X2)
| r1_filter_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f128]) ).
fof(f173,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ r2_hidden(sK2(X0,X1,X2),X1)
| ~ r2_hidden(sK2(X0,X1,X2),X2)
| r1_filter_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f128]) ).
fof(f175,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k18_filter_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_lattice4(k22_filter_2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f178,plain,
! [X0] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f180,plain,
! [X0] :
( ~ l2_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f181,plain,
! [X0] :
( ~ l3_lattices(X0)
| l2_lattices(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f182,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f183,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,[],[f81]) ).
fof(f185,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,[],[f83]) ).
fof(f193,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X1,k18_filter_2(X0,X2))
| r3_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f148]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| r2_hidden(X1,k18_filter_2(X0,X2)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f227,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v13_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| r3_lattices(X0,k5_lattices(X0),X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f230,plain,
! [X2,X3,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| r3_lattices(X0,X3,X2) ),
inference(cnf_transformation,[],[f152]) ).
fof(f232,plain,
! [X2,X3,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_49,negated_conjecture,
~ r1_filter_2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),
inference(cnf_transformation,[],[f158]) ).
tcf(c_50,negated_conjecture,
v13_lattices(sK0),
inference(cnf_transformation,[],[f157]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f156]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f155]) ).
tcf(c_53,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_54,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f153]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X0)
| r1_filter_2(X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ r2_hidden(sK2(X0,X1,X2),X2)
| ~ r2_hidden(sK2(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| r1_filter_2(X1,X0,X2)
| r2_hidden(sK2(X1,X0,X2),X2)
| r2_hidden(sK2(X1,X0,X2),X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| r1_filter_2(X1,X0,X2)
| m1_subset_1(sK2(X1,X0,X2),X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_filter_2(k18_filter_2(X1,X0),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m2_lattice4(k22_filter_2(X1,X0,X2),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_72,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0))
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_74,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_75,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_76,plain,
! [X0: $i] :
( l2_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_78,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,[],[f183]) ).
tcf(c_79,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,[],[f185]) ).
tcf(c_87,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(X1,k18_filter_2(X0,X2))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X2)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ r2_hidden(X0,k18_filter_2(X1,X2)) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,k5_lattices(X1),X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X3)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ r3_lattices(X1,X2,X3)
| ~ r2_hidden(X0,k22_filter_2(X1,X2,X3)) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_135,plain,
( l2_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_136,plain,
( l1_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_137,plain,
( l1_struct_0(sK0)
| ~ l2_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_148,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_150,plain,
( v3_struct_0(sK0)
| m1_subset_1(k5_lattices(sK0),u1_struct_0(sK0))
| ~ l1_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_filter_2(X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ r2_hidden(sK2(X0,X1,X2),X2)
| ~ r2_hidden(sK2(X0,X1,X2),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_123]) ).
tcf(c_2133,plain,
( v3_struct_0(sK0)
| m2_filter_2(k18_filter_2(sK0,sK1),sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_2147,plain,
( v3_struct_0(sK0)
| r3_lattices(sK0,k5_lattices(sK0),sK1)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ v13_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_2160,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| m2_lattice4(k22_filter_2(sK0,X0,sK1),sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_2305,plain,
( v3_struct_0(sK0)
| m2_lattice4(k18_filter_2(sK0,sK1),sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m2_filter_2(k18_filter_2(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_2310,plain,
( v3_struct_0(sK0)
| m2_lattice4(k22_filter_2(sK0,k5_lattices(sK0),sK1),sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(k5_lattices(sK0),u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_2160]) ).
tcf(c_2981,plain,
( v3_struct_0(sK0)
| m1_subset_1(k22_filter_2(sK0,k5_lattices(sK0),sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m2_lattice4(k22_filter_2(sK0,k5_lattices(sK0),sK1),sK0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_3459,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| r2_hidden(X0,k18_filter_2(sK0,sK1))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_3475,plain,
( v1_xboole_0(u1_struct_0(sK0))
| r1_filter_2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1))
| r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k18_filter_2(sK0,sK1))
| r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k22_filter_2(sK0,k5_lattices(sK0),sK1))
| ~ m1_subset_1(k18_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(k22_filter_2(sK0,k5_lattices(sK0),sK1),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3476,plain,
( v1_xboole_0(u1_struct_0(sK0))
| r1_filter_2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1))
| m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0))
| ~ m1_subset_1(k18_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(k22_filter_2(sK0,k5_lattices(sK0),sK1),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3518,plain,
( v3_struct_0(sK0)
| m1_subset_1(k18_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m2_lattice4(k18_filter_2(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_3666,plain,
( r1_filter_2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1))
| ~ m1_subset_1(k18_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(k22_filter_2(sK0,k5_lattices(sK0),sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k18_filter_2(sK0,sK1))
| ~ r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k22_filter_2(sK0,k5_lattices(sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_327]) ).
tcf(c_3692,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k22_filter_2(sK0,X1,X0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X0)
| ~ m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)))
| ~ r3_lattices(sK0,sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),X0) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_3697,plain,
( v3_struct_0(sK0)
| r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k18_filter_2(sK0,sK1))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r3_lattices(sK0,sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),sK1)
| ~ m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_3459]) ).
tcf(c_4195,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k22_filter_2(sK0,k5_lattices(sK0),X0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ m1_subset_1(k5_lattices(sK0),u1_struct_0(sK0))
| ~ r3_lattices(sK0,k5_lattices(sK0),X0)
| ~ m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0))
| ~ r3_lattices(sK0,sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),X0)
| ~ r3_lattices(sK0,k5_lattices(sK0),sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1))) ),
inference(instantiation,[status(thm)],[c_3692]) ).
tcf(c_4290,plain,
( v3_struct_0(sK0)
| r3_lattices(sK0,sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),sK1)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0))
| ~ r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k18_filter_2(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_4293,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| r3_lattices(sK0,sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),sK1)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0))
| ~ r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k22_filter_2(sK0,X0,sK1)) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_6144,plain,
( v3_struct_0(sK0)
| r3_lattices(sK0,k5_lattices(sK0),sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ v13_lattices(sK0)
| ~ m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_6859,plain,
( v3_struct_0(sK0)
| r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k22_filter_2(sK0,k5_lattices(sK0),sK1))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r3_lattices(sK0,k5_lattices(sK0),sK1)
| ~ m1_subset_1(k5_lattices(sK0),u1_struct_0(sK0))
| ~ r3_lattices(sK0,sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),sK1)
| ~ m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0))
| ~ r3_lattices(sK0,k5_lattices(sK0),sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1))) ),
inference(instantiation,[status(thm)],[c_4195]) ).
tcf(c_7104,plain,
( v3_struct_0(sK0)
| r3_lattices(sK0,sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),sK1)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r3_lattices(sK0,k5_lattices(sK0),sK1)
| ~ m1_subset_1(k5_lattices(sK0),u1_struct_0(sK0))
| ~ m1_subset_1(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),u1_struct_0(sK0))
| ~ r2_hidden(sK2(u1_struct_0(sK0),k18_filter_2(sK0,sK1),k22_filter_2(sK0,k5_lattices(sK0),sK1)),k22_filter_2(sK0,k5_lattices(sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_4293]) ).
tcf(c_7515,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7104,c_6859,c_6144,c_4290,c_3697,c_3666,c_3518,c_3476,c_3475,c_2981,c_2310,c_2305,c_2147,c_2133,c_49,c_150,c_148,c_137,c_136,c_135,c_51,c_52,c_50,c_53,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT330+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 21:11:39 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.46 % Proving...
% 29.64/5.83 % SZS status Started for theBenchmark.p
% 29.64/5.83 % SZS status Theorem for theBenchmark.p
% 29.64/5.83
% 29.64/5.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.64/5.83
% 29.64/5.83 % ------ iProver source info
% 29.64/5.83
% 29.64/5.83 % git: date: 2026-07-19 20:42:38 +0200
% 29.64/5.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.64/5.83 % git: non_committed_changes: false
% 29.64/5.83
% 29.64/5.83 % ------ Parsing...
% 29.64/5.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 29.64/5.83
% 29.64/5.83 % ------ Preprocessing...%
% 29.64/5.83
% 29.64/5.83 % ------ Preprocessing...%
% 29.64/5.83
% 29.64/5.83 % ------ Preprocessing...
% 29.64/5.83 % ------ Proving...
% 29.64/5.83 % ------ Problem Properties
% 29.64/5.83
% 29.64/5.83 %
% 29.64/5.83 % clauses 80
% 29.64/5.83 % conjectures 6
% 29.64/5.83 % EPR 33
% 29.64/5.83 % Horn 42
% 29.64/5.83 % unary 20
% 29.64/5.83 % binary 11
% 29.64/5.83 % lits 296
% 29.64/5.83 % lits eq 7
% 29.64/5.83 % fd_pure 0
% 29.64/5.83 % fd_pseudo 0
% 29.64/5.83 % fd_cond 1
% 29.64/5.83 % fd_pseudo_cond 4
% 29.64/5.83 % AC symbols 0
% 29.64/5.83
% 29.64/5.83 % ------ Input Options Time Limit: Unbounded
% 29.64/5.83
% 29.64/5.83
% 29.64/5.83 % ------
% 29.64/5.83 % Current options:
% 29.64/5.83 % ------
% 29.64/5.83
% 29.64/5.83
% 29.64/5.83 %
% 29.64/5.83
% 29.64/5.83 % ------ Proving...
% 29.64/5.83 %
% 29.64/5.83
% 29.64/5.83 % SZS status Theorem for theBenchmark.p
% 29.64/5.83
% 29.64/5.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.64/5.83
%------------------------------------------------------------------------------