%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT310+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:59:13 PM UTC 2026
% Result : Theorem 4.03s 1.24s
% Output : CNFRefutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 13
% Syntax : Number of formulae : 170 ( 46 unt; 6 def)
% Number of atoms : 893 ( 64 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1035 ( 420 ~; 515 |; 76 &)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 16 ( 14 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 232 ( 1 sgn 221 !; 11 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [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) )
=> ! [X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2) )
=> ! [X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X3) )
=> ( r1_tarski(k19_filter_2(X0,k19_filter_2(X0,X1)),k19_filter_2(X0,X1))
& ( r1_tarski(X2,X3)
=> r1_tarski(k19_filter_2(X0,X2),k19_filter_2(X0,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_2) ).
fof(f2,negated_conjecture,
~ ! [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) )
=> ! [X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2) )
=> ! [X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X3) )
=> ( r1_tarski(k19_filter_2(X0,k19_filter_2(X0,X1)),k19_filter_2(X0,X1))
& ( r1_tarski(X2,X3)
=> r1_tarski(k19_filter_2(X0,X2),k19_filter_2(X0,X3)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,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) )
=> ! [X2] :
( m2_filter_2(X2,X0)
=> ( X2 = k19_filter_2(X0,X1)
<=> ( ! [X3] :
( m2_filter_2(X3,X0)
=> ( r1_tarski(X1,X3)
=> r1_tarski(X2,X3) ) )
& r1_tarski(X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_2) ).
fof(f8,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1)
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m2_filter_2(k19_filter_2(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_filter_2) ).
fof(f16,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/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(f17,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/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(f36,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( r1_tarski(X1,X2)
& r1_tarski(X0,X1) )
=> r1_tarski(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f46,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f36]) ).
fof(f48,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)
& ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2)
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X3)
& ( ~ r1_tarski(k19_filter_2(X0,k19_filter_2(X0,X1)),k19_filter_2(X0,X1))
| ( r1_tarski(X2,X3)
& ~ r1_tarski(k19_filter_2(X0,X2),k19_filter_2(X0,X3)) ) ) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f49,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)
& ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2)
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X3)
& ( ~ r1_tarski(k19_filter_2(X0,k19_filter_2(X0,X1)),k19_filter_2(X0,X1))
| ( r1_tarski(X2,X3)
& ~ r1_tarski(k19_filter_2(X0,X2),k19_filter_2(X0,X3)) ) ) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f55,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)
| ! [X2] :
( ~ m2_filter_2(X2,X0)
| ( X2 = k19_filter_2(X0,X1)
<=> ( ! [X3] :
( ~ m2_filter_2(X3,X0)
| ~ r1_tarski(X1,X3)
| r1_tarski(X2,X3) )
& r1_tarski(X1,X2) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f56,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)
| ! [X2] :
( ~ m2_filter_2(X2,X0)
| ( X2 = k19_filter_2(X0,X1)
<=> ( ! [X3] :
( ~ m2_filter_2(X3,X0)
| ~ r1_tarski(X1,X3)
| r1_tarski(X2,X3) )
& r1_tarski(X1,X2) ) ) ) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k19_filter_2(X0,X1),X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k19_filter_2(X0,X1),X0) ),
inference(flattening,[],[f57]) ).
fof(f62,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,[],[f16]) ).
fof(f63,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,[],[f62]) ).
fof(f64,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,[],[f17]) ).
fof(f65,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,[],[f64]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(X0,X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(X0,X2) ),
inference(flattening,[],[f78]) ).
fof(f88,plain,
( l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0)
& m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK1)
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK2)
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK3)
& ( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ( r1_tarski(sK2,sK3)
& ~ r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f49]) ).
fof(f89,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)
| ! [X2] :
( ~ m2_filter_2(X2,X0)
| ( ( k19_filter_2(X0,X1) != X2
| ( ! [X3] :
( ~ m2_filter_2(X3,X0)
| ~ r1_tarski(X1,X3)
| r1_tarski(X2,X3) )
& r1_tarski(X1,X2) ) )
& ( ? [X3] :
( m2_filter_2(X3,X0)
& r1_tarski(X1,X3)
& ~ r1_tarski(X2,X3) )
| ~ r1_tarski(X1,X2)
| X2 = k19_filter_2(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f90,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)
| ! [X2] :
( ~ m2_filter_2(X2,X0)
| ( ( k19_filter_2(X0,X1) != X2
| ( ! [X3] :
( ~ m2_filter_2(X3,X0)
| ~ r1_tarski(X1,X3)
| r1_tarski(X2,X3) )
& r1_tarski(X1,X2) ) )
& ( ? [X3] :
( m2_filter_2(X3,X0)
& r1_tarski(X1,X3)
& ~ r1_tarski(X2,X3) )
| ~ r1_tarski(X1,X2)
| X2 = k19_filter_2(X0,X1) ) ) ) ) ),
inference(flattening,[],[f89]) ).
fof(f91,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)
| ! [X2] :
( ~ m2_filter_2(X2,X0)
| ( ( k19_filter_2(X0,X1) != X2
| ( ! [X4] :
( ~ m2_filter_2(X4,X0)
| ~ r1_tarski(X1,X4)
| r1_tarski(X2,X4) )
& r1_tarski(X1,X2) ) )
& ( ? [X3] :
( m2_filter_2(X3,X0)
& r1_tarski(X1,X3)
& ~ r1_tarski(X2,X3) )
| ~ r1_tarski(X1,X2)
| X2 = k19_filter_2(X0,X1) ) ) ) ) ),
inference(rectify,[],[f90]) ).
fof(f92,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)
| ! [X2] :
( ~ m2_filter_2(X2,X0)
| ( ( k19_filter_2(X0,X1) != X2
| ( ! [X4] :
( ~ m2_filter_2(X4,X0)
| ~ r1_tarski(X1,X4)
| r1_tarski(X2,X4) )
& r1_tarski(X1,X2) ) )
& ( ( m2_filter_2(sK4(X0,X1,X2),X0)
& r1_tarski(X1,sK4(X0,X1,X2))
& ~ r1_tarski(X2,sK4(X0,X1,X2)) )
| ~ r1_tarski(X1,X2)
| X2 = k19_filter_2(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f91]) ).
fof(f108,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f88]) ).
fof(f109,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f88]) ).
fof(f110,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f88]) ).
fof(f111,plain,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f88]) ).
fof(f112,plain,
~ v1_xboole_0(sK1),
inference(cnf_transformation,[],[f88]) ).
fof(f113,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f88]) ).
fof(f114,plain,
~ v1_xboole_0(sK2),
inference(cnf_transformation,[],[f88]) ).
fof(f115,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f88]) ).
fof(f116,plain,
~ v1_xboole_0(sK3),
inference(cnf_transformation,[],[f88]) ).
fof(f117,plain,
( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| r1_tarski(sK2,sK3) ),
inference(cnf_transformation,[],[f88]) ).
fof(f118,plain,
( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ~ r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f129,plain,
! [X2,X0,X1,X4] :
( ~ 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)
| ~ m2_filter_2(X2,X0)
| k19_filter_2(X0,X1) != X2
| ~ m2_filter_2(X4,X0)
| ~ r1_tarski(X1,X4)
| r1_tarski(X2,X4) ),
inference(cnf_transformation,[],[f92]) ).
fof(f130,plain,
! [X2,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)
| ~ m2_filter_2(X2,X0)
| k19_filter_2(X0,X1) != X2
| r1_tarski(X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f131,plain,
! [X2,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)
| ~ m2_filter_2(X2,X0)
| m2_filter_2(sK4(X0,X1,X2),X0)
| ~ r1_tarski(X1,X2)
| k19_filter_2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f132,plain,
! [X2,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)
| ~ m2_filter_2(X2,X0)
| r1_tarski(X1,sK4(X0,X1,X2))
| ~ r1_tarski(X1,X2)
| k19_filter_2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f133,plain,
! [X2,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)
| ~ m2_filter_2(X2,X0)
| ~ r1_tarski(X2,sK4(X0,X1,X2))
| ~ r1_tarski(X1,X2)
| k19_filter_2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f134,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k19_filter_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f139,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,[],[f63]) ).
fof(f140,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(X1,X0)
| ~ v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f141,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,[],[f65]) ).
fof(f164,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(X0,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f175,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)
| ~ m2_filter_2(k19_filter_2(X0,X1),X0)
| r1_tarski(X1,k19_filter_2(X0,X1)) ),
inference(equality_resolution,[],[f130]) ).
fof(f176,plain,
! [X0,X1,X4] :
( ~ 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)
| ~ m2_filter_2(k19_filter_2(X0,X1),X0)
| ~ m2_filter_2(X4,X0)
| ~ r1_tarski(X1,X4)
| r1_tarski(k19_filter_2(X0,X1),X4) ),
inference(equality_resolution,[],[f129]) ).
tcf(c_49,negated_conjecture,
( ~ r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3))
| ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1)) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_50,negated_conjecture,
( r1_tarski(sK2,sK3)
| ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_51,negated_conjecture,
~ v1_xboole_0(sK3),
inference(cnf_transformation,[],[f116]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f115]) ).
tcf(c_53,negated_conjecture,
~ v1_xboole_0(sK2),
inference(cnf_transformation,[],[f114]) ).
tcf(c_54,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f113]) ).
tcf(c_55,negated_conjecture,
~ v1_xboole_0(sK1),
inference(cnf_transformation,[],[f112]) ).
tcf(c_56,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f111]) ).
tcf(c_57,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f110]) ).
tcf(c_58,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f109]) ).
tcf(c_59,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f108]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v1_xboole_0(X2)
| ( k19_filter_2(X1,X2) = X0 )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X0,X1)
| ~ r1_tarski(X2,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_tarski(X0,sK4(X1,X2,X0)) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v1_xboole_0(X0)
| r1_tarski(X0,sK4(X1,X0,X2))
| ( k19_filter_2(X1,X0) = X2 )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X2,X1)
| ~ r1_tarski(X0,X2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v1_xboole_0(X0)
| m2_filter_2(sK4(X1,X0,X2),X1)
| ( k19_filter_2(X1,X0) = X2 )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X2,X1)
| ~ r1_tarski(X0,X2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_xboole_0(X1)
| r1_tarski(X1,k19_filter_2(X0,X1))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_filter_2(k19_filter_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| v1_xboole_0(X1)
| r1_tarski(k19_filter_2(X0,X1),X2)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m2_filter_2(X2,X0)
| ~ r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_filter_2(k19_filter_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_xboole_0(X0)
| m2_filter_2(k19_filter_2(X1,X0),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v1_xboole_0(X0)
| ~ m2_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_79,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,[],[f139]) ).
tcf(c_80,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,[],[f141]) ).
tcf(c_103,plain,
! [X0: $i] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f164]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_tarski(X2,X1)
| ~ r1_tarski(X2,X0)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_xboole_0(X0)
| r1_tarski(X0,k19_filter_2(X1,X0))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_71,c_73]) ).
tcf(c_581,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v1_xboole_0(X0)
| r1_tarski(k19_filter_2(X1,X0),X2)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X2,X1)
| ~ r1_tarski(X0,X2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_72,c_73]) ).
tcf(c_1054,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_79,c_80]) ).
tcf(c_1055,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_1054]) ).
tcf(c_1274,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_58,c_1055]) ).
tcf(c_1275,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_1274]) ).
tcf(c_1277,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_1275,c_59,c_57,c_1275]) ).
tcf(c_1278,plain,
! [X0: $i] :
( m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m2_filter_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_1277]) ).
tcf(c_1286,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| v1_xboole_0(X1)
| r1_tarski(k19_filter_2(X0,X1),X2)
| ~ l3_lattices(X0)
| ~ m2_filter_2(X2,X0)
| ~ r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_581]) ).
tcf(c_1287,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v1_xboole_0(X0)
| r1_tarski(k19_filter_2(sK0,X0),X1)
| ~ l3_lattices(sK0)
| ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_1286]) ).
tcf(c_1289,plain,
! [X0: $i,X1: $i] :
( ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| r1_tarski(k19_filter_2(sK0,X0),X1)
| v1_xboole_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1287,c_59,c_57,c_1287]) ).
tcf(c_1290,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| r1_tarski(k19_filter_2(sK0,X0),X1)
| ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_1289]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_xboole_0(X1)
| r1_tarski(X1,k19_filter_2(X0,X1))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_580]) ).
tcf(c_1308,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v1_xboole_0(X0)
| r1_tarski(X0,k19_filter_2(sK0,X0))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_1307]) ).
tcf(c_1310,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| r1_tarski(X0,k19_filter_2(sK0,X0))
| v1_xboole_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1308,c_59,c_57,c_1308]) ).
tcf(c_1311,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| r1_tarski(X0,k19_filter_2(sK0,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_1310]) ).
tcf(c_1322,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_78]) ).
tcf(c_1323,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| ~ v1_xboole_0(X0)
| ~ m2_filter_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_1322]) ).
tcf(c_1325,plain,
! [X0: $i] :
( ~ v1_xboole_0(X0)
| ~ m2_filter_2(X0,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_1323,c_59,c_57,c_1323]) ).
tcf(c_1334,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_xboole_0(X1)
| m2_filter_2(k19_filter_2(X0,X1),X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_73]) ).
tcf(c_1335,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v1_xboole_0(X0)
| m2_filter_2(k19_filter_2(sK0,X0),sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_1334]) ).
tcf(c_1337,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| m2_filter_2(k19_filter_2(sK0,X0),sK0)
| v1_xboole_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1335,c_59,c_57,c_1335]) ).
tcf(c_1338,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| m2_filter_2(k19_filter_2(sK0,X0),sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_1337]) ).
tcf(c_1349,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| v1_xboole_0(X1)
| m2_filter_2(sK4(X0,X1,X2),X0)
| ( k19_filter_2(X0,X1) = X2 )
| ~ l3_lattices(X0)
| ~ m2_filter_2(X2,X0)
| ~ r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_70]) ).
tcf(c_1350,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v1_xboole_0(X0)
| m2_filter_2(sK4(sK0,X0,X1),sK0)
| ( k19_filter_2(sK0,X0) = X1 )
| ~ l3_lattices(sK0)
| ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_1349]) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i] :
( ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ( k19_filter_2(sK0,X0) = X1 )
| m2_filter_2(sK4(sK0,X0,X1),sK0)
| v1_xboole_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1350,c_59,c_57,c_1350]) ).
tcf(c_1353,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| m2_filter_2(sK4(sK0,X0,X1),sK0)
| ( k19_filter_2(sK0,X0) = X1 )
| ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_1352]) ).
tcf(c_1373,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| v1_xboole_0(X1)
| r1_tarski(X1,sK4(X0,X1,X2))
| ( k19_filter_2(X0,X1) = X2 )
| ~ l3_lattices(X0)
| ~ m2_filter_2(X2,X0)
| ~ r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_69]) ).
tcf(c_1374,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v1_xboole_0(X0)
| r1_tarski(X0,sK4(sK0,X0,X1))
| ( k19_filter_2(sK0,X0) = X1 )
| ~ l3_lattices(sK0)
| ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_1373]) ).
tcf(c_1376,plain,
! [X0: $i,X1: $i] :
( ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ( k19_filter_2(sK0,X0) = X1 )
| r1_tarski(X0,sK4(sK0,X0,X1))
| v1_xboole_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1374,c_59,c_57,c_1374]) ).
tcf(c_1377,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| r1_tarski(X0,sK4(sK0,X0,X1))
| ( k19_filter_2(sK0,X0) = X1 )
| ~ m2_filter_2(X1,sK0)
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_1376]) ).
tcf(c_1397,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| v1_xboole_0(X2)
| ( k19_filter_2(X0,X2) = X1 )
| ~ l3_lattices(X0)
| ~ m2_filter_2(X1,X0)
| ~ r1_tarski(X2,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,sK4(X0,X2,X1))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_68]) ).
tcf(c_1398,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v1_xboole_0(X1)
| ( k19_filter_2(sK0,X1) = X0 )
| ~ l3_lattices(sK0)
| ~ m2_filter_2(X0,sK0)
| ~ r1_tarski(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ r1_tarski(X0,sK4(sK0,X1,X0)) ),
inference(unflattening,[status(thm)],[c_1397]) ).
tcf(c_1400,plain,
! [X0: $i,X1: $i] :
( ~ m2_filter_2(X0,sK0)
| ~ r1_tarski(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ r1_tarski(X0,sK4(sK0,X1,X0))
| ( k19_filter_2(sK0,X1) = X0 )
| v1_xboole_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1398,c_59,c_57,c_1398]) ).
tcf(c_1401,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| ( k19_filter_2(sK0,X1) = X0 )
| ~ m2_filter_2(X0,sK0)
| ~ r1_tarski(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ r1_tarski(X0,sK4(sK0,X1,X0)) ),
inference(renaming,[status(thm)],[c_1400]) ).
tcf(c_4359,plain,
! [X0: $i] :
( ~ m2_filter_2(X0,sK0)
| ~ v1_xboole_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_1325]) ).
tcf(c_4360,plain,
! [X0: $i] :
( ~ v1_xboole_0(X0)
| ~ m2_filter_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_4359]) ).
tcf(c_4415,plain,
! [X0: $i] :
( m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m2_filter_2(X0,sK0) ),
inference(prop_impl_just,[status(thm)],[c_1278]) ).
tcf(c_7592,definition,
iPr_def_11 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_7593,definition,
iPr_def_12 = k1_zfmisc_1(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_7597,definition,
iPr_def_16 = k19_filter_2(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_7598,definition,
iPr_def_17 = k19_filter_2(sK0,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_7599,definition,
iPr_def_18 = k19_filter_2(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_7600,definition,
iPr_def_19 = k19_filter_2(sK0,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_7608,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| ( k19_filter_2(sK0,X1) = X0 )
| ~ m2_filter_2(X0,sK0)
| ~ m1_subset_1(X1,iPr_def_12)
| ~ r1_tarski(X1,X0)
| ~ r1_tarski(X0,sK4(sK0,X1,X0)) ),
inference(demodulation,[status(thm)],[c_1401]) ).
tcf(c_7609,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| r1_tarski(X0,sK4(sK0,X0,X1))
| ( k19_filter_2(sK0,X0) = X1 )
| ~ m2_filter_2(X1,sK0)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r1_tarski(X0,X1) ),
inference(demodulation,[status(thm)],[c_1377]) ).
tcf(c_7610,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| m2_filter_2(sK4(sK0,X0,X1),sK0)
| ( k19_filter_2(sK0,X0) = X1 )
| ~ m2_filter_2(X1,sK0)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r1_tarski(X0,X1) ),
inference(demodulation,[status(thm)],[c_1353]) ).
tcf(c_7611,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| m2_filter_2(k19_filter_2(sK0,X0),sK0)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_1338]) ).
tcf(c_7612,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| r1_tarski(X0,k19_filter_2(sK0,X0))
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_1311]) ).
tcf(c_7613,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| r1_tarski(k19_filter_2(sK0,X0),X1)
| ~ m2_filter_2(X1,sK0)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r1_tarski(X0,X1) ),
inference(demodulation,[status(thm)],[c_1290]) ).
tcf(c_7615,negated_conjecture,
m1_subset_1(sK1,iPr_def_12),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_7616,negated_conjecture,
~ v1_xboole_0(sK1),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_7617,negated_conjecture,
m1_subset_1(sK2,iPr_def_12),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_7618,negated_conjecture,
~ v1_xboole_0(sK2),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_7619,negated_conjecture,
m1_subset_1(sK3,iPr_def_12),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_7620,negated_conjecture,
~ v1_xboole_0(sK3),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_7621,negated_conjecture,
( r1_tarski(sK2,sK3)
| ~ r1_tarski(iPr_def_17,iPr_def_16) ),
inference(demodulation,[status(thm)],[c_50,c_7597,c_7598]) ).
tcf(c_7622,negated_conjecture,
( ~ r1_tarski(iPr_def_18,iPr_def_19)
| ~ r1_tarski(iPr_def_17,iPr_def_16) ),
inference(demodulation,[status(thm)],[c_49,c_7600,c_7599]) ).
tcf(c_8854,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| v1_xboole_0(X0)
| ( k19_filter_2(sK0,X0) = k19_filter_2(sK0,X1) )
| ~ m1_subset_1(X1,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ m2_filter_2(k19_filter_2(sK0,X0),sK0)
| ~ r1_tarski(X1,k19_filter_2(sK0,X0))
| ~ m2_filter_2(sK4(sK0,X1,k19_filter_2(sK0,X0)),sK0)
| ~ r1_tarski(X0,sK4(sK0,X1,k19_filter_2(sK0,X0))) ),
inference(superposition,[status(thm)],[c_7613,c_7608]) ).
tcf(c_8872,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| v1_xboole_0(X0)
| ( k19_filter_2(sK0,X0) = k19_filter_2(sK0,X1) )
| ~ m1_subset_1(X1,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r1_tarski(X0,sK4(sK0,X1,k19_filter_2(sK0,X0)))
| ~ m2_filter_2(sK4(sK0,X1,k19_filter_2(sK0,X0)),sK0)
| ~ r1_tarski(X1,k19_filter_2(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_8854,c_7611,c_8854]) ).
tcf(c_8873,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| v1_xboole_0(X0)
| ( k19_filter_2(sK0,X0) = k19_filter_2(sK0,X1) )
| ~ m1_subset_1(X1,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r1_tarski(X1,k19_filter_2(sK0,X0))
| ~ m2_filter_2(sK4(sK0,X1,k19_filter_2(sK0,X0)),sK0)
| ~ r1_tarski(X0,sK4(sK0,X1,k19_filter_2(sK0,X0))) ),
inference(renaming,[status(thm)],[c_8872]) ).
tcf(c_8891,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| v1_xboole_0(X0)
| v1_xboole_0(k19_filter_2(sK0,X0))
| ( k19_filter_2(sK0,k19_filter_2(sK0,X0)) = k19_filter_2(sK0,X1) )
| ~ m1_subset_1(X1,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ m1_subset_1(k19_filter_2(sK0,X0),iPr_def_12)
| ~ r1_tarski(X1,k19_filter_2(sK0,k19_filter_2(sK0,X0)))
| ~ m2_filter_2(sK4(sK0,X1,k19_filter_2(sK0,k19_filter_2(sK0,X0))),sK0)
| ~ r1_tarski(X0,sK4(sK0,X1,k19_filter_2(sK0,k19_filter_2(sK0,X0)))) ),
inference(superposition,[status(thm)],[c_7613,c_8873]) ).
tcf(c_8925,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| v1_xboole_0(k19_filter_2(sK0,X0))
| ( k19_filter_2(sK0,k19_filter_2(sK0,X0)) = k19_filter_2(sK0,X0) )
| ~ m1_subset_1(X0,iPr_def_12)
| ~ m1_subset_1(k19_filter_2(sK0,X0),iPr_def_12)
| ~ m2_filter_2(k19_filter_2(sK0,k19_filter_2(sK0,X0)),sK0)
| ~ r1_tarski(X0,k19_filter_2(sK0,k19_filter_2(sK0,X0)))
| ~ m2_filter_2(sK4(sK0,X0,k19_filter_2(sK0,k19_filter_2(sK0,X0))),sK0) ),
inference(superposition,[status(thm)],[c_7609,c_8891]) ).
tcf(c_8956,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| v1_xboole_0(k19_filter_2(sK0,X0))
| ( k19_filter_2(sK0,k19_filter_2(sK0,X0)) = k19_filter_2(sK0,X0) )
| ~ m1_subset_1(X0,iPr_def_12)
| ~ m1_subset_1(k19_filter_2(sK0,X0),iPr_def_12)
| ~ r1_tarski(X0,k19_filter_2(sK0,k19_filter_2(sK0,X0)))
| ~ m2_filter_2(sK4(sK0,X0,k19_filter_2(sK0,k19_filter_2(sK0,X0))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8925,c_7611]) ).
tcf(c_8978,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| v1_xboole_0(k19_filter_2(sK0,X0))
| ( k19_filter_2(sK0,k19_filter_2(sK0,X0)) = k19_filter_2(sK0,X0) )
| ~ m1_subset_1(X0,iPr_def_12)
| ~ m1_subset_1(k19_filter_2(sK0,X0),iPr_def_12)
| ~ m2_filter_2(k19_filter_2(sK0,k19_filter_2(sK0,X0)),sK0)
| ~ r1_tarski(X0,k19_filter_2(sK0,k19_filter_2(sK0,X0))) ),
inference(superposition,[status(thm)],[c_7610,c_8956]) ).
tcf(c_8994,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| v1_xboole_0(k19_filter_2(sK0,X0))
| ( k19_filter_2(sK0,k19_filter_2(sK0,X0)) = k19_filter_2(sK0,X0) )
| ~ m1_subset_1(X0,iPr_def_12)
| ~ m1_subset_1(k19_filter_2(sK0,X0),iPr_def_12)
| ~ r1_tarski(X0,k19_filter_2(sK0,k19_filter_2(sK0,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8978,c_7611]) ).
tcf(c_9544,plain,
( v1_xboole_0(sK1)
| v1_xboole_0(k19_filter_2(sK0,sK1))
| ( k19_filter_2(sK0,k19_filter_2(sK0,sK1)) = k19_filter_2(sK0,sK1) )
| ~ m1_subset_1(sK1,iPr_def_12)
| ~ m1_subset_1(k19_filter_2(sK0,sK1),iPr_def_12)
| ~ r1_tarski(sK1,k19_filter_2(sK0,iPr_def_16)) ),
inference(superposition,[status(thm)],[c_7597,c_8994]) ).
tcf(c_9548,plain,
( v1_xboole_0(sK1)
| r1_tarski(sK1,iPr_def_16)
| ~ m1_subset_1(sK1,iPr_def_12) ),
inference(superposition,[status(thm)],[c_7597,c_7612]) ).
tcf(c_9549,plain,
( v1_xboole_0(sK1)
| m2_filter_2(iPr_def_16,sK0)
| ~ m1_subset_1(sK1,iPr_def_12) ),
inference(superposition,[status(thm)],[c_7597,c_7611]) ).
tcf(c_9550,plain,
m2_filter_2(iPr_def_16,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_9549,c_7616,c_7615]) ).
tcf(c_9551,plain,
r1_tarski(sK1,iPr_def_16),
inference(forward_subsumption_resolution,[status(thm)],[c_9548,c_7616,c_7615]) ).
tcf(c_9556,plain,
( v1_xboole_0(iPr_def_16)
| v1_xboole_0(sK1)
| ( iPr_def_16 = iPr_def_17 )
| ~ m1_subset_1(iPr_def_16,iPr_def_12)
| ~ m1_subset_1(sK1,iPr_def_12)
| ~ r1_tarski(sK1,iPr_def_17) ),
inference(light_normalisation,[status(thm)],[c_9544,c_7597,c_7598]) ).
tcf(c_9557,plain,
( v1_xboole_0(iPr_def_16)
| ( iPr_def_16 = iPr_def_17 )
| ~ m1_subset_1(iPr_def_16,iPr_def_12)
| ~ r1_tarski(sK1,iPr_def_17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9556,c_7616,c_7615]) ).
tcf(c_9928,plain,
! [X0: $i] :
( v1_xboole_0(sK2)
| r1_tarski(iPr_def_18,X0)
| ~ m1_subset_1(sK2,iPr_def_12)
| ~ m2_filter_2(X0,sK0)
| ~ r1_tarski(sK2,X0) ),
inference(superposition,[status(thm)],[c_7599,c_7613]) ).
tcf(c_9933,plain,
! [X0: $i] :
( r1_tarski(iPr_def_18,X0)
| ~ m2_filter_2(X0,sK0)
| ~ r1_tarski(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9928,c_7618,c_7617]) ).
tcf(c_10049,plain,
( v1_xboole_0(sK3)
| r1_tarski(sK3,iPr_def_19)
| ~ m1_subset_1(sK3,iPr_def_12) ),
inference(superposition,[status(thm)],[c_7600,c_7612]) ).
tcf(c_10050,plain,
( v1_xboole_0(sK3)
| m2_filter_2(iPr_def_19,sK0)
| ~ m1_subset_1(sK3,iPr_def_12) ),
inference(superposition,[status(thm)],[c_7600,c_7611]) ).
tcf(c_10051,plain,
m2_filter_2(iPr_def_19,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_10050,c_7620,c_7619]) ).
tcf(c_10052,plain,
r1_tarski(sK3,iPr_def_19),
inference(forward_subsumption_resolution,[status(thm)],[c_10049,c_7620,c_7619]) ).
tcf(c_10191,plain,
( r1_tarski(iPr_def_18,iPr_def_19)
| ~ r1_tarski(sK2,iPr_def_19) ),
inference(superposition,[status(thm)],[c_10051,c_9933]) ).
tcf(c_10512,plain,
! [X0: $i] :
( m1_subset_1(X0,iPr_def_12)
| ~ m2_filter_2(X0,sK0) ),
inference(light_normalisation,[status(thm)],[c_4415,c_7592,c_7593]) ).
tcf(c_10522,plain,
m1_subset_1(iPr_def_16,iPr_def_12),
inference(superposition,[status(thm)],[c_9550,c_10512]) ).
tcf(c_10540,plain,
( v1_xboole_0(iPr_def_16)
| ( iPr_def_16 = iPr_def_17 )
| ~ r1_tarski(sK1,iPr_def_17) ),
inference(backward_subsumption_resolution,[status(thm)],[c_9557,c_10522]) ).
tcf(c_10829,plain,
! [X0: $i] :
( r1_tarski(sK1,X0)
| ~ r1_tarski(iPr_def_16,X0) ),
inference(superposition,[status(thm)],[c_9551,c_105]) ).
tcf(c_11152,plain,
( v1_xboole_0(iPr_def_16)
| r1_tarski(sK1,k19_filter_2(sK0,iPr_def_16))
| ~ m1_subset_1(iPr_def_16,iPr_def_12) ),
inference(superposition,[status(thm)],[c_7612,c_10829]) ).
tcf(c_11154,plain,
( v1_xboole_0(iPr_def_16)
| r1_tarski(sK1,iPr_def_17)
| ~ m1_subset_1(iPr_def_16,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_11152,c_7598]) ).
tcf(c_11155,plain,
( v1_xboole_0(iPr_def_16)
| r1_tarski(sK1,iPr_def_17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11154,c_10522]) ).
tcf(c_11216,plain,
( v1_xboole_0(iPr_def_16)
| ( iPr_def_16 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_10540,c_9557,c_10522,c_11155]) ).
tcf(c_11714,plain,
~ v1_xboole_0(iPr_def_16),
inference(superposition,[status(thm)],[c_9550,c_4360]) ).
tcf(c_11727,plain,
iPr_def_16 = iPr_def_17,
inference(backward_subsumption_resolution,[status(thm)],[c_11216,c_11714]) ).
tcf(c_11739,plain,
( ~ r1_tarski(iPr_def_18,iPr_def_19)
| ~ r1_tarski(iPr_def_16,iPr_def_16) ),
inference(demodulation,[status(thm)],[c_7622,c_11727]) ).
tcf(c_11740,plain,
( r1_tarski(sK2,sK3)
| ~ r1_tarski(iPr_def_16,iPr_def_16) ),
inference(demodulation,[status(thm)],[c_7621,c_11727]) ).
tcf(c_11741,plain,
r1_tarski(sK2,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_11740,c_103]) ).
tcf(c_11742,plain,
~ r1_tarski(iPr_def_18,iPr_def_19),
inference(forward_subsumption_resolution,[status(thm)],[c_11739,c_103]) ).
tcf(c_11743,plain,
~ r1_tarski(sK2,iPr_def_19),
inference(backward_subsumption_resolution,[status(thm)],[c_10191,c_11742]) ).
tcf(c_11918,plain,
! [X0: $i] :
( r1_tarski(sK2,X0)
| ~ r1_tarski(sK3,X0) ),
inference(superposition,[status(thm)],[c_11741,c_105]) ).
tcf(c_12472,plain,
r1_tarski(sK2,iPr_def_19),
inference(superposition,[status(thm)],[c_10052,c_11918]) ).
tcf(c_12482,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12472,c_11743]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT310+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 21:01:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 4.03/1.24 % SZS status Started for theBenchmark.p
% 4.03/1.24 % SZS status Theorem for theBenchmark.p
% 4.03/1.24
% 4.03/1.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.03/1.24
% 4.03/1.24 % ------ iProver source info
% 4.03/1.24
% 4.03/1.24 % git: date: 2026-07-19 20:42:38 +0200
% 4.03/1.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.03/1.24 % git: non_committed_changes: false
% 4.03/1.24
% 4.03/1.24 % ------ Parsing...
% 4.03/1.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.03/1.24
% 4.03/1.24 % ------ 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: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 4.03/1.24
% 4.03/1.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.03/1.24
% 4.03/1.24 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.03/1.24 % ------ Proving...
% 4.03/1.24 % ------ Problem Properties
% 4.03/1.24
% 4.03/1.24 %
% 4.03/1.24 % clauses 71
% 4.03/1.24 % conjectures 9
% 4.03/1.24 % EPR 31
% 4.03/1.24 % Horn 59
% 4.03/1.24 % unary 36
% 4.03/1.24 % binary 24
% 4.03/1.24 % lits 128
% 4.03/1.24 % lits eq 15
% 4.03/1.24 % fd_pure 0
% 4.03/1.24 % fd_pseudo 0
% 4.03/1.24 % fd_cond 1
% 4.03/1.24 % fd_pseudo_cond 4
% 4.03/1.24 % AC symbols 0
% 4.03/1.24
% 4.03/1.24 % ------ Schedule dynamic 5 is on
% 4.03/1.24
% 4.03/1.24 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.03/1.24
% 4.03/1.24
% 4.03/1.24 % ------
% 4.03/1.24 % Current options:
% 4.03/1.24 % ------
% 4.03/1.24
% 4.03/1.24
% 4.03/1.24 %
% 4.03/1.24
% 4.03/1.24 % ------ Proving...
% 4.03/1.24 %
% 4.03/1.24
% 4.03/1.24 % SZS status Theorem for theBenchmark.p
% 4.03/1.24
% 4.03/1.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.03/1.25
% 4.03/1.25
%------------------------------------------------------------------------------