%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT329+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 : n002.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 01:59:20 PM UTC 2026
% Result : Theorem 12.63s 2.80s
% Output : CNFRefutation 15.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 25
% Syntax : Number of formulae : 277 ( 39 unt; 5 def)
% Number of atoms : 1468 ( 78 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 1580 ( 677 ~; 764 |; 94 &)
% ( 10 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 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 : 21 ( 19 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 467 ( 0 sgn 455 !; 12 ?; 237 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( v14_lattices(X0)
=> r1_filter_2(u1_struct_0(X0),k2_filter_2(X0,X1),k22_filter_2(X0,X1,k6_lattices(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_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))
=> ( v14_lattices(X0)
=> r1_filter_2(u1_struct_0(X0),k2_filter_2(X0,X1),k22_filter_2(X0,X1,k6_lattices(X0))) ) ) ),
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(f8,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k2_filter_0(X0,X1) = a_2_0_filter_0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_filter_0) ).
fof(f11,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(f12,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_filter_0(k2_filter_0(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_filter_0) ).
fof(f14,axiom,
! [X0] :
( ( l2_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k6_lattices(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).
fof(f15,axiom,
! [X0] :
( l1_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f17,axiom,
! [X0] :
( l2_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f18,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] :
( m1_filter_0(X1,X0)
=> ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_0) ).
fof(f22,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(f32,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( r2_hidden(X0,a_2_0_filter_0(X1,X2))
<=> ? [X3] :
( r3_lattices(X1,X2,X3)
& X0 = X3
& m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
fof(f43,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k2_filter_2(X0,X1) = k2_filter_0(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
fof(f52,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f53,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f56,axiom,
! [X0] :
( ( l3_lattices(X0)
& v14_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> r3_lattices(X0,X1,k6_lattices(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_lattices) ).
fof(f57,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) )
=> m1_subset_1(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f58,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(f59,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(f66,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& v14_lattices(X0)
& ~ r1_filter_2(u1_struct_0(X0),k2_filter_2(X0,X1),k22_filter_2(X0,X1,k6_lattices(X0))) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f67,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& v14_lattices(X0)
& ~ r1_filter_2(u1_struct_0(X0),k2_filter_2(X0,X1),k22_filter_2(X0,X1,k6_lattices(X0))) ) ),
inference(flattening,[],[f66]) ).
fof(f73,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(f74,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k2_filter_0(X0,X1) = a_2_0_filter_0(X0,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f75,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k2_filter_0(X0,X1) = a_2_0_filter_0(X0,X1) ) ),
inference(flattening,[],[f74]) ).
fof(f76,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,[],[f11]) ).
fof(f77,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,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_filter_0(k2_filter_0(X0,X1),X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f79,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_filter_0(k2_filter_0(X0,X1),X0) ),
inference(flattening,[],[f78]) ).
fof(f82,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f83,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f85,plain,
! [X0] :
( ~ l2_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f86,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f87,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_filter_0(X1,X0)
| ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f88,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_filter_0(X1,X0)
| ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1) ) ) ),
inference(flattening,[],[f87]) ).
fof(f91,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,[],[f22]) ).
fof(f92,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,[],[f91]) ).
fof(f99,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f32]) ).
fof(f100,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( r2_hidden(X0,a_2_0_filter_0(X1,X2))
<=> ? [X3] :
( r3_lattices(X1,X2,X3)
& X0 = X3
& m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( r2_hidden(X0,a_2_0_filter_0(X1,X2))
<=> ? [X3] :
( r3_lattices(X1,X2,X3)
& X0 = X3
& m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
inference(flattening,[],[f101]) ).
fof(f108,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k2_filter_2(X0,X1) = k2_filter_0(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f109,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k2_filter_2(X0,X1) = k2_filter_0(X0,X1) ),
inference(flattening,[],[f108]) ).
fof(f124,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f125,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f126,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f125]) ).
fof(f129,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v14_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| r3_lattices(X0,X1,k6_lattices(X0)) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f130,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v14_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| r3_lattices(X0,X1,k6_lattices(X0)) ) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(ennf_transformation,[],[f57]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f134,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,[],[f59]) ).
fof(f135,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,[],[f134]) ).
fof(f139,plain,
( l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0)
& m1_subset_1(sK1,u1_struct_0(sK0))
& v14_lattices(sK0)
& ~ r1_filter_2(u1_struct_0(sK0),k2_filter_2(sK0,sK1),k22_filter_2(sK0,sK1,k6_lattices(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f67]) ).
fof(f140,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,[],[f73]) ).
fof(f141,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,[],[f140]) ).
fof(f142,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,[],[f141]) ).
fof(f143,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))],[f142]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_filter_0(X1,X2))
| ? [X3] :
( r3_lattices(X1,X2,X3)
& X0 = X3
& m1_subset_1(X3,u1_struct_0(X1)) ) )
& ( ! [X3] :
( ~ r3_lattices(X1,X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| r2_hidden(X0,a_2_0_filter_0(X1,X2)) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_filter_0(X1,X2))
| ? [X4] :
( r3_lattices(X1,X2,X4)
& X0 = X4
& m1_subset_1(X4,u1_struct_0(X1)) ) )
& ( ! [X3] :
( ~ r3_lattices(X1,X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| r2_hidden(X0,a_2_0_filter_0(X1,X2)) ) ) ),
inference(rectify,[],[f152]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_filter_0(X1,X2))
| ( r3_lattices(X1,X2,sK11(X0,X1,X2))
& sK11(X0,X1,X2) = X0
& m1_subset_1(sK11(X0,X1,X2),u1_struct_0(X1)) ) )
& ( ! [X3] :
( ~ r3_lattices(X1,X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| r2_hidden(X0,a_2_0_filter_0(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X2))],[f153]) ).
fof(f168,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,[],[f135]) ).
fof(f169,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,[],[f168]) ).
fof(f170,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f139]) ).
fof(f171,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f139]) ).
fof(f172,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f139]) ).
fof(f173,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f139]) ).
fof(f174,plain,
v14_lattices(sK0),
inference(cnf_transformation,[],[f139]) ).
fof(f175,plain,
~ r1_filter_2(u1_struct_0(sK0),k2_filter_2(sK0,sK1),k22_filter_2(sK0,sK1,k6_lattices(sK0))),
inference(cnf_transformation,[],[f139]) ).
fof(f188,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,[],[f143]) ).
fof(f189,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,[],[f143]) ).
fof(f190,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,[],[f143]) ).
fof(f191,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| k2_filter_0(X0,X1) = a_2_0_filter_0(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f192,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,[],[f77]) ).
fof(f193,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)
| ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f194,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_filter_0(k2_filter_0(X0,X1),X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f196,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f197,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f198,plain,
! [X0] :
( ~ l2_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f199,plain,
! [X0] :
( ~ l3_lattices(X0)
| l2_lattices(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f200,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f201,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_filter_0(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f88]) ).
fof(f205,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,[],[f92]) ).
fof(f214,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r2_hidden(X0,a_2_0_filter_0(X1,X2))
| r3_lattices(X1,X2,sK11(X0,X1,X2)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r2_hidden(X0,a_2_0_filter_0(X1,X2))
| sK11(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f154]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r2_hidden(X0,a_2_0_filter_0(X1,X2))
| m1_subset_1(sK11(X0,X1,X2),u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r3_lattices(X1,X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r2_hidden(X0,a_2_0_filter_0(X1,X2)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f233,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k2_filter_2(X0,X1) = k2_filter_0(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f246,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f247,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f251,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v14_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| r3_lattices(X0,X1,k6_lattices(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(cnf_transformation,[],[f132]) ).
fof(f253,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f255,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,X1,X3) ),
inference(cnf_transformation,[],[f169]) ).
fof(f256,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,[],[f169]) ).
fof(f260,plain,
! [X2,X3,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r2_hidden(X3,a_2_0_filter_0(X1,X2)) ),
inference(equality_resolution,[],[f220]) ).
tcf(c_49,negated_conjecture,
~ r1_filter_2(u1_struct_0(sK0),k2_filter_2(sK0,sK1),k22_filter_2(sK0,sK1,k6_lattices(sK0))),
inference(cnf_transformation,[],[f175]) ).
tcf(c_50,negated_conjecture,
v14_lattices(sK0),
inference(cnf_transformation,[],[f174]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f173]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f172]) ).
tcf(c_53,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f171]) ).
tcf(c_54,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f170]) ).
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,[],[f190]) ).
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,[],[f189]) ).
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,[],[f188]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k2_filter_0(X1,X0) = a_2_0_filter_0(X1,X0) )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_70,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,[],[f192]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_filter_0(k2_filter_0(X1,X0),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_73,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0))
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_74,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_75,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_76,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_77,plain,
! [X0: $i] :
( l2_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f199]) ).
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)
| ~ m1_filter_0(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_82,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,[],[f205]) ).
tcf(c_91,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(X2,a_2_0_filter_0(X0,X1))
| ~ 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,[],[f260]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_subset_1(sK11(X0,X1,X2),u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X0,a_2_0_filter_0(X1,X2)) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| ( sK11(X0,X1,X2) = X0 )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X0,a_2_0_filter_0(X1,X2)) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X2,sK11(X0,X1,X2))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X0,a_2_0_filter_0(X1,X2)) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k2_filter_2(X1,X0) = k2_filter_0(X1,X0) )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,k6_lattices(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X2,X1)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_130,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,[],[f253]) ).
tcf(c_131,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,[],[f256]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X2,X0)
| ~ 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,[],[f255]) ).
tcf(c_142,plain,
( l2_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_144,plain,
( l1_struct_0(sK0)
| ~ l2_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_155,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_157,plain,
( v3_struct_0(sK0)
| m1_subset_1(k6_lattices(sK0),u1_struct_0(sK0))
| ~ l2_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_341,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_130]) ).
tcf(c_1513,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_74]) ).
tcf(c_1514,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_1513]) ).
tcf(c_1530,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,X1,k6_lattices(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_128]) ).
tcf(c_1531,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| r3_lattices(sK0,X0,k6_lattices(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1530]) ).
tcf(c_1533,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| r3_lattices(sK0,X0,k6_lattices(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1531,c_54,c_53,c_52,c_1531]) ).
tcf(c_1534,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,k6_lattices(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1533]) ).
tcf(c_1546,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_73]) ).
tcf(c_1547,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0))
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_1546]) ).
tcf(c_1632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X4)
| v3_struct_0(X0)
| m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X4)))
| ~ l3_lattices(X4)
| ~ l3_lattices(X0)
| ~ v10_lattices(X4)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != X4 )
| ( k22_filter_2(X0,X1,X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_82]) ).
tcf(c_1633,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_subset_1(k22_filter_2(X1,X0,X2),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(unflattening,[status(thm)],[c_1632]) ).
tcf(c_1726,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_1514,c_91]) ).
tcf(c_1727,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_1726]) ).
tcf(c_1885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X3)
| v3_struct_0(X0)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X3)))
| ~ l3_lattices(X3)
| ~ l3_lattices(X0)
| ~ v10_lattices(X3)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != X3 )
| ( k2_filter_0(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_79]) ).
tcf(c_1886,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(k2_filter_0(X1,X0),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(unflattening,[status(thm)],[c_1885]) ).
tcf(c_2121,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m1_subset_1(k2_filter_0(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_1886]) ).
tcf(c_2122,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| m1_subset_1(k2_filter_0(sK0,X0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2121]) ).
tcf(c_2124,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| m1_subset_1(k2_filter_0(sK0,X0),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_2122,c_54,c_52,c_2122]) ).
tcf(c_2125,plain,
! [X0: $i] :
( m1_subset_1(k2_filter_0(sK0,X0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2124]) ).
tcf(c_2133,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| m1_subset_1(k22_filter_2(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_1633]) ).
tcf(c_2134,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| m1_subset_1(k22_filter_2(sK0,X0,X1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2133]) ).
tcf(c_2136,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| m1_subset_1(k22_filter_2(sK0,X0,X1),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_2134,c_54,c_52,c_2134]) ).
tcf(c_2137,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(k22_filter_2(sK0,X0,X1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2136]) ).
tcf(c_2185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,X2,X1)
| ~ l3_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,X2,X3)
| ~ r2_hidden(X1,k22_filter_2(X0,X2,X3))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_132]) ).
tcf(c_2186,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK0)
| r3_lattices(sK0,X1,X0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(unflattening,[status(thm)],[c_2185]) ).
tcf(c_2187,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2))
| r3_lattices(sK0,X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_2186,c_54,c_52,c_2186]) ).
tcf(c_2188,plain,
! [X0: $i,X1: $i,X2: $i] :
( r3_lattices(sK0,X1,X0)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(renaming,[status(thm)],[c_2187]) ).
tcf(c_2225,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k2_filter_2(X0,X1) = k2_filter_0(X0,X1) )
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_110]) ).
tcf(c_2226,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k2_filter_2(sK0,X0) = k2_filter_0(sK0,X0) )
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2225]) ).
tcf(c_2228,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k2_filter_2(sK0,X0) = k2_filter_0(sK0,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_2226,c_54,c_52,c_2226]) ).
tcf(c_2229,plain,
! [X0: $i] :
( ( k2_filter_2(sK0,X0) = k2_filter_0(sK0,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2228]) ).
tcf(c_2237,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,X2,sK11(X1,X0,X2))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X1,a_2_0_filter_0(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_97]) ).
tcf(c_2238,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r3_lattices(sK0,X1,sK11(X0,sK0,X1))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_2237]) ).
tcf(c_2240,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1))
| r3_lattices(sK0,X1,sK11(X0,sK0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_2238,c_54,c_52,c_2238]) ).
tcf(c_2241,plain,
! [X0: $i,X1: $i] :
( r3_lattices(sK0,X1,sK11(X0,sK0,X1))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(renaming,[status(thm)],[c_2240]) ).
tcf(c_2252,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( sK11(X1,X0,X2) = X1 )
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X1,a_2_0_filter_0(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_96]) ).
tcf(c_2253,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| ( sK11(X0,sK0,X1) = X0 )
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_2252]) ).
tcf(c_2255,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1))
| ( sK11(X0,sK0,X1) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_2253,c_54,c_52,c_2253]) ).
tcf(c_2256,plain,
! [X0: $i,X1: $i] :
( ( sK11(X0,sK0,X1) = X0 )
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(renaming,[status(thm)],[c_2255]) ).
tcf(c_2267,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| m1_subset_1(sK11(X1,X0,X2),u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X1,a_2_0_filter_0(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_95]) ).
tcf(c_2268,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| m1_subset_1(sK11(X0,sK0,X1),u1_struct_0(sK0))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_2267]) ).
tcf(c_2270,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1))
| m1_subset_1(sK11(X0,sK0,X1),u1_struct_0(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_2268,c_54,c_52,c_2268]) ).
tcf(c_2271,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(sK11(X0,sK0,X1),u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(renaming,[status(thm)],[c_2270]) ).
tcf(c_2282,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k2_filter_0(X0,X1) = a_2_0_filter_0(X0,X1) )
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_68]) ).
tcf(c_2283,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k2_filter_0(sK0,X0) = a_2_0_filter_0(sK0,X0) )
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2282]) ).
tcf(c_2285,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k2_filter_0(sK0,X0) = a_2_0_filter_0(sK0,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_2283,c_54,c_52,c_2283]) ).
tcf(c_2286,plain,
! [X0: $i] :
( ( k2_filter_0(sK0,X0) = a_2_0_filter_0(sK0,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2285]) ).
tcf(c_2336,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)
| ~ 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)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_131]) ).
tcf(c_2337,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK0)
| r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_2336]) ).
tcf(c_2339,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1)
| r2_hidden(X2,k22_filter_2(sK0,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_2337,c_54,c_52,c_2337]) ).
tcf(c_2340,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(renaming,[status(thm)],[c_2339]) ).
tcf(c_2388,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(X2,a_2_0_filter_0(X0,X1))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_94]) ).
tcf(c_2389,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r2_hidden(X1,a_2_0_filter_0(sK0,X0))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_2388]) ).
tcf(c_2391,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,X1)
| r2_hidden(X1,a_2_0_filter_0(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_2389,c_54,c_52,c_2389]) ).
tcf(c_2392,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,a_2_0_filter_0(sK0,X0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,X1) ),
inference(renaming,[status(thm)],[c_2391]) ).
tcf(c_2406,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v1_xboole_0(k22_filter_2(X0,X1,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_69]) ).
tcf(c_2407,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ v1_xboole_0(k22_filter_2(sK0,X0,X1)) ),
inference(unflattening,[status(thm)],[c_2406]) ).
tcf(c_2409,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ v1_xboole_0(k22_filter_2(sK0,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_2407,c_54,c_52,c_2407]) ).
tcf(c_2489,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_1727]) ).
tcf(c_2490,plain,
( v3_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2489]) ).
tcf(c_2491,plain,
~ v1_xboole_0(u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_2490,c_54,c_52,c_142,c_144,c_155]) ).
tcf(c_2510,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_1547]) ).
tcf(c_2511,plain,
( v3_struct_0(sK0)
| m1_subset_1(k6_lattices(sK0),u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2510]) ).
tcf(c_2512,plain,
m1_subset_1(k6_lattices(sK0),u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_2511,c_54,c_52,c_142,c_157]) ).
tcf(c_3780,definition,
iPr_def_12 = k6_lattices(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3781,definition,
iPr_def_13 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_3783,definition,
iPr_def_15 = k1_zfmisc_1(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_3788,definition,
iPr_def_20 = k2_filter_2(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_3789,definition,
iPr_def_21 = k22_filter_2(sK0,sK1,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_3790,plain,
m1_subset_1(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_2512,c_3781,c_3780]) ).
tcf(c_3793,plain,
~ v1_xboole_0(iPr_def_13),
inference(demodulation,[status(thm)],[c_2491]) ).
tcf(c_3794,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ v1_xboole_0(k22_filter_2(sK0,X0,X1)) ),
inference(demodulation,[status(thm)],[c_2409]) ).
tcf(c_3795,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,a_2_0_filter_0(sK0,X0))
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,X0,X1) ),
inference(demodulation,[status(thm)],[c_2392]) ).
tcf(c_3798,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ m1_subset_1(X2,iPr_def_13)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(demodulation,[status(thm)],[c_2340]) ).
tcf(c_3805,plain,
! [X0: $i] :
( ( k2_filter_0(sK0,X0) = a_2_0_filter_0(sK0,X0) )
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2286]) ).
tcf(c_3806,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(sK11(X0,sK0,X1),iPr_def_13)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_2271]) ).
tcf(c_3807,plain,
! [X0: $i,X1: $i] :
( ( sK11(X0,sK0,X1) = X0 )
| ~ m1_subset_1(X1,iPr_def_13)
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_2256]) ).
tcf(c_3808,plain,
! [X0: $i,X1: $i] :
( r3_lattices(sK0,X1,sK11(X0,sK0,X1))
| ~ m1_subset_1(X1,iPr_def_13)
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_2241]) ).
tcf(c_3809,plain,
! [X0: $i] :
( ( k2_filter_2(sK0,X0) = k2_filter_0(sK0,X0) )
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2229]) ).
tcf(c_3811,plain,
! [X0: $i,X1: $i,X2: $i] :
( r3_lattices(sK0,X1,X0)
| ~ m1_subset_1(X2,iPr_def_13)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(demodulation,[status(thm)],[c_2188]) ).
tcf(c_3816,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(k22_filter_2(sK0,X0,X1),iPr_def_15)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2137]) ).
tcf(c_3817,plain,
! [X0: $i] :
( m1_subset_1(k2_filter_0(sK0,X0),iPr_def_15)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2125]) ).
tcf(c_3821,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_1534]) ).
tcf(c_3823,negated_conjecture,
m1_subset_1(sK1,iPr_def_13),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_3824,negated_conjecture,
~ r1_filter_2(iPr_def_13,iPr_def_20,iPr_def_21),
inference(demodulation,[status(thm)],[c_49,c_3789,c_3788]) ).
tcf(c_4940,plain,
k2_filter_0(sK0,sK1) = a_2_0_filter_0(sK0,sK1),
inference(superposition,[status(thm)],[c_3823,c_3805]) ).
tcf(c_4947,plain,
k2_filter_2(sK0,sK1) = k2_filter_0(sK0,sK1),
inference(superposition,[status(thm)],[c_3823,c_3809]) ).
tcf(c_4948,plain,
k2_filter_0(sK0,sK1) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_4947,c_3788]) ).
tcf(c_4949,plain,
a_2_0_filter_0(sK0,sK1) = iPr_def_20,
inference(demodulation,[status(thm)],[c_4940,c_4948]) ).
tcf(c_4951,plain,
( m1_subset_1(iPr_def_20,iPr_def_15)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4948,c_3817]) ).
tcf(c_4952,plain,
m1_subset_1(iPr_def_20,iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_4951,c_3823]) ).
tcf(c_4995,plain,
! [X0: $i] :
( ( sK11(X0,sK0,sK1) = X0 )
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_20) ),
inference(superposition,[status(thm)],[c_4949,c_3807]) ).
tcf(c_4996,plain,
! [X0: $i] :
( ( sK11(X0,sK0,sK1) = X0 )
| ~ r2_hidden(X0,iPr_def_20) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4995,c_3823]) ).
tcf(c_5018,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_20)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,X0) ),
inference(superposition,[status(thm)],[c_4949,c_3795]) ).
tcf(c_5019,plain,
! [X0: $i,X1: $i] :
( ( sK11(X1,sK0,X0) = X1 )
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,X0,X1) ),
inference(superposition,[status(thm)],[c_3795,c_3807]) ).
tcf(c_5020,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_20)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5018,c_3823]) ).
tcf(c_5058,plain,
( r2_hidden(iPr_def_12,iPr_def_20)
| ~ m1_subset_1(iPr_def_12,iPr_def_13)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(superposition,[status(thm)],[c_3821,c_5020]) ).
tcf(c_5060,plain,
r2_hidden(iPr_def_12,iPr_def_20),
inference(forward_subsumption_resolution,[status(thm)],[c_5058,c_3790,c_3823]) ).
tcf(c_5068,plain,
sK11(iPr_def_12,sK0,sK1) = iPr_def_12,
inference(superposition,[status(thm)],[c_5060,c_4996]) ).
tcf(c_5097,plain,
( r3_lattices(sK0,sK1,iPr_def_12)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(iPr_def_12,a_2_0_filter_0(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_5068,c_3808]) ).
tcf(c_5100,plain,
( r3_lattices(sK0,sK1,iPr_def_12)
| ~ r2_hidden(iPr_def_12,iPr_def_20)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_5097,c_4949]) ).
tcf(c_5101,plain,
r3_lattices(sK0,sK1,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_5100,c_5060,c_3823]) ).
tcf(c_5254,plain,
! [X0: $i] :
( r3_lattices(sK0,sK1,X0)
| ~ m1_subset_1(iPr_def_12,iPr_def_13)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_21)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3789,c_3811]) ).
tcf(c_5255,plain,
( m1_subset_1(iPr_def_21,iPr_def_15)
| ~ m1_subset_1(iPr_def_12,iPr_def_13)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(superposition,[status(thm)],[c_3789,c_3816]) ).
tcf(c_5256,plain,
( ~ v1_xboole_0(iPr_def_21)
| ~ m1_subset_1(iPr_def_12,iPr_def_13)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(superposition,[status(thm)],[c_3789,c_3794]) ).
tcf(c_5257,plain,
~ v1_xboole_0(iPr_def_21),
inference(forward_subsumption_resolution,[status(thm)],[c_5256,c_3790,c_3823]) ).
tcf(c_5258,plain,
m1_subset_1(iPr_def_21,iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_5255,c_3790,c_3823]) ).
tcf(c_5259,plain,
! [X0: $i] :
( r3_lattices(sK0,sK1,X0)
| ~ r2_hidden(X0,iPr_def_21)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5254,c_3790,c_3823,c_5101]) ).
tcf(c_5385,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_20)
| ~ r2_hidden(X0,iPr_def_21)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_5259,c_5020]) ).
tcf(c_5500,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,iPr_def_13)
| ~ m1_subset_1(X1,iPr_def_15)
| ~ r2_hidden(X0,X1) ),
inference(superposition,[status(thm)],[c_3783,c_129]) ).
tcf(c_5574,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_21)
| ~ m1_subset_1(iPr_def_12,iPr_def_13)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,iPr_def_12)
| ~ r3_lattices(sK0,sK1,X0)
| ~ r3_lattices(sK0,X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3789,c_3798]) ).
tcf(c_5580,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_21)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,X0)
| ~ r3_lattices(sK0,X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5574,c_3790,c_3823,c_5101]) ).
tcf(c_5614,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_21)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_5580,c_3821,c_5580]) ).
tcf(c_5624,plain,
! [X0: $i] :
( r2_hidden(sK11(X0,sK0,sK1),iPr_def_21)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,sK1))
| ~ m1_subset_1(sK11(X0,sK0,sK1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_3808,c_5614]) ).
tcf(c_5635,plain,
! [X0: $i] :
( r2_hidden(sK11(X0,sK0,sK1),iPr_def_21)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_20)
| ~ m1_subset_1(sK11(X0,sK0,sK1),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_5624,c_4949]) ).
tcf(c_5636,plain,
! [X0: $i] :
( r2_hidden(sK11(X0,sK0,sK1),iPr_def_21)
| ~ r2_hidden(X0,iPr_def_20)
| ~ m1_subset_1(sK11(X0,sK0,sK1),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5635,c_3823]) ).
tcf(c_5655,plain,
! [X0: $i] :
( r2_hidden(sK11(X0,sK0,sK1),iPr_def_21)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_20)
| ~ r2_hidden(X0,a_2_0_filter_0(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_3806,c_5636]) ).
tcf(c_5661,plain,
! [X0: $i] :
( r2_hidden(sK11(X0,sK0,sK1),iPr_def_21)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_5655,c_4949]) ).
tcf(c_5662,plain,
! [X0: $i] :
( r2_hidden(sK11(X0,sK0,sK1),iPr_def_21)
| ~ r2_hidden(X0,iPr_def_20) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5661,c_3823]) ).
tcf(c_5678,plain,
! [X0: $i] :
( m1_subset_1(sK11(X0,sK0,sK1),iPr_def_21)
| ~ r2_hidden(X0,iPr_def_20) ),
inference(superposition,[status(thm)],[c_5662,c_123]) ).
tcf(c_6601,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r1_filter_2(X1,iPr_def_20,X0)
| r2_hidden(sK2(X1,iPr_def_20,X0),X0)
| ( sK11(sK2(X1,iPr_def_20,X0),sK0,sK1) = sK2(X1,iPr_def_20,X0) )
| ~ m1_subset_1(iPr_def_20,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(superposition,[status(thm)],[c_64,c_4996]) ).
tcf(c_13329,plain,
! [X0: $i] :
( ( sK11(X0,sK0,sK1) = X0 )
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_21)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_5259,c_5019]) ).
tcf(c_13340,plain,
! [X0: $i] :
( ( sK11(X0,sK0,sK1) = X0 )
| ~ r2_hidden(X0,iPr_def_21)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13329,c_3823]) ).
tcf(c_13986,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| r1_filter_2(X0,iPr_def_20,iPr_def_21)
| ( sK11(sK2(X0,iPr_def_20,iPr_def_21),sK0,sK1) = sK2(X0,iPr_def_20,iPr_def_21) )
| ~ m1_subset_1(iPr_def_21,k1_zfmisc_1(X0))
| ~ m1_subset_1(iPr_def_20,k1_zfmisc_1(X0))
| ~ m1_subset_1(sK2(X0,iPr_def_20,iPr_def_21),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6601,c_13340]) ).
tcf(c_15180,plain,
( v1_xboole_0(iPr_def_13)
| r1_filter_2(iPr_def_13,iPr_def_20,iPr_def_21)
| ( sK11(sK2(iPr_def_13,iPr_def_20,iPr_def_21),sK0,sK1) = sK2(iPr_def_13,iPr_def_20,iPr_def_21) )
| ~ m1_subset_1(iPr_def_21,k1_zfmisc_1(iPr_def_13))
| ~ m1_subset_1(iPr_def_20,k1_zfmisc_1(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_65,c_13986]) ).
tcf(c_15181,plain,
( v1_xboole_0(iPr_def_13)
| r1_filter_2(iPr_def_13,iPr_def_20,iPr_def_21)
| ( sK11(sK2(iPr_def_13,iPr_def_20,iPr_def_21),sK0,sK1) = sK2(iPr_def_13,iPr_def_20,iPr_def_21) )
| ~ m1_subset_1(iPr_def_21,iPr_def_15)
| ~ m1_subset_1(iPr_def_20,iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_15180,c_3783]) ).
tcf(c_15182,plain,
sK11(sK2(iPr_def_13,iPr_def_20,iPr_def_21),sK0,sK1) = sK2(iPr_def_13,iPr_def_20,iPr_def_21),
inference(forward_subsumption_resolution,[status(thm)],[c_15181,c_3793,c_3824,c_5258,c_4952]) ).
tcf(c_15186,plain,
( m1_subset_1(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21)
| ~ r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_20) ),
inference(superposition,[status(thm)],[c_15182,c_5678]) ).
tcf(c_16835,plain,
( v1_xboole_0(iPr_def_13)
| r1_filter_2(iPr_def_13,iPr_def_20,iPr_def_21)
| r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21)
| m1_subset_1(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21)
| ~ m1_subset_1(iPr_def_21,k1_zfmisc_1(iPr_def_13))
| ~ m1_subset_1(iPr_def_20,k1_zfmisc_1(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_64,c_15186]) ).
tcf(c_16836,plain,
( v1_xboole_0(iPr_def_13)
| r1_filter_2(iPr_def_13,iPr_def_20,iPr_def_21)
| r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21)
| m1_subset_1(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21)
| ~ m1_subset_1(iPr_def_21,iPr_def_15)
| ~ m1_subset_1(iPr_def_20,iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_16835,c_3783]) ).
tcf(c_16837,plain,
( r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21)
| m1_subset_1(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16836,c_3793,c_3824,c_5258,c_4952]) ).
tcf(c_16842,plain,
m1_subset_1(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21),
inference(forward_subsumption_resolution,[status(thm)],[c_16837,c_123]) ).
tcf(c_16843,plain,
( v1_xboole_0(iPr_def_21)
| r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21) ),
inference(superposition,[status(thm)],[c_16842,c_124]) ).
tcf(c_16844,plain,
r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21),
inference(forward_subsumption_resolution,[status(thm)],[c_16843,c_5257]) ).
tcf(c_17739,plain,
( m1_subset_1(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_13)
| ~ m1_subset_1(iPr_def_21,iPr_def_15) ),
inference(superposition,[status(thm)],[c_16844,c_5500]) ).
tcf(c_17774,plain,
m1_subset_1(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_17739,c_5258]) ).
tcf(c_18100,plain,
( r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_20)
| ~ r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21) ),
inference(superposition,[status(thm)],[c_17774,c_5385]) ).
tcf(c_18105,plain,
r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_20),
inference(forward_subsumption_resolution,[status(thm)],[c_18100,c_16844]) ).
tcf(c_18115,plain,
( r1_filter_2(iPr_def_13,iPr_def_20,iPr_def_21)
| ~ m1_subset_1(iPr_def_21,k1_zfmisc_1(iPr_def_13))
| ~ m1_subset_1(iPr_def_20,k1_zfmisc_1(iPr_def_13))
| ~ r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21) ),
inference(superposition,[status(thm)],[c_18105,c_341]) ).
tcf(c_18171,plain,
( r1_filter_2(iPr_def_13,iPr_def_20,iPr_def_21)
| ~ m1_subset_1(iPr_def_21,iPr_def_15)
| ~ m1_subset_1(iPr_def_20,iPr_def_15)
| ~ r2_hidden(sK2(iPr_def_13,iPr_def_20,iPr_def_21),iPr_def_21) ),
inference(light_normalisation,[status(thm)],[c_18115,c_3783]) ).
tcf(c_18172,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_18171,c_3824,c_5258,c_4952,c_16844]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT329+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.42 % Computer : n002.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 21:10:48 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 0.25/0.50
% 0.25/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.50
% 0.25/0.50 % Detected problem language: tptp
% 0.25/0.52 % Proving...
% 12.63/2.80 % SZS status Started for theBenchmark.p
% 12.63/2.80 % SZS status Theorem for theBenchmark.p
% 12.63/2.80
% 12.63/2.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.63/2.80
% 12.63/2.80 % ------ iProver source info
% 12.63/2.80
% 12.63/2.80 % git: date: 2026-07-19 20:42:38 +0200
% 12.63/2.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.63/2.80 % git: non_committed_changes: false
% 12.63/2.80
% 12.63/2.80 % ------ Parsing...
% 12.63/2.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.63/2.80
% 12.63/2.80 % ------ 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:16:0s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e %
% 12.63/2.80
% 12.63/2.80 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.63/2.80
% 12.63/2.80 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 12.63/2.80 % ------ Proving...
% 12.63/2.80 % ------ Problem Properties
% 12.63/2.80
% 12.63/2.80 %
% 12.63/2.80 % clauses 91
% 12.63/2.80 % conjectures 3
% 12.63/2.80 % EPR 28
% 12.63/2.80 % Horn 76
% 12.63/2.80 % unary 36
% 12.63/2.80 % binary 29
% 12.63/2.80 % lits 200
% 12.63/2.80 % lits eq 18
% 12.63/2.80 % fd_pure 0
% 12.63/2.80 % fd_pseudo 0
% 12.63/2.80 % fd_cond 1
% 12.63/2.80 % fd_pseudo_cond 4
% 12.63/2.80 % AC symbols 0
% 12.63/2.80
% 12.63/2.80 % ------ Schedule dynamic 5 is on
% 12.63/2.80
% 12.63/2.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 12.63/2.80
% 12.63/2.80
% 12.63/2.80 % ------
% 12.63/2.80 % Current options:
% 12.63/2.80 % ------
% 12.63/2.80
% 12.63/2.80
% 12.63/2.80 %
% 12.63/2.80
% 12.63/2.80 % ------ Proving...
% 12.63/2.80 %
% 12.63/2.80
% 12.63/2.80 % SZS status Theorem for theBenchmark.p
% 12.63/2.80
% 12.63/2.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.23/2.80
% 15.23/2.80
%------------------------------------------------------------------------------